Ultrafast Spectroscopy and Coherent Control of Tryptophan-Based Compounds

MASTER THESISIN PHYSICS

Ultrafast spectroscopy and coherent control of Tryptophan-based compounds

Author: Supervisor: Luana Olivieri Prof. Tullio Scopigno

Co-Supervisors: Dr. Giovanni Batignani Dr. Luigi Bonacina

Academic year 2016

iii

Acknowledgements

Prima di tutto vorrei esprimere la mia gratitudine ai miei relatori il Prof. Tullio Scopigno e il Prof. Jean-Pierre Wolf che mi hanno dato la possibilità di partecipare a questo progetto.

Un profondo e sincero ringraziamento va al Dott. Luigi Bonacina e al Dott. Julien Gateau che mi hanno guidato durante l’esperienza a Ginevra, insegnandomi molto dal punto di vista sia pratico che teorico sul controllo coerente di sistemi quantistici. Allo stesso modo, un sentito ringraziamento va al Dott. Giovanni Batignani per il suo aiuto e supporto negli esperimenti di pump-probe (e per la sua inﬁnita disponibilità).

Vorrei poi ringraziare Elise Schubert, Michel Moret, Denis Mongin, Va- syl Kilin, Nicolas Berti, Gustavo Sousa, Gabriel Campargue, Carino Fer- rante e Alessandra Virga per aver creato una stimolante e confortevole at- mosfera lavorativa.

Sono particolarmente debitrice alla mia famiglia e a tutti i miei amici e colleghi. In particolare vorrei ringraziare Giuseppe Bellanti per l’ imperit- uro supporto e il costante incoraggiamento profuso che mi ha sostenuto nei momenti più difﬁcili di questa esperienza.

In ﬁne, vorrei ringraziare l’università "La Sapienza" e l’università di Ginevra per avermi ﬁnanziato quest’esperienza attraverso la borsa di stu- dio "SEMP".

Contents

Acknowledgements iii

Introduction ix

1 Tryptophan1 1.0.1 Ultrafast dynamics of Tryptophan...... 2 1.0.2 Raman scattering on Tryptophan...... 4 1.1 Tryptophan contained in proteins...... 6 1.1.1 Human Serum Albumin...... 6 1.1.2 Immunoglobulin G...... 7

2 Coherent control9 2.1 Coherent control over a molecular wavepacket...... 12 2.1.1 Examples of molecular discrimination...... 14 2.2 Optimal quantum control...... 18 2.2.1 Example: three levels system...... 20 2.3 Multiobjective Genetic Algorithm...... 22

3 Transient Absorption and Stimulated Raman Spectroscopies 25 3.1 Interaction picture and diagram theory...... 28 3.1.1 Double sided Feynman diagrams of a χ3 process.. 32 3.2 Ultrafast Transient Absorption Spectroscopy...... 34 3.2.1 Singular value decomposition...... 39 3.3 Stimulated Raman Scattering...... 40

4 Experimental setups 45 4.1 Setup employed in GAP Biophotonics lab...... 45 4.1.1 Sample preparation and handling...... 47 4.2 Experimental setup used in Femtoscopy lab...... 49 4.3 Pulse characterization...... 52 4.3.1 Cross-Correlation...... 52 4.3.2 Frequency-Resolved Optical Gating...... 53 4.3.3 Self-Diffraction FROG (SD FROG)...... 54 4.3.4 Polarization-Gated FROG (PG FROG)...... 57 4.4 Pulse Shaping...... 59 4.4.1 MEMS mirrors...... 59 4.4.2 Geometries of pulse shaper...... 60 vi

4.4.3 Spectral resolution...... 61 4.5 UV compression with a prism pair...... 64 4.5.1 Propagation of ultrashort light pulse...... 64 4.5.2 Pulse compression with a prism pair...... 69

5 Time resolved ﬂuorescence depletion of tryptophan and tryptophan contained in proteins 71 5.1 Preliminary optimization: NSGA-II applied on cross-correlation signal...... 71 5.2 Time resolved ﬂuorescence depletion spectroscopy...... 73 5.2.1 Preliminary measurements...... 74 5.2.2 Depletion curves acquired with unshaped pulse... 78 5.2.3 Optimal Dynamics Discrimination applied to IgG and HSA...... 79

6 Pump probe experiments on Tryptophan 85 6.1 Transient Absorption measurement of Tryptophan...... 85 6.1.1 PG FROG measurements...... 85 6.1.2 Pulse compression performed by prism pair..... 87 6.1.3 Evaluation of the white light’s chirp...... 89 6.1.4 Transient Absorption measurement of Tryptophan. 90 6.1.5 Glotaran software...... 91 6.1.6 Estimation of the spectral components with Glotaran 94 6.1.7 DAS spectra treated with superposition process... 97 6.1.8 Results...... 101 6.2 Stimulated Raman Scattering...... 105

7 Conclusion and Outlook 109

A Labwindows software for FROG measurements 111

B Orhogonalized DAS components 113

Bibliography 117 to Giuseppe Bellanti and my family

Introduction

The chance to observe and manipulate ultrafast dynamics is an intriguing goal in physics and chemistry. The development of femtosecond laser sources in 60’s paved the way to the realization of spectroscopic pump- prove techniques able to track electronic reconfiguration and visualize structural rearrangements in the femtosecond time scale. More recently, a fascinating perspective in the ultrafast community is to obtain an active control over complex systems dynamics. Processes like the breaking or the formation of specific chemical bonds are often hampered by the rapid redistribution through all the molecules of the energy locally deposited by mean of a femtosecond laser source, causing a leak of the selectivity. Thereby, the field of quantum coherent control emerged from the goal to drive a quantum system from an initial state to a desired final state by exploiting constructive quantum-mechanical interferences: it gives the chance to enhance the transition amplitude of a selected final state and at the same time exploits destructive interference to suppress undesired final states. The initial ideas exploited phase-controlled laser fields to manipulate quantum-mechanical phases, as proposed by Brumer and Shapiro [1], or precisely timed sequences of ultrashort pulses, as proposed by Tannor and Rice [2,3]. In 1992, H. Rabitz and coworkers introduced the concept of optimal control, in their seminal paper "Teaching laser to control molecules" [4]. They proposed to use a search algorithm to optimize the laser pulse characteristics in a feedback loop configuration to reach most efficiently the desired target. Thus today, a large number of parameters (such as the amplitude and the phase of each spectral component within the laser pulse) has to be controlled with new pulse shaping techniques and the help of efficient genetic- type optimization algorithms [5,6].

Within the context of coherent quantum control, quantum manipulation techniques have been applied to unravel microscopic informations on the system and discriminate between different, but very similar, compounds. In this respect, Optimal Dynamic Discrimination (ODD) is a powerful theory that is based on the enhancement or reduction of fluorescence of a specific molecule by driving it preferentially into other relaxation pathways. It has been recently demonstrated experimentally achieving the discrimination between small molecules like Riboflavin and Flavin mononucleotide, x Contents

Tryptophan and Tyrosine, Tryptophan and Ala-Tryptophan [7,8,9].

Even if the ODD theory allows measuring a target objective, which en- able the identification and discrimination between different compounds, there is not yet a procedure able to combine the informations obtained from the shaped pulse to the dynamics that take place in the excited state. Pump- probe techniques based on ultrafast transient absorption (TA) are able to extract these informations while non-linear Raman spectroscopies can unveil the structural conformations of the system. Transient absorption spectroscopy in picosecond and femtosecond time domains is a sensitive spectroscopic technique for studying the time evolution of excited states and the lifetimes of short-lived intermediates, and it is also useful to follow the energy flow among different chromophores composing the macromolecules. The Stimulated Raman scattering (SRS) was one of the first nonlinear optical processes experimentally observed (1962) and its pump-probe version has recently been used to unveil the vibrational and rotational modes of liquids and gases [10]. Moreover, the combination of TA and SRS gives the chance to define a Fem- tosecond stimulated Raman Scattering (FSRS) experiment. FSRS is an ultrafast nonlinear optical technique able to access the vibrational structural informations of the excited states combining high temporal precision and high spectral resolution within a three-pulse scheme experiment [11]. An actinic pump pulse excites the molecule and initiates the photochemical reaction. The transient structure of the molecule, represented by its Raman spectrum, is then visualized at various time delays by the combination of a narrowband Raman pump pulse and a broadband probe pulse.

This thesis addresses the study of the ultrafast dynamics of Tryptophan and Tryptophan-containing proteins within a Swiss NCCR - Molecular Ul- trafast Science Technology (MUST) project, thanks to the collaboration of two physics groups: the Femtoscopy group of Rome led by prof. Tullio Scopigno and GAP Biophotonics group of Geneve guided by prof. Jean- Pierre Wolf that was possible thanks to the Swiss-European Mobility Pro- gram (SEMP) internship. This work aims to study the application of the optimal dynamics discrimination theory to two proteins that contains Tryptophan, human serum albumin (HSA) and immunoglobulin G (IgG), with the help of coherent control experimental apparatus. In fact, since its great sensitivity to environment, Tryptophan’s ﬂuorescence can be the perfect probe for the detection of different proteins and larger molecules [12] (see Chapter1). At the same time, TA is a powerful tool to unravel the dynamics of the excited states, while Contents xi

SRS experiments can unveil structural informations. Chapter1 points out the Tryptophan’s structure and the literature linked to its ultrafast dynamic, as well as human serum albumin and immunoglobulin G’s roles in human serum. In Chapter2 we deﬁne the coherent control and the ODD theories, outlining the role of the Genetic Algorithm in the discrimination process, while Chapter3 contains the transient absorption and the stimulated Raman scattering theories. In Chapter4 we describe the experimental apparatus used for all the measurements taken during this work: the setups employ in GAP Biophotonics lab. in Geneva and in Femtoscopy lab. in Rome. In particular, a SD FROG stage is mounted in the GAP’s setup and the software that controls the delay line and the CCD camera was built in Labwindows environment (see appendixA). In Chapter5 we investigate the time-resolved ﬂuorescence of human serum albumin (HSA), Immunoglobulin G (IgG) and Trp. In particular, an ODD test is applied to discriminate between HSA and IgG in buffer solutions. Chapter6 contains the investigation of the ground state normal modes and the excited states of Trp, made through the ultrafast transient absorption and a stimulate Raman scattering measurements. In chapter7 we present the conclusion of our work indicating possible future developments in the study of Tryptophan-based compounds.

Chapter 1

Tryptophan

Tryptophan (Trp) is one of over 20 amino-acids which made up the primary structure of proteins and usually dominates their fluorescence. Since Trp’s fluorescence is strongly influenced by its local environment, it can be often exploited to investigate the protein structure, conformation, fold- ing/unfolding, substrate binding and protein-protein interactions [13, 14].

The structure of Trp is shown in ﬁgure 1.1: its side chain is composed of an indole, which is a chromophore responsible for most of the UV absorption and ﬂuorescence in proteins.

(A) (B)

FIGURE 1.1: Structure of Tryptophan (A) the bidimensional structure; (B) the 3D structure. Both the ﬁg- ures are taken from http://www.chemspider.com .

The indole’s excited state 1ππ∗ is characterized by two low-lying, nearly degenerate singlet states responsible for the absorption band centered at 1 1 280 nm (see ﬁgure 5.7b)[15, 16]. La and Lb absorption bands are populated through transitions among the highest occupied molecular orbitals (HOMO) and lowest unoccupied molecular orbitals (LUMO)

1 La : HOMO → LUMO HOMO − 1 → LUMO + 1 2 Chapter 1. Tryptophan in a ration 3:1 ;

1 Lb : HOMO − 1 → LUMO HOMO → LUMO + 1

1 in an equal mixture [17]. Even if Lb has lower energy and dominates the emission in a nonpolar environment, the degeneration between the two absorption band is removed in a polar solvent and a new energetic order is 1 deﬁned: the La energy is decreased by interaction with the solvent, and dominates the emission [18]. 1 In addition, the absorption presents a band centered at 220 nm, named Ba 1 and Bb, that is due to higher intense transitions in the 190 nm - 230 nm region. They are characterized by greater energetic transitions from HOMO to higher lying LUMO, LUMO+1 and LUMO+2 [15].

(A) (B)

FIGURE 1.2: (A) Indole potential energy proﬁles of the lowest excited states 1ππ∗ (squares and diamonds), the lowest 1πσ∗ state (triangles) and the electronic ground state (circles) as a function of the NH stretch reaction coordinate. From [19]. (B) Absorption spectrum of Trp in pH7 aqueous solution. The absorption band at 280 nm is attributed 1 1 1 to La and Lb, while the absorption at 220 nm is due to B states [17, 18, 15]. Taken from [20]

1.0.1 Ultrafast dynamics of Tryptophan

The ultrafast dynamics of Tryptophan is generally linked to the quenching 1 of the excited state S1 (usually related to Lb absorption peaks) which depends signiﬁcantly on the environment and on the molecular conﬁguration Chapter 1. Tryptophan 3

[21, 22]. In aqueous solution, besides sub-ps photoionization [23, 24] and intersystem crossing [25, 19, 26] at long times (nanoseconds), the intermediate, picosecond time scale is characterized by a multi-exponential ﬂuorescence decay. The picosecond time scale has been investigated by ultrafast transient absorption technique, and has been inquired the quenching of S1 excited state ( with λ ∼ 320 nm) that has a characteristic time of 1.1 ps due to the solvent dipoles reorientations. Linked to the S1 quenching, an ESA band centered at 360 nm rises simultaneously (see ﬁgure 1.3)[27].

(A) (B)

FIGURE 1.3: (A): Time-resolved absorption spectra of tryptophan at pH 7, highlighting the formation of the 425 nm band due to the formation of P photoproduct and an energetic shift in the 300-400 nm range due to S1 quenching. (B): DADS obtained from global analysis of transient absorption spectra from 300 to 550 nm. Positive and negative amplitudes denote respectively the decay and growth of transient absorption bands on the corresponding time constant. Taken from [27].

Moreover, as outlined in ﬁgure 1.3b, a new species rises at 425 nm with a characteristic time constant of 0.9 ns: it has been assigned to the primary P photoproduct, a triplet state termed T1, that results from the intramolecular + proton transfer from NH3 of zwitterionic form of Trp at pH 7.4 to the indole moiety (see ﬁgure 1.4)[27, 26, 25]. The ESA bands for λ > 430 nm has been ascribed to the solvation process whose peak is estimated around 700-720 nm [24], while a peak due to Trp radical cations near 560-580 nm was observed only on the nanosecond time scale and in acid condition [27, 28, 25]. 4 Chapter 1. Tryptophan

+ FIGURE 1.4: Intramolecular proton transfer from NH3 of zwitterionic form of Trp to the indole moiety. Taken from [26].

1.0.2 Raman scattering on Tryptophan

Raman bands of Tryptophan residues are strong enough to be readily identified in the spectra of proteins and their frequencies and intensities are considered to reflect the environment of the residues [12]. The Raman spectrum of Tryptophan at a neutral buffer is reported in figure 1.5 : the intensity of the peaks are influenced by varying the Raman wavelength and reach their maximum at λ ∼ 200 − 220 nm (at resonant condition with the absorption band reported in figure 1.2b) while decreasing at upper wavelengths [20, 29]. The most important normal modes are identified in table 1.1 and discussed below.

FIGURE 1.5: Resonance Raman spectra of aqueous tryptophan (1 mM) with 200-, 218-, 240-nm and 266-nm excitation. Numbers in parentheses correlate with benzene or pyrrole mode (π) assignments [29].

The 1623 cm−1 Raman line (W1) is assignable to the highest frequency bond-stretching vibration of the indole ring [35], and with 1555 cm−1 (W3) seem to come from the degenerate stretching Raman line of benzene at 1596 Chapter 1. Tryptophan 5

Mode Frequency [cm−1] Mode Frequency [cm−1] a,b b W1 1615-1622 W8 1305 b a,b W2 1575 W10 1235-1238 a,b b W3 1552-1555 W13 1127 b,e a,b W4 1488-1496 W16 1011-1016 a,b a,b W5 1457-1462 W17 875-880 e a,b W6 1420-1440 W18 759-760 b W7 1360,1341 15 or δ NH c 1148 c 1256 5 πf,c 1276-1305 R’ φ f 607 δ CHπ f 1064

TABLE 1.1: Tryptophan mode’s frequency a: data are taken from [30]; b: data are taken from [31]; c: from [29]; d: from [32]; e: from [33]; f : from [34]. cm−1. Normal mode W3 is also implicated to C-C stretching in the pyrrole nucleus [32] and its off-resonance intensity makes it a good marker for Tryptophan in proteins [36]. The 1436 and 1344 cm−1 peaks (W6 and W7) can be linked respectively with 1480 and 1380 cm−1 Raman lines of pyrrole . In particular, the normal mode W6 is mainly due to NH in-plane bending that shows a strong dependence upon the strength of hydrogen bonding [33]. Thus W6 can shift from 1422 (no hydrogen bonding) to 1441 cm−1 (strong hydrogen bonding). A shift to 1382 cm−1 has been reported in case of N-deuteration [35]. Harada and Miura’s works [32, 37] identify the origin of the doublet at 1360 and 1340 cm−1: they are assigned to Fermi resonance involving a fundamental (W7) expected near 1350 cm−1 and one or more combination modes of out-of-plane vibrations. The relative intensity ration is a useful marker of the hydrophobicity of the ring. The tryptophan Fermi doublet is also observed in UVRR spectra of proteins [29]. The W17 normal mode at 880 cm−1 involves both the deformation of the six-membered ring and displacement of the NH group along the direction of the N-H bond [32]. It is also a good marker for NH bond: from 883 cm−1 (no hydrogen bonding) to 871 cm−1 (strong hydrogen bonding) [37]. This component is detectable also in more complex tryptophan-based proteins [36]. The Raman line at 760 cm−1 (W8) has been assigned to a mode in which breathing vibrations of benzene and pyrrole take place in phase. Other components are detected in other articles [29, 32, 34] and recog- nized through the Wilson’s formalism for Benzene’s normal modes [38, 39] and Lord’s formalism for Pyrrole’s normal mode [40]. 6 Chapter 1. Tryptophan

1.1 Tryptophan contained in proteins

Proteins are the building blocks of life since an arbitrary composition of them can lead to every living cells. They are polymers consisting of at least one sequence of amino-acids linked together in a polypeptide chain. Each amino-acid has its own position in the protein, dictated by the nucleotide sequence of genes. Any small change or damage in the sequence can mis- lead the overall protein function and can bring about some dangerous diseases. Therefore, understanding how proteins work requires informations about their structures and dynamics. The complex 3D structure of a protein has been investigated in the last decades with different techniques as X ray crystallography [41], Nuclear Magnetic Resonance (NMR) [42] and Circular Dichroism (CD) [43]. Futhermore,the development of femtosecond laser sources disclosed the way to ultrafast spectroscopy studies. In particular, it is grown the capability to follow in real time the structural and energetic changes of electronic and vibrational excited states. In this part we focus on a few examples of serum proteins for their relevant role in diagnostics of diseases [44]. In particular our study revolves around the serum albumin protein, which is responsible for transport of various compounds through the blood vessels and Immunoglobulin G (IgG) which is a protein of the immune system, an antibody that defends the body against foreign substances.

1.1.1 Human Serum Albumin

Human serum albumin (HSA) is one of the most abundant protein in plasma and constitutes approximately half of the proteins found in human blood. This protein consists of 585 residues set in a single polypeptide chain stabi- lized by 17 disulfide links, with three R-helical domains (I-II-III), each one contains two subdomains A and B (figure 1.6). The crystal structure analyses indicate that the principal regions of ligand binding sites in albumin are situated in hydrophobic cavities placed in subdomains IIA and IIIA. These binding sites are known as Sudlow I and Sud- low II, respectively, and the only tryptophan residue in HSA is located in Sudlow I (Trp-214) [45, 46, 47]. HSA plays an important role in transporting various types of endoge- nous and exogenous compounds like fatty acids, ions, heavy metals, hor- mones, amino acids, drugs. As a consequence, it is well known as a marker for good nutrition and health: e.g. a decrease in HSA concentration indicates a negative acute- phase marker of inflammation or infection. Moreover, it deals with regulation of osmotic pressure in blood, which is 1.1. Tryptophan contained in proteins 7

FIGURE 1.6: Human Serum Albumin’s structure notice the presence of one tryptophan residue (TRP 214). Picture taken from [45]. important for the distribution of body ﬂuids between intravascular com- partments and tissues that is also very crucial for the regulation of body temperature.

1.1.2 Immunoglobulin G

Antibodies, also know as Immunoglobulins (Ig), are the constituent proteins of the immune system whose task is the identiﬁcation and neutral- ization of pathogens such as bacteria and viruses . There are 5 classes of immunoglobulins differing considerably in their structures and biological functions: IgG, IgE, IgM, IgD and IgA (ﬁgure 1.7).

FIGURE 1.7: The 5 classes of Immunoglobulins: G, E, M, A, D.

A basic structure of an immunoglobulin is a Y-shaped molecule composed of two regions: an heavy chain ("H", coloured in blue) that consists of long constant polypeptide regions of about 55 kDa and a light chain ("L", the orange part) of about 22kDa . Both regions have a constant ("C") and a 8 Chapter 1. Tryptophan variable ("V") part. The diversity combinations of variable regions results in the ability to bind different antigens and provides a variety targets of immunoglobulin. The H and L chains are bound by disulfide bonds (black links in the figure mentioned). The higen region, composed of one or two disulfide bonds between the two heavy chains, is responsible for the great flexibility of the immunoglobulin Y-shape.

The most common type of antibody is immunoglobulin G (ﬁgure 1.8), it composed about 75 % of immunoglobulins present in blood serum.

(A) (B)

FIGURE 1.8: Schematic representations of Immunoglobulin G structure. The IgG molecule is composed by constant (C) and variable (V) domains for each light (L) or heavy (H) chain: VL , CL, VH , CH .

Its Y-shape is usually decomposed in two regions: two Fragments Antigens-

Binding Fab which are the tips that interacts with the antigens and a Frag- ment crystallizable Fc part. IgG is often used as a biomarker of unhealthy situations, e.g. increased level of immunoglobulin G in serum indicate possible infections, allergies, autoimmune disorders, cirrhosis, chronic inﬂammations, and its microscopic distribution is also investigated in relation to cancer [48]. 9

Chapter 2

Coherent control

The possibility to measure, to unveil and manipulate ultrafast phenomena is an intriguing goal in physics and chemistry. As Werschnik and Gross outline in their paper [49], even if laser was invented in the 1960’s only in the last decades an application of Quantum Optimal Control Theory (QOCT) was possible. This is mainly due to the advent of femtosecond lasers in the 1980’s and the growing ability to create tailored pulses thank to the technological advances.

The Quantum Optimal Control Theory is based on the capability to optimize the experimental tools until a desired product is obtained. Optimal control experiments cover a wide domain of topics, including: control over isomerization of proteins [50], control over molecular dissociation and ionization [51, 52] , fragmentation [53, 54, 55], control of attosecond dynamics [56], and many other applications. As an example of quantum control, the selection of chemical reactions for a triatomic molecule can be mentioned (see ﬁg.2.1)[2,3, 57]. The Tannor-

(A) (B) (C) (D)

FIGURE 2.1: Example of control over the evolution of a wavepacket. A transition from the local minimum in the groundstate of a triatomic molecule ABC (B) to the excited state generates a wavepacket. A second interaction induces the wavepacket to end up in one of the two different products of the groundstate : A+BC (A) or AB+C (C). (D): Sketch of the Tannor- Kosloff-Rice scheme. Taken from [2, 57]

Kosloff-Rice scheme depicted in figure 2.1d shows that a wavepacket is created on the first excited state by an ultrashort pump pulse; with the help of a 10 Chapter 2. Coherent control second laser pulse of the proper wavelength and time delay with respect to the excitation event, the wavepacket can be dumped into the desired product channel. Thus, different reaction channels can be accessed selectively depending on the pump-dump delay time . An experimental application of Tannor-Kosloff-Rice is reported in Baumert’s article studying Na2 prod- + ucts: as it is shown in fig. 2.2, there is a variation of the ratio between Na2 and Na+ products by adjusting the pump-probe delay time [58].

+ FIGURE 2.2: Controlling the Na2 production versus the Na+ production in a Tannor-Kosloff-Rice-like scheme by adjusting the pump-probe delay time. Taken from [58].

As part of quantum control, the Coherent Control Theory focuses on the ability to design a field that can drive molecules to the desired final states. In theory, optimally laser pulse can be calculated by solving the time-dependent Schroedinger equation of the system; however a full description of the evolution of the wavepacket as well as a priori knowledge of Hamiltonians are needed for this purpose. In particular, for a complex system, such as large molecules in the condensed phase, the molecular Hamiltonian is known usually to a limited degree and solving the Schroedinger equation is chal- lenging. Most important, even if a field is generated theoretically on the basis of an approximate Hamiltonian, it may not be sufficient suitable due to errors arising from the Hamiltonian itself as well as from uncertainties coming from the laboratory. However, tailored laser pulses that steer the quantum system from its initial state to a desired final state can be found using the phase-shape control that is widely studied in different contexts: constructive or destructive interferences between quantum paths can coherently manage the excitation probability in a two-photon transition [59, 60, 61] and in the attosecond timescale [62], in chemical processes as isomerization [63], chemical bond breaking [64] or can steer the fluorescence of dye molecules [65]. This approach enables also applications based on quantum coherent evolution in a Josephson-junction qubits [66, 67] as well as on quantum information processing [68]. Chapter 2. Coherent control 11

The great potentials of the Coherent Control theory are here exploited, applying them to the Optimal Dynamics Discrimination (ODD) theory introduced by Judson and co-workers in 1992 [4], in order to discriminate between large molecules with the same absorption and emission spectra taking advantages from their different dynamics. The ODD Theory points out the importance of phase control over the wavepacket and introduces the physical quantity of discrimination (for example ﬂuorescence’s depletion). This target observable is the feedback signal in a multiobjective algorithm and it is iteratively optimized improving the laser pulse characteristics, until an optimally shaped laser ﬁeld is found. In this framework, there is no need to have a priori informations of the molecular system.

In section 2.1, the dynamics of a wavepacket in a molecular potential energy is treated qualitatively, underlining the contribution of the anharmonic term of the potential and two different successful examples of discrimination are shown. The ODD theory is presented in section 2.2, highlighting the importance of phase control. Finally, the multiobjective algorithm NSGA II used in the experiments is explained in section 2.3. 12 Chapter 2. Coherent control

2.1 Coherent control over a molecular wavepacket

In condensed matter, the interaction between a molecule and an electromagnetic ﬁeld leads to a new arrangement of the electronic density and the molecule is said to be electronically excited. Quantistically, the light-matter interaction is described by the time dependent Schroedinger equation

∂ ı |Ψ(r, t)i = H |Ψ(r, t)i ∂t (2.1) H = H0 − µ (t)

H0 = T + V (r)

in the atomic units : ~ = m = e = 1. Here |Ψ(r, t)i is the wave function, µ is the dipole operator, (t) is the time-dependent electric field and T and V are the kinetic and potential energy operators respectively. The latter is a tricky term that makes an analytical solution somewhat challeng- ing, depending on how many atoms compose the molecules, how and how much they interact with each other and in which environment they are (i.e. including terms as anharmonic vibrational couplings, fluctuations, electrostatic interaction between solvent and solute,etc.). As the mass of the atomic nuclei is ∼ 103 times heavier than electrons’s mass, their velocities are slower. As a consequence, while the electrons move through the electronic states during a transition, the nuclear coordinates of the molecules does not change. This is summed up in the well known Franck- Condon principle, depicted in figure (2.3): the electronic levels are delineated with a morse-like potential that is harmonic for the lowest energetic states; the horizontal lines are the vibrational eigenvalues

ωi.

FIGURE 2.3: Representation of Franck-Condon principle

If the spectral width of the pump-pulse is broader than the vibrational spacing and short in time compared with the vibrational period of the molecule, 2.1. Coherent control over a molecular wavepacket 13 several vibrational states become populated generating a coherent superposition of wave functions called "wavepacket". It evolves in time through the quantum mechanical phase space as

X −ı(ωit+φi) |Ψ(t)i = ci e |ψii (2.2) i

where |ψii are the eigenfunctions, ci and φi represent their amplitudes and phases respectively and ωi are the transition frequencies of the ith vibrational levels.

When the molecular wavepacket is generated, it periodically oscillates back and forth in the bound state potential energy surface. If there are no external perturbations, it continues oscillating without losing energy until it fluoresces decaying from the excited state. Otherwise, it could undergo another transition to a second excited state interacting with the probe-pulse. The variation of fluorescence due to the depopulation of the first excited state is called "Depletion". As it is pointed out in the following sections, it is the physical observable for discriminate between molecules using a pump- probe technique.

In the case of asymmetric potential that is usually associated with the introduction of a Morse-like potential that brings an anharmonic term, the wavepacket undergoes a broadening (see ﬁg. 2.4).

FIGURE 2.4: Broadening due to the potential’s anharmonic term. Adapted from [69].

In fact, the Morse potential

−2α(R−R0) −α(R−R0) V (R) = De e − 2e (2.3) 14 Chapter 2. Coherent control

where −De is the energetic minimum calculated in the equilibrium distance

R0, brings to the eigenvalues

1 1 E = ω (ν + ) − β(ν + )2 (2.4) ν ~ 0 2 2

2 ~ω0 with β = known as the anharmonicity constant. 4De The anharmonic term brings about a variation of the vibrational energies’s spacing ∆Eν = ~ω0 − 2β~ω0(ν + 1) that is smaller for the highest states ∆EH < ∆EL, leading to different oscillation periods TH > TL. As a consequence, the lower energy ("red") components of the molecular wavepacket advance the higher energy ("blue") components after some oscillations [69, 70, 71]. In addition to the wavepacket dispersion, the anharmonicity causes another phenomenon: the decoherence. Thus, the bigger is the anharmonicity, the shorter is the time until the wavepacket has completely spread out on all the possible conﬁgurations and the initial phase’s information is lost.

The manipulation of both the phase φn and the amplitude cn of each component of laser pulse, namely the "Coherent Control" approach, can suppress the wavepacket dispersion, making possible to collected all the components of the wavepacket in phase at a specific delay time T short enough to ignore the decoherence effects (shorter than a few picoseconds). As a result, there is a significant enhancement of the fluorescence depletion and the example in section 2.2.1 clarifies the importance of this argument.

2.1.1 Examples of molecular discrimination

GAP Biophotonics group has already succeeded in discriminating between molecules with the same absorption and emission bands and fluorescence’s dynamics. Thank to the use of tailored pulses, they measured a variation of the time-resolved fluorescence [7,8,9]. Figure 2.5 shows a scheme of the pump-probe technique that is used to acquire a time-resolved fluorescence trace. At time t = 0, a short pulse excites molecules from the ground state to the excited state state with a defined phase conditions, forming a coherent superposition of vibrational states. The molecular wavepacket evolves in time differently in the two molecules under investigation and the evolution can be probed at time t = T by a second pulse, which transfers the population to an higher state (ionizing and dissociative), depleting the fluorescence signal. Thus, a time- resolved fluorescence trace can be acquired changing the time T . 2.1. Coherent control over a molecular wavepacket 15

FIGURE 2.5: Pump-probe scheme for acquiring a time- resolved ﬂuorescence trace.

The first result was achieved in 2009 by the work of Roth et alii applying ODD to discrimination of riboflavin (RBF) and flavin mononucleotide (FMN) [7]. Not only was it possible to distinguish two otherwise spectro- scopically indistinguishable molecules, but retrieval of their relative concentrations in a mixture was demonstrated, thereby making ODD directly applicable for concrete applications in chemistry and biology. More recent result involves Rondi’s paper [8]: the two molecules investigated, Tyrosine (Tyr) and Tryptophan (Trp), are two of the 20 amino-acids that made up proteins and the main contributors in protein’s fluorescence.

FIGURE 2.6: Time-resolved Fluorescence depletion for Trp (black) and Tyr (red). (a) pulse shaped (b) pulse unshaped. From [8] 16 Chapter 2. Coherent control

They are characterized by the same absorption band centred at 270 nm and fluorescence bands around 350 nm for Trp and around 310 nm for Tyr. Pulse-shaping technique is used here to manipulate the phase of the UV field inducing different time-resolved fluorescence depletion traces (upper panel in fig. 2.6) with a significant signal’s variation of ∼ 35%. In fact, Trp undergoes rapid fluorescence depletion reaching a minimum at 600 fs, which can be attributed to the opening of a Franck-Condon window toward higher lying ionizing states. In contrast, Tyr fluorescence decreases until 600 fs and then continues less abruptly until 7 ps. Lower panel in figure 2.6 shows that the same time-resolved fluorescence trace is measured with unshaped UV pulse, making impossible a dynamical discrimination. The second example concerns the discrimination between Tryptophan and Ala-Tryptophan (ala-Trp) [9]. The absorption and emission bands are measured for both molecules and collected in figure 2.7a. In this case, the fluorescence emission band of Ala-Trp coming from the chromophore is only barely perturbed by the alanyl residue.

(A)

(B)

FIGURE 2.7: (A): Absorption and emission bands of some compounds. (B): T-R Fluorescence depletion for Trp (blue) and Ala-Trp (red). (a) pulse shaped (b) pulse unshaped. Taken from [9].

Even in this case, the time-resolved ﬂuorescence traces in ﬁg. 2.7b present 2.1. Coherent control over a molecular wavepacket 17 a different dynamics in the case of UV pulse shaped. This former experiment, involving two systems with almost equivalent energetic structures, suggests us that a similar result can be obtained for tryptophan contained in larger molecules as proteins. 18 Chapter 2. Coherent control

2.2 Optimal quantum control

Taking advantages of the formulation contained in Li’s paper [72], let us consider an example of quantum systems represented by multiple chemical species, that we intend to discriminate. Each of them are characterized ν ν ν ν by N active control states |φ0i,|φ1i,. . . ,|φN−1i and a detection level |Γ i . For each νth species, the solution of the time dependent Schroedinger equation is a wavepacket that is a superposition of all possible states

N−1 ν X ν ν ν ν |ψ (t)i = ci (t) |φi i + d (t) |Γ i (2.5) i=0

Let suppose that at time zero only the ground state is populated

ν ν |ψ (0)i = |φ0i (2.6)

ν After the ﬁrst interaction c(t) that lasts 0 6 t < T , only the |φi i with 0 < i < N − 1 are occupied

ν ν ν |ψ (T )i = Uc (T, 0) |ψ (0)i N−1 (2.7) X ν ν = ci (T ) |φ i i=0

ν where Uc (T, 0) is the propagator describing the evolution of the initial state under the inﬂuence of the ﬁeld c(t). As the detection state is not populated dν(T ) = 0, thus the normalization constrain is

N−1 X ν 2 |ci (T )| = 1 (2.8) i=0

0 At time T the second interaction d(t)comes and interacts for T 6 t 6 T ; thereby the wavepacket becomes

ν 0 ν 0 ν |ψ (T + T )i = Ud (T ,T ) |ψ (T )i (2.9)

ν 0 0 where Ud (T ,T ) is the propagator from time T to T .

Let us suppose that our system is controllable in the sense explained by Werschnik et alii in [49], our goal is reduced to ﬁnd a measurable quantity J ν, that could change among the species, and a tailored laser pulse that can maximise it only for a ξth species :

J ξ = max J ν with J ν = hΓν| Oν |Γνi (2.10) (t) 2.2. Optimal quantum control 19 where J that is deﬁned as the expectation value of an operator Oν. The latter is usually a projector over a single state, in our case the state of our system after the two interactions (at time T + T 0)

ν ν 0 ν 0 O = |ψi (T + T )i hψi (T + T )| (2.11) but we can also employ a multi-objective target operator deﬁning

ν X ν O = βi Oi (2.12) i

Oν could also be define in other ways: as local or non-local operator depending on the specific system taken into account [49]. The sole restriction is that Oν has to be an hermitian operator. If the operator taken into account is the one described in eq.(2.11) and the ν ν transition from the ground state |φ0i to the final one |Γ i is negligible, as it is in our experimental condition described in section 4.1, our signal is a ν depletion of fluorescence from the excited states |φi i with i 6= 0. Using equations (2.7) and (2.9)

ν ν ν 0 ν 0 ν J = hΓ |ψi (T + T )i hψi (T + T )|Γ i N−1 (2.13) X ν ν ν ν 2 = | ci (T ) hΓ | Ud |φi i | i=0

ν ν ν If energetical structure does not change too much among the species hΓ | Ud |φi i ≡ ν Di ≈ Di ∈ R, thus

N−1 ν X ν 2 ν 2 J = | ci (T )Di| = |c (T ) · D| (2.14) i=0

If we want to detect the ξth species among a mixture of different ν compounds one of the possible relevant quantity that we investigate is 1

X L = J ξ − J ν (2.15) ν6=ξ

Finally, L is maximized when we ﬁnd the shape of the laser pulse c(t) ν which drives the transition from an initial state of the νth species |φ0i to a ν ξ ν ﬁnal state |ψi (T )i in such a way that J is optimized and all the other J for ν 6= ξ are minimized . This happens if the scalar product in eq.(2.14) is maximum: when the vector cξ(T ) is parallel to D. Otherwise, J ν are

1We could add several other terms in order to get closer to an optimized description of the system: requiring for example that the power losses due to the dispersion in the perpendicular direction of the laser field is minimal, or that the final state satisfies the Schroedinger equation at each time [49]. Even if these are proper conditions they are not necessary in this case. 20 Chapter 2. Coherent control minimized if the scalar product is zero: here cν(T ) is perpendicular to D (see fig. 2.8).

FIGURE 2.8: Representation of the conditions for discrimination between species. Adapted from [72].

In the next paragraph we made a very simple example that clariﬁes the condition written above, outlining the importance of the phase control over the wavepacket.

2.2.1 Example: three levels system

FIGURE 2.9: Three level system scheme: at time zero c interacts with the ground state populating the ﬁrst excited state, while at time T the second pulse leads the transitions to the detection level.

Let us suppose that there are different probabilities to enhance the second transitions: for example D0 = 0 and D1 = D. Thus, referring to eq.(2.14)

1 ν X ν 2 J = | ci (T )Di| i=0 ν ν 2 (2.16) = |c0(T )D0 + c1(T )D1| ν 2 = |c1(T )D| 2.2. Optimal quantum control 21

As a consequence, the more we populate the state with the highest probability of a second transition (|1iν in this case) the more the signal increases. ν ν In fact a parallel vector of the form c// = (0, c1(T )) has a greater feedback ν ν instead of a perpendicular one c⊥ = (c0(T ), 0). Moreover, as D doesn’t depend on the speciﬁc species due to the fact that the energetic structures are almost the same for the species taken into account, the signal depends on the value of the coefﬁcient of the state that will be depopulated only at time T, when the second transition occurs. A second argument is the following: from eq.(2.7) the evolution in time of the wavepacket is

ν ν ν |Ψ (T )i = c0(T ) |0iν + c1(T ) |1iν (2.17)

ν ν ν ν ıφi (T ) So, from eq.(2.14) reminding that ci (T ) is a complex number ci (T ) = ci e while Di ∈ R

ν ν ν 2 ν ν 2 J = Re(c0(T )D0 + c1(T )D1 + Im(c0(T )D0 + c1(T )D1 (2.18) ν 2 ν 2 ν ν ν ν = (c0D0) + (c1D1) + 2(c0D0)(c1D1) cos(φ0(T ) − φ1(T ))

Therefore, it is evident that the optimization of the signal relies also on a speciﬁc phase’s difference condition between the two states at time T . In particular ν ν ν max J implies cos(φ0(T ) − φ1(T )) = 1 φi leading to ν ν φ0(T ) = φ1(T )

Thus, the wavepacket’s components should be in phase at time T (see ﬁg. 2.5) to enhanced the depopulation of the excited state. This case could be easily extended to the general one with N+1 states

N N ν X ν 2 X ν 2 J = Re( ci (T )Di) + Im( ci (T )Di) i i N N X ν 2 X X ν ν ν ν ν ν = (ci Di) + 2 ci Dicj Dj[cos(φi (T )) cos(φj (T )) + sin(φi (T )) sin(φj (T ))] i i j6=i N N X ν 2 X X ν ν ν ν = (ci Di) + 2 ci Dicj Dj cos(φi (T ) − φj (T )) i i j6=i (2.19)

ν ν that leads to φi (T ) = φj (T ) for i 6= j. This simple example outlines the great importance of phase control over the wavepackets to discriminate between differente species. 22 Chapter 2. Coherent control

2.3 Multiobjective Genetic Algorithm

After Judson and Rabitz’s work [4], closed loop learning procedures based on genetic algorithms have contributed to achieve coherent-control’s experiments. An example of the closed-loop learning algorithm scheme is shown in fig (2.10) : at first step the Genetic Algorithm (GA) starts generating an initial random population of pulse’s shapes, that is materialized by a pulse shaper and applied to the molecular system. The observable, for example fluorescence, is recorded by a suitable detector and then compared. Step by step, an optimally shape should be found by converging to the best solution found by the GA.

FIGURE 2.10: Closed-loop learning algorithm scheme.

Genetic algorithms are optimization methods based on several metaphors from biological evolution. Firstly, let consider a population of N "parents solutions" Pi of the ith step of the closed-loop method. With a mixture of this possible pulse shapes, we can collect a group of N "children solutions"

Qi that acquires a combination of parents genes. Secondly, the population of children solutions can be affected by some mu- tations that leads to a corruption of genes, with a low rate of probability.

Finally, as the solutions Pi and Qi are not equally suitable, half of the population is rejected. As a result, only a few individuals among the global population can pass their genetic information onto succeeding generations (the i+1th step). The approach called Elitist Non-Dominated Sorted Genetic Algorithm (NSGA-II), developed by Deb et al. [6], is capable to handle simultaneously several targets and increases the versatility and the robustness of the GA approach [5]. 2.3. Multiobjective Genetic Algorithm 23

In the Optimal Dynamics Discrimination point of view, the optimization goal is the selective enhancement of the signal from a speciﬁc molecule in competition with a second one, characterized by similar or overlapping absorption and emission bands. Thus, one of the target objective is typically deﬁned as the ratio between the signals simultaneously generated by the two systems J ξ L = (2.20) 1 J ν the second target is the signal we want to maximize or minimize for example ξ L2 = J (2.21)

The other features that increase the potentialities of NSGA-II approach compared with GA are the following points, depicted in ﬁgure 2.11.

Nondominated sorting approach.

The parents and children solutions Pi and Qi are sorted according to nondominant definition: a solution dominates another solution, if it is not worse in any of the objectives, and is strictly better in at least one. A solution is called nondominated, if there is no solution that dominates it. If some equivalent solutions are nondominated, they are ranked in the first 1 1 front Fi of the ith step. If the size of Fi is smaller than N, all its members are retained in the next parent population Pi+1. The remaining individuals 2 of Pi+1 are selected in the next nondominated front Fi , which is the group 1 of solutions that are dominated only by Fi individuals. The process ends when the parent population Pi+1 is filled .

FIGURE 2.11: Scheme of NSGA II procedure. The individuals are sorted according to nondominant deﬁnition into non-dominated fronts. When the new parent population is ﬁlled, the solutions are submitted to the crowding-distance control. Adapted from [6]. 24 Chapter 2. Coherent control

Diversity preservation.

After the parent population Pi+1 is ﬁlled, the individuals are sorted according to the crowding distance operator, which is introduced for preserving the population diversity. The crowding distance is an estimate of the density of solutions: it is the perimeter of cuboid formed using the nearest neighbors of the ith solution as the vertices and it is calculated by NSGA-II (see ﬁgure 2.12). Diversity is preserved by retaining the solutions that have the bigger crowding distances for the next generation.

FIGURE 2.12: Crowding distance calculation for the solutions (ﬁlled circles) belonging to the same pareto front (or nondominated front) using two objectives J1 and J2. From [6] 25

Chapter 3

Transient Absorption and Stimulated Raman Spectroscopies

Transient absorption technique was developed more than 60 years ago by Manfred Eigen, Ronald G. W. Norrish and George Porter, awarded in 1967 for this important achievement with the Nobel Prize in Chemistry [73]. They firstly developed experimental apparatus with millisecond time resolution based on extremely powerful arc flash lamps as excitation sources. The stirring technological achievements of recent years, particularly the advent of femtosecond laser sources paved the way to monitor photophys- ical and photochemical processes, either intramolecular or intermolecular, that follow the absorption of a photon by a molecule on picosecond and subpicosecond timescales. When a ground state molecule absorbs a photon it is promoted to an excited state. From this higher energy state the molecule can relax back to the ground state via some other intermediate excited state of singlet or triplet spin multiplicity [74] or chemically react to form products i.e. photodissociations and photoionizations may occur [75, 76]. The formation of polaron pairs, polarons, and triplet excitons [77], charge recombination [78], electron-phonon relaxation [79] as well as other forms of cooling [80] can be monitored by detecting the absorption spectrum in suitable wavelength windows, typically in the UV-Vis-NIR range. Photoisomers and other metastable species can also be investigated [81]. Although the transient absorption technique gives informations about the electronic reconfiguration that follows the interaction with the pump pulse, it is lack of structural sensitivity: it may lead to contrasting scenar- ios regarding the change in the molecule’s reconfiguration as testified for example by the different hypotheses formulated on hemeproteins photodynamics and based on TA measurements [82, 83]. As a result, a kinetic analysis cannot be achieved unambiguously by a single spectroscopic technique. 26 Chapter 3. Transient Absorption and Stimulated Raman Spectroscopies

It is essential to separate the contributions from the often simultaneous events that may occur. For this purpose, Femtosecond stimulated Raman spectroscopy (FSRS) is a powerful tool: providing high spectral resolution and high time precision in triggering the generation of vibrational coherences (∼ 50 fs), it enables the measurement of speciﬁc molecular vibrational structure [11]. In addition, under electronic resonance condition, the FSRS technique is able to selectively enhance different cromophores or electronic states, removing the ambiguities created by the TA measurement [84, 81].

Femtoscopy group succeded in combining the two techniques to unveil the photodynamics of methyl-phenylthiophene (MPT), one of the building block of photoactive materials [85]. The transient absorption of MPT (figure 3.1a) shows the evolution of the absorption outlining the formation of two contributions: the first one at early times (∼ 500 fs) centred at 480 nm and the second one around 366 nm which appears later (∼ 100 ps). The FSRS measurements (figure 3.1b) unveils the dynamical evolution of this two transient species, selectively isolating the contributions tuning the Raman pulse (RP) into electronic resonance with the singlet (480 nm) and triplet (366 nm) excited states. Moreover, the article is an example of the importance of resonance condition: the FSRS spectra at both RP wavelengths show a strong resonant enhancement with respect to the (off resonance) ground-state stimulated

Raman (SR) spectrum measured at λRP = 366 nm. In this case the FSRS suits better than SR technique, increasing the signal from ∼ 0.1% to ∼ 1%.

In this chapter we introduce the density matrix formalism and the interaction picture (section 3.1) that are useful to deal with nonlinear polarization. The χ(3) processes are described with diagram theory (section 3.1.1) in order to outline the most important contributions to the transient absorption signal (section 3.2) . Finally, in section 3.3 we introduce the femtosecond stimulated Raman scattering technique. Chapter 3. Transient Absorption and Stimulated Raman Spectroscopies 27

(A)

(B)

FIGURE 3.1: Example of photodynamical study achieved with a combination of TA (A) and FSRS (B) techniques. Taken from [85]. 28 Chapter 3. Transient Absorption and Stimulated Raman Spectroscopies

3.1 Interaction picture and diagram theory

The solution of the Schroedinger equation

d ı |ψ(t)i = − H |ψ(t)i (3.1) dt ~ is a wavefunction that can be expressed as a coherent superposition of eigenstates |ni with complex coefﬁcients cn

X |ψi = cn |ni (3.2) n we can deﬁne the probability to ﬁnd the system in the eigenstate |ii

2 2 Pi = | < i|ψ > | = |ci| (3.3)

Similarly, we can deﬁne the density matrix

X ρ := |ψi hψ| = ρn,m |ni hm| (3.4) n,m

∗ where ρn,m = cncm. This formalism allows us to deﬁne the population states (n = m) and the coherences between pure states (n 6= m). Moreover, deﬁning X ρ := Pk |ψki hψk| (3.5) k where Pk is the probability, the density matrix permits to treat the statistical ensembles [86]. The Schroedinger equation in the density matrix formalism leads to the Liouville-Von Neumann equation

d d ı ρ(t) = (|ψi hψ|) = − H, ρ(t) (3.6) dt dt ~

Moreover, in quantum mechanics the expectation value of an operator A is deﬁned as X ∗ hAidef = hψ| A |ψi = cncmAm,n (3.7) n,m while it becomes in the density matrix’s formalism

X hAidef = ρn,mAm,n ⇒ hAidef = Tr(Aρ) (3.8) n,m 3.1. Interaction picture and diagram theory 29

The interaction picture

If the Hamiltonian is time-dependent trough an interaction term H0(t) which is weaker compared to time-independent part H0, the system’s evolution can be treated perturbatively, in the so-called "interaction picture". The Hamiltonian related to a light-matter interaction can be described in the semiclassical limit as

0 H(t) = H0 + H (t) = H0 + µE(t) (3.9) where µ is the quantic dipole operator and E(t) is the classical electric ﬁeld. Let us deﬁne the wavefunction in the interaction picture as

|ψ(t)i = U0(t, t0) |ψI (t)i (3.10)

ı − H0(t−t0) here U0(t, t0) = e ~ is the propagator related to the Hamiltonian H0. Applying this formalism to the Schroedinger equation, we ﬁnd out a similar equation

† 0 HI (t) = U0 (t, t0)H (t)U0(t, t0) (3.12)

Solving the Schroedinger equation for the interaction picture (equation 3.11) iteratively in the density matrix formalism (eq.3.6) leads to

Z t ı ρI (t) = ρI (t0) + − dτ HI (τ), ρI (τ) ~ t0 Z t ı = ρI (t0) + − dτ HI (τ), ρI (t0) + ~ t0 2 Z t Z τ ı + − dτ dτ1 HI (τ), HI (τ1), ρI (τ1) ~ t0 t0 ∞ n Z t Z τ2 X ı = ρI (t0) + − dτn ... dτ1 HI (τn),... HI (τ1), ρI (t0) ... n=1 ~ t0 t0 (3.13) 30 Chapter 3. Transient Absorption and Stimulated Raman Spectroscopies

th Thereby, the n order component of the density matrix with respect to HI interaction is

n Z t Z τ2 (n) ı † ρ(t) = − dτn ... dτ1U0(t, t0) HI (τn),... HI (τ1), ρ(t0) ... U0 (t, t0) ~ t0 t0 (3.14) where

† HI (τk) = U0 (τk, t0)µE(t)U0(τk, t0) † = E(τk)U0 (τk, t0)µU0(τk, t0) (3.15)

= E(τk)µI (τk)

While in the Schroedinger picture the dipole operator is time independent, in the interaction picture it depends on the propagator U0(τk, t0).

The nonlinear polarization

In the case of linear optics the induce polarization depends linearly on the electric ﬁeld, accordingly to

(1) P = 0χ E

(1) where 0 is the permittivity of free space and χ is the linear susceptibility tensor. The nonlinearities, that can be exploited by the great amount of power released by pulsed lasers, are described in terms of a power series in the ﬁeld strength. The power of E or the χ’s superscript reveal the order of nonlinearity . (1) (2) 2 (3) 3 P = 0 χ E + χ E + χ E + ...

In χ(n) processes there are n interactions among n different ﬁelds or it may happen that the same ﬁeld interacts more than once with the system.

The macroscopic polarization is given by the expectation value of the dipole operator

P (t) := hµ(t)idef → P (t) = Tr(µ(t)ρ(t)) (3.16)

Thus, assuming that ρ(t0) is an equilibrium density matrix that does not evolve in time we can send t0 → −∞. Keeping in mind the invariance of trace to cyclic permutation, we obtain 3.1. Interaction picture and diagram theory 31 the nth order nonlinear polarization

n Z t Z τn Z τ2 (n) ı P (t) = − dτn dτn−1 ... dτ1 E(τn)E(τn−1) ...E(τ1)· ~ −∞ −∞ −∞ hµI (t) · µI (τn), µI (τn−1),... µI (τ1), ρ(−∞) ... i (3.17)

Changing variables from instant variables to time intervals τ1 = 0; τ2 −

τ1 = t1; ... and forgetting about the subscript I of the dipole operator, the equation becomes

n Z ∞ Z ∞ Z ∞ (n) ı P (t) = − dtn dtn−1 ... dt1 ~ 0 0 0

E(t − tn)E(t − tn − tn−1) ...E(t − tn − tn−1 − · · · − t1)· hµ(tn + tn−1 + ··· + t1) · µ(tn−1 + ··· + t1),... µ(0), ρ(−∞) ... i (3.18) or equivalently

Z ∞ Z ∞ Z ∞ (n) P (t) = dtn dtn−1 ... dt1 0 0 0 n E(t − tn)E(t − tn − tn−1) ...E(t − tn − tn−1 − · · · − t1) · S (tn, tn−1, . . . , t1) (3.19)

(n) where S ({tn}) is the nonlinear response function

n n ı S ({tn}) = − hµ(tn + ··· + t1) · µ(tn−1 + ··· + t1),... µ(0), ρ(−∞) ... i ~ (3.20) 32 Chapter 3. Transient Absorption and Stimulated Raman Spectroscopies

3.1.1 Double sided Feynman diagrams of a χ3 process

In the case of a third order nonlinear process, the polarization is described by the product of three ﬁelds

Z ∞ Z ∞ Z ∞ (3) (3) P (t) = dt3 dt2 dt1E(t−t3)E(t−t3−t2)E(t−t3−t2−t1)S (t3, t2, t1) 0 0 0 (3.21) while the response function is the expectation value of the product of four dipole operators that leads to a Four-Wave Mixing (FWM): three dipole are introduced by the Hamiltonian through the interaction with the electric ﬁelds, the forth, that is out of the commutators, comes from the free induction decay.

3 (3) ı S (t3, t2, t1) = − hµ(t3 + t2 + t1) · µ(t2 + t1), µ(t1), µ(0), ρ(−∞) i ~ (3.22) Thereby, unrolling the previous equation we note that the commutators make the dipoles act on both sides of the density matrix. The signal acquired is composed of the sum of all the following contributions that are depicted in ﬁg 3.2.

+ hµ(t3 + t2 + t1) · µ(t2 + t1)µ(t1)µ(0)ρ(−∞)i ⇒ S3 ∗ − hµ(t3 + t2 + t1) · µ(t1)µ(0)ρ(−∞)µ(t2 + t1)i → S4 ∗ − hµ(t3 + t2 + t1) · µ(t2 + t1)µ(t1)ρ(−∞)µ(0)i → S2 ∗ + hµ(t3 + t2 + t1) · µ(t1)ρ(−∞)µ(0)µ(t2 + t1)i → S1 (3.23) − hµ(t3 + t2 + t1) · µ(t2 + t1)µ(0)ρ(−∞)µ(t1)i ⇒ S1

+ hµ(t3 + t2 + t1) · µ(0)ρ(−∞)µ(t1)µ(t2 + t1)i ⇒ S2

+ hµ(t3 + t2 + t1) · µ(t2 + t1)ρ(−∞)µ(0)µ(t1)i ⇒ S4 ∗ − hµ(t3 + t2 + t1) · ρ(−∞)µ(0)µ(t1)µ(t2 + t1)i → S3

∗ Here, Si are the complex conjugate of Si because of the trace invariance under cyclic permutation: e.g. Tr(ABC) = Tr(BCA)=Tr(CBA) .

The Feynman’s diagrams, reported in ﬁgure 3.2, are a common way to visualize the nonlinear response function and they can be interpreted by means of the following rules.

1. The last interaction must end in a population state of the form |ni hn|.

2. Vertical lines represent the time evolution of the ket and bra of the density matrix, while the time is running from the bottom to the top. The initial ground state is ρ(−∞) = |Ai hA| 3.1. Interaction picture and diagram theory 33

3. Interactions with the light ﬁeld are represented by arrows. An arrow pointing towards the system represents an up-climbing of the corresponding side of the density matrix due to the interaction with the −ıωt ﬁeld E0e , while an arrow pointing away represents a de-excitation ıωt due to interaction with the pulse E0e .

4. The last interaction represents the signal generated by free induction decay; it is indicated with a dashed line and must points away (because of rule 1). The emitted light has a frequency and wavevector which is the sum of the input frequencies and wavevectors (considering the appropriate signs).

5. Each diagram has a sign (−1)m, where m is the number of interactions from the right, because of each time an interaction is from the right in the commutator it carries a minus sign.

3 FIGURE 3.2: Feynman’s diagrams related to a χ process composed by the contributions outline in eq. 3.23.

All these terms illustrated above and in ﬁgure 3.2 are obtained under the rotating wave approximation (RWA): we are neglecting all the response functions that do not conserve the energy as the diagrams with de-excitation from the ground state, etc. In particular, that approximation removes the terms with high frequency oscillations that are neglectable in resonant condition. 34 Chapter 3. Transient Absorption and Stimulated Raman Spectroscopies

3.2 Ultrafast Transient Absorption Spectroscopy

In transient absorption (TA) spectroscopy, a fraction of the molecules is promoted to an electronically excited state by means of an excitation (or pump) pulse. Depending on the type of experiment, this fraction typically ranges from 0.1% to 10 %. Figure 3.3 illustrates TA technique: a probe pulse whose intensity is low enough to avoid multiphoton/multistep processes during probing, is sent through the sample with a temporal delay τ with respect to the pump pulse. After the sample, the pump beam is blocked while the probe spectrum is acquired with and without the presence of the pump.

FIGURE 3.3: Transient absorption experimental scheme. Adapted from [87].

Measuring the absorption from both photoexcited AON (τ, ω) and un-photoexcited AOFF (ω) molecules’ spectra enables to deﬁne the differential transient absorption as AON (τ, ω) ∆A(τ, ω) = − log (3.24) AOFF (ω)

Deﬁning AON (τ, ω) = |EON (τ, ω)|2 and AOFF (ω) = |EOFF (ω)|2 we get

(3) 2 ES + E ∆A(τ, ω) = − log NL 2 ES (3) Im(ESP ) (3.25) = − log 1 − 2 2 |ES| (3) Im(ESP ) (3) ∝ 2 2 ∝ Im(P ) |ES| where we set (3) (3) ENL = −ıP (3.26)

By changing the time delay τ between the pump and the probe and recording a ∆A spectrum at each time delay, a ∆A(τ, ω) map as a function of τ and frequency ω is obtained. 3.2. Ultrafast Transient Absorption Spectroscopy 35

In general, a ∆A spectrum contains contributions from various 3rd order nonlinear processes that are outlined in ﬁgure 3.4. They are here explained referring to the diagram theory reported in section 3.1.1 and in particular to ﬁgure 3.23.

FIGURE 3.4: A typical TA spectrum (solid blue line) and its components: ESA (solid line), SE (dotted line), GSB (dashed line).Adapted from [87]

The diagrams are built under the constrains:

1. the pump pulse interacts ﬁrst.

2. the pump pulse interacts twice simultaneously.

As a consequence

3. the probe is the last interaction delayed with respect to pump ﬁeld

τ = t2.

4. the free induction decay’s frequency is equal to ωPROBE, thus heterodyne detection is required. 36 Chapter 3. Transient Absorption and Stimulated Raman Spectroscopies

1. Excited-State Absorption (ESA), diagram S1. The population of the excited state |Bi hB| is due to two simultaneous interactions with the pump. Optically allowed transitions from this state to higher excited states may exist in certain energy regions, and interaction with the probe pulse at the corresponding wavelengths will occur leading to a coherent state |Ci hB|. A free induction decay leaves the system to the population state |Bi hB| 1 within the coherence time t3 < , where Γ is the dephasing rate. ΓCB The response function associated to this process is

(3) ı S = − hµ(t3 + t2) · µ(t2)µ(0)ρ(−∞)µ(0)i (3.27) ESA ~3 and with monochromatic ﬁelds leads to

2 2 2 µABµBC |Epump| Eprobe δ(ω − ωprobe)ΓCB ∆A(ω)ESA ∝ 3 2 2 (3.28) ~ ((ωCB − ωprobe) + ΓCB)

Thus a positive signal in the ∆A spectrum is observed in the wavelength region of excited-state absorption represented as a solid black line in ﬁgure 3.4.

FIGURE 3.5: Ladder diagram for Excited state absorption processes. solid arrow: interaction with the ket; dashed arrow: interaction with the bra; waivy arrow: free induction decay. 3.2. Ultrafast Transient Absorption Spectroscopy 37

2. Stimulated Emission (SE), diagram S2. During the physical process of stimulated emission, a photon from the probe pulse induces emission of another photon from the excited state |Bi hC|, which returns to the lower energy state |Ci hC|. The photon produced by stimulated emission has the same frequency and is emitted in the same direction as the probe photon, and hence both will be detected. The response function associated to this process is

(3) ı S = hµ(t3 + t2) · µ(0)ρ(−∞)µ(0)µ(t2)i (3.29) SE ~3 and with monochromatic ﬁelds leads to

2 2 2 µAC µCB|Epump| Eprobe δ(ω − ωprobe)ΓCB ∆A(ω)SE ∝ − 3 2 2 ~ ((ωCB − ωprobe) + ΓCB) (3.30) Stimulated emission results in an increase of light intensity on the detector, corresponding to a negative ∆A signal, as schematically indicated by a dotted line in ﬁg. 3.4.

FIGURE 3.6: Ladder diagram for stimulated emission processes. solid arrow: interaction with the ket; dashed arrow: interaction with the bra; waivy arrow: free induction decay. 38 Chapter 3. Transient Absorption and Stimulated Raman Spectroscopies

3. Ground-State Bleach signal (GSB), diagrams S3 and S4. As a fraction of the molecules has been promoted to the excited state through the action of the pump pulse, the number of molecules in the ground state has been decreased. Thereby, the ground-state absorption in the excited sample is less than that in the non-excited sample. The response function associated to this process is

(3) ı SGSB = 3 hµ(t3 + t2) · µ(t2)µ(0)µ(0)ρ(−∞)i ~ (3.31) + hµ(t3 + t2) · µ(t2)ρ(−∞)µ(0)µ(0)i

and with monochromatic ﬁelds leads to

2 2 2 µAC µAB|Epump| Eprobe δ(ω − ωprobe)ΓAB ∆A(ω)GSB ∝ −2 3 2 2 ~ ((ωAB − ωprobe) + ΓAB) (3.32) Consequently, a negative signal in the ∆A spectrum is observed in the wavelength region of ground state absorption, as schematically indicated by a dashed line in ﬁg. 3.4.

(A)

(B)

FIGURE 3.7: Ladder diagram for ground state bleaching processes. (A): S3, (B): S4. solid arrow: interaction with the ket; dashed arrow: interaction with the bra; waivy arrow: free induction decay. 3.2. Ultrafast Transient Absorption Spectroscopy 39

3.2.1 Singular value decomposition

The singular value decomposition is an useful tool that allows us to extract the spectral components resulting from the different species that occur in the generation of the transient absorption’s signal. With reference to G.H. Golub arguments [88, 89], let us deﬁne the decomposition process.

Theorem 3.2.1. If A is a real m-by-n matrix, then there exist orthogonal matrices

mxm nxn U = [u1, . . . , um] ∈ R and V = [v1, . . . , vn] ∈ R (3.33) such that

T mxn U AV = Σ = diag(σ1, . . . , σp) ∈ R , p = min{m, n} (3.34) where σ1 > σ2 > ··· > σp > 0

The σi are the singular values of A, the ui are the left singular vectors of A, the vi are right singular vectors of A and the equation

A = UΣV T (3.35) is called the Singular Value Decomposition (SVD) of matrix A.

mxn Corollary 3.2.1. If A ∈ R and rank(A)=r, then

r X T A = σiuivi (3.36) i=1

Thereby, if A = Ψ(λ, t)

X Ψ(λ, t) = un(t)σnvn(λ) (3.37) n where vn(λ) are the spectral components whose dynamics are controlled by un(t) and σn quantiﬁes the importance of the nth spectrum. 40 Chapter 3. Transient Absorption and Stimulated Raman Spectroscopies

3.3 Stimulated Raman Scattering

The Stimulated Raman Scattering (SRS) is a 3rd order pump-probe technique. Thereby, its signal can be obtained as the sum of the processes depicted in the diagrams reported in section 3.1.1 and opportunely dressed with the combination of the fields. As transient absorption technique, it involves two interactions with the pump pulse and one with the probe field but, on the contrary, SRS does not force the first two interactions to be driven by the pump field. In fact, in a typical SRS experiment, the Raman pulse, which provides the spectral resolution, is temporally overlapped with the the probe pulse and typically lasts a few picoseconds.

The diagrams in ﬁgure 3.2 are dressed with each combination of the probe pulse ES (Stokes) and the pump ER (Raman). Let us consider A the ground state, B the vibrational excited state of the electronic ground state and C the electronic excited state.

1. Stimulated Raman Scattering (SRS) I SRS I set of diagrams is characterized by having the Stokes ﬁeld leav- ing the bra side, thus ending on the population state |Bi hB|. The interactions take place among the energy levels eA 6 eB < eC .

FIGURE 3.8: Stimulated Raman Scattering I Feynman diagrams R: Raman pulse (blue arrow), S: Stokes pulse (orange arrow). 3.3. Stimulated Raman Scattering 41

2. Stimulated Raman Scattering (SRS) II SRS II set of diagrams is characterized by having the Stokes ﬁeld en- tering the ket side and the two Raman interactions on the bra.

FIGURE 3.9: Stimulated Raman Scattering II Feynman diagrams R: Raman pulse (blue arrow), S: Stokes pulse (orange arrow).

3. Inverse Raman Scattering (IRS) IRS set of diagrams is characterized by having all the interactions on one side (ket or bra).

FIGURE 3.10: Inverse Raman Scattering Feynman diagrams R: Raman pulse (blue arrow), S: Stokes pulse (orange arrow). 42 Chapter 3. Transient Absorption and Stimulated Raman Spectroscopies

Similarly to the transient absorption technique, SRS needs an heterodyne detection over the Stokes ﬁeld. The modulations due to the Raman scattering generally appear as Lorentzian peaks set at lower frequencies (Raman Gain in the red side) with respect to Raman pulse or at greater frequencies (Raman Loss in the blue side), see ﬁgure 3.11.

FIGURE 3.11: Raman Gain and Raman Loss.

In order to understand an SRS signal, let us calculate the P (3) contributions due to RRS I diagram. In non-resonance condition the contributions coming from all the diagrams (except RRS I and IRS I) cancel each other out, while in resonance condition the diagrams contribute with broad peaks. Reminding eq. 3.25 the Raman Gain (RG) is deﬁned as

RG(ω) ∝ Im(P (3)(ω)) (3.38)

RRS I contribution

Figure 3.12 represents the ladder diagram related to RRS I scheme depicted in ﬁgure 3.8: the interactions with the bra-side and ket-side are shown by dashed and solid arrows respectively, while the free induction decay is represented by a vertical wavy arrow.

FIGURE 3.12: RRS I ladder diagram. R: Raman pulse (blue arrow), S: Stoke pulse (orange arrow). 3.3. Stimulated Raman Scattering 43

From equations 3.19 and 3.20

Z ∞ Z ∞ Z ∞ (3) ∗ 3 P (t)RRS I = dt1 dt2 dt3 ER(t−t3) ES(t−t3−t2) ER(t−t3−t2−t1)·S (t3, t2, t1) 0 0 0 (3.39) 3 3 ı B C C B S (t3, t2, t1) = − hµC (t3 + t2 + t1) · µA(t2 + t1)ρ(−∞)µA(0)µC (t1)i ~ (3.40) or equivalently, considering the evolution of the coherent states depicted in ﬁg. 3.12

2 2 Z ∞ Z ∞ Z ∞ (3) ıµAC µCB P (t)RRS I = 3 dt1 dt2 dt3 ER(t − t3) ~ 0 0 0 ∗ −ıω˜AC t1 −ıω˜AB t2 −ıω˜CB t3 ES(t − t3 − t2) ER(t − t3 − t2 − t1)e e e (3.41) where

ω˜AC = −ωAC − ıΓAC

ω˜AB = −ωAB − ıΓAB (3.42)

ω˜CB = ωCB − ıΓCB

ej − ei with ωij = the frequency between two states and Γ the dephasing ~ rate. For the sake of simplicity, let us suppose ER and ES are monochromatic ﬁelds

−ıωR(t−t3) ER(t − t3) = AR e

−ıωS (t−t3−t2) ES(t − t3 − t2) = AS e (3.43)

∗ ∗ +ıωR(t−t3−t2−t1) ER(t − t3 − t2 − t1) = AR e

2 2 2 Z ∞ Z ∞ Z ∞ (3) ıµAC µCB|AR| AS P (t)RRS I = 3 dt1 dt2 dt3 ~ 0 0 0 (3.44) · e−ıωR(t−t3)e−ıωS (t−t3−t2)e+ıωR(t−t3−t2−t1) · e−ıω˜AC t1 e−ıω˜AB t2 e−ıω˜CB t3

Taking into account the following integral

Z ∞ ı dx eıAx = (3.45) 0 A the polarization becomes

2 2 2 3 −ıωS t (3) ıµAC µCB|AR| AS i e P (t)RRS I = 3 ~ (ωS − ω˜CB)(ωS − ωR − ω˜AB)(−ωR − ω˜AC ) (3.46) 44 Chapter 3. Transient Absorption and Stimulated Raman Spectroscopies √ 2πµ2 µ2 |A |2A δ(ω − ω ) P (3)(ω) = AC CB R S S RRS I 3 (ω − ω˜ )(ω − ω − ω˜ )(−ω − ω˜ ) √ ~ S CB S R AB R AC 2 2 2 2πµAC µCB|AR| AS δ(ω − ωS) = 3 ~ (ωS − ωCB + ıΓCB)(ωS − ωR + ωAB + ıΓAB)(−ωR + ωAC + ıΓAC ) (3.47)

In resonance condition ωR = ωAC and ωS = ωBC

2 2 2 R µAC µCB|AR| AS δ(ω − ωS)ΓAB RG(ω)RRS I ∝ 3 2 2 ~ ΓCBΓAC ((−ωS + ωR − ωAB) + ΓAB) (3.48)

In the non resonant case ωR < ωAC and ωS < ωCB (see ﬁg. 3.13)

FIGURE 3.13: RRS I ladder diagram in the non resonant case. R: Raman pulse (blue arrow), S: Stoke pulse (orange arrow).

2 2 2 NR µAC µCB|AR| AS δ(ω − ωS)ΓAB RG(ω)RRS I ∝ 3 2 2 ~ (ωBC − ωS)(ωAC − ωR)((−ωS + ωR − ωAB) + ΓAB) (3.49) In both resonance and non-resonance cases the Raman Gain is a positive Lorenztian peak, but there is an enhancement of cross section in the resonance condition (see ﬁgure 3.14).

−5 x 10 5 ω *1.2 S ω *1.3 4 S ω *1.5 S ω *1.8 3 S ω * 2 S 2 Intensity (a.u.)

0 790 800 810 820 830 RRS I contribution cm−1

−1 FIGURE 3.14: RRS I simulated peak at 801.3 cm at different values of ωBC (shown in the legend). Black line: resonance case. Colored line: non-resonance case at −1 −1 different ωBC values; ΓAB = (500 fs) ; ΓBC = ΓAC = (10 fs) . 45

Chapter 4

Experimental setups

4.1 Setup employed in GAP Biophotonics lab

Figure 4.1 shows the setup used for discrimination experiments of proteins that is described in Chapter5. The laser source consists of a commercial ampliﬁed Ti:Sapphire system with a repetition rate of 1 kHz and 27 nm band - width centred at 800 nm. The Infra-Red (IR) pulse is split into two beams: the ﬁrst one goes to a delay line and through a chopper at 500 Hz , while the second one is sent to a Deep Ultra-Violet (DUV) stage where the third harmonic is generated centred at λ = 266 nm with a bandwidth of 3 nm FWHM.

FIGURE 4.1: Schematic layout of the experimental setup used for discrimination experiments of proteins. BS: Beam Splitter, L: Lens, HWP: Half-Wave Plate, SHG: Second Harmonic Generation, DL: Delay Line, THG: Third Harmonic Generation, FC: Flow-Cell, PMT: PhotoMultiplier Tube.

The UV beam that acts as a pump is then sent to the pulse shaper that is controlled by the genetic algorithm through the computer. Shaping is done in a folded 4-f conﬁguration that consists of a highly dispersive grating 46 Chapter 4. Experimental setups

(3.600 mm−1), a f = 30 cm spherical lens and a MEMS array of 100 Al-coated micro-mirrors (more information in section 4.4). With the present arrangement, the spectral resolution at the Fourier plane is 0.1 nm/pixel, allowing a temporal shaping window of 2 ps FWHM1. The DUV can be sent to the Self-Diffractiion Frequency Resolved Optical Gating (SD FROG) stage that fully characterized the pulse (see section 4.3). Otherwise, the DUV and IR arms are spatially recombined at a dichroic mirror and temporally overlapped by acting on a delay stage placed on the IR path. An 50% aluminium coated beam splitter is then used to produce two DUV-IR pulse pairs used to simultaneously interrogate two samples. The beams are focused into two identical and home-made ﬂow-cells, using parabolic Al-coated mirrors. Fluorescence collection are made with double set of lenses and are detected by a PhotoMultiplier Tubes (PMT). The PMT signal is integrated with a boxcar ampliﬁer and digitalized by a Data Ac- Quisition (DAQ) device. The pulse energies at the sample were tipically 140 − 240 nJ for the DUV (never more than 300 nJ when photodamage effects become evident), and 3µ J for the IR pulse.

Third Harmonic Generation

The Third Harmonic Generation (THG) process is exhibited in ﬁgure 4.2: the 800 nm pulse’s parallel polarization is changed into a perpendicular one by an half-wave plate and the beam is then focused on a BBO for the generation of its second harmonic (400 nm). The two ﬁelds are then sepa- rated by a dichroic in order to send the fundamental in a delay stage and to another half-wave plate. The delay line guarantees the temporal overlap while the HWP changes the polarization of the IR into a parallel one, necessary for the sum-frequency process.

FIGURE 4.2: Scheme of Third Harmonic Generation HWP: a Half-Wave Plate, SHG: Second Harmonic Generation, SFG: Sum Frequency Generation, DS: Delay Stage used to compensate the group velocity mismatch between 800 nm and 400 nm. Adapted from [90].

1 see section 4.4.3 for calculations 4.1. Setup employed in GAP Biophotonics lab 47

The two pulses are collected by a dichroic and focused on a second BBO for the Sum-Frequency (SF) process that generates a DUV pulse centred at λ = 266 nm. The SF generation needs a type I of phase matching: both the input pulses have the same polarization parallel to the laboratory plane, while the output signal has a perpendicular one. The IR and 400 nm residuals are removed using dichroic mirrors along the line.

4.1.1 Sample preparation and handling

Sample preparation

The compounds used in this work were purchased in form of pow- der and successively dissolved in the Dulbecco’s Phosphate Buffered Saline (DPBS) with the concentrations reported in tab.4.1 (pH 7).

Substance Molecular mass [g/mol] Molarity Trp 204.23 1 mM HSA 67·103 0.1 mM IgG 150·103 0.01 mM

TABLE 4.1: Concentration of Tryptophan, Human Serum Albumin and Immunoglobulin G solutions.

The ﬂow-cells

The first sample holder, already used for discrimination experiments by Afonina [90], consists in a cuvette with 0.1 mm optical path, able to contain small volumes of the sample 0.5 ml. A second sample holder is an high flux, sub-ml, capillary flow-cell that is realized by GAP Biophotonics group in collaboration with EDFL/CNRS/CSEM [91] (see figure 4.3). While the 0.1 mm thin window of the 0.5 mm cross-

FIGURE 4.3: Pictures of the flow-cell’s main components (A): General view of the flow-cell showing the bubble chamber and the turbisc pump; (B) a zoom of the capillary junction; (C) square capillary that is the window employed for analysis. Adapted from [91]. section capillary ensures an optimal temporal resolution and a steady beam 48 Chapter 4. Experimental setups deviation, the turbisc pump generates flows up to ∼ 0.35 ml/s that are suitable to pump laser repetition rates up to ∼ 14 kHz. In addition, a de- cantation chamber (the "bubble chamber") efficiently removes bubbles and allows the addition of chemical compounds while preserving the closed atmosphere. This flow-cell overcomes the usual limitations given by the restriction of the amount of liquid sample available because the minimal useable amount of sample is ∼ 250 µl, while the high flux limits the photodamage induced by the high repetition rate of light sources providing new sample at each laser shot. 4.2. Experimental setup used in Femtoscopy lab 49

4.2 Experimental setup used in Femtoscopy lab

Figure 4.4 shows the setup used for pump probe experiments on Trypto- phan that is described in Chapter6. The laser source consists of a commercial ampliﬁed Ti:Sapphire (Coher- ent Legend) system with a repetition rate of 1 kHz producing 3.5 mJ pulses with 50 fs of duration (28 nm FWHM bandwidth), centred at 800 nm. The Infra-Red (IR) pulse is split into three beams by means of two beam split- ters: the ﬁrst beam splitter (50T/50R) generates the Raman pulse (RP) line, while the second one (30T/70R) produces the Actinic pump (AP) and white light continuum (WLC) lines.

FIGURE 4.4: Experimental setup used in Femtoscopy lab WLC: white light continuum, BS: beam splitter, BBO: Beta Barium Boriate, HWP: zero-order half waveplate at 800 nm, VA: variable attenuator, CR: chopper for Raman pulse, CA: chopper for actinic pump, D: dichroic, DL: delay line, G: grating, S: slit, FC: ﬂow-cell.

In the Raman pulse line, the fundamental enters a two stage OPA (TOPAS- C) in order to generate a tunable pulse centered in the range 950-1200 nm that undergoes a second harmonics (SH) process in a long (25 mm) beta barium boriate (BBO) crystal . The long BBO is useful to generate a narrowband pulse with bandwidth ∼ 0.25-0.5 nm FWHM centered at a wavelength that satisﬁes the phase-matching condition, generally in the range 430-600 nm. In fact, the bandwidth is inversely proportional to the length of the 50 Chapter 4. Experimental setups crystal L that acts as a spectral compressor

1 ∆ν ∝ (4.1) GVM · L where GVM is the group velocity mismatch. Then a double-pass (2f) spectral filter with a single grating (1800 lines/inch, 410 nm blaze) and an ad- justable slit in the collimated region of the spectrally dispersed beam are used in order to improve the spectral profile of the SH generated Raman pulse and, most important, to rectify its temporal profile. [92]. The generation of the pulse centred at 266 nm is performed in the Ac- tinic pump line of figure 4.4. The IR pulse is led on a BBO for a second harmonic generation, creating a 400 nm pulse with a crossed polarization. The fundamental’s polarization is changed by a zero-order half waveplate (HWP) centered at 800 nm.

Both pulses cross a CaCO3 crystal in order to recollect the right temporal overlap: the Calcite is a negative uniaxial birefringent crystal that change the pulse’s velocity with respect to the second one. In fact in a uniaxial birefringent crystal, light whose polarization is perpendicular to the optical axis is governed by a refractive index no (for the "ordinary" axis) whereas light whose polarization is in the direction of the optical axis sees an optical index ne (for "extraordinary"). The magnitude of the birefringence is quantified by the difference ne − no; for Calcite the difference is negative and thus the crystal is said to have a negative birefringence. In our case, the polarization of the fundamental is perpendicular to the optic axis while the 400 nm’s polarization is parallel. Thereby, the two pulses experience a different velocity in the crystal enabling to restore the temporal overlap between them. They are then sent on a second BBO for the sum frequency process that generates the 266 nm field. A prisms pair is used for compression of the deep ultraviolet pulse (see section 4.5) and a delay line guarantees a temporal overlap with the other beams on the sample. The 400 nm and 800 nm residuals are removed using dichroic mirrors along the line. Finally, the white light generation (WLG) is achieved focusing the IR pulse on a Sapphire crystal. A variable attenuator and an iris are used in order to control the IR pulse energy and diameter and controlling the WLC spectral profile and stability. The Raman, the actinic and the probe pulses are focused into a flow-cell using parabolic Al-coated mirrors, parabolic mirror and a lens respectively. After the sample, the WLC signal enters the monochromator (acton sp 2500i) which has three gratings with respectively 150, 1200 and 2400 grooves/mm. For the SRS we apply principally the second grating. The monochromator disperses the beams onto a CCD camera (Princeton pixis 400 with 1340x400 4.2. Experimental setup used in Femtoscopy lab 51 pixels). An home built acquisition software, based on MATLAB platform, acquires the spectrum and manipulate the delay lines.

In an ultrafast transient absorption measurement, discussed in section 6.1.4, the Raman pulse line is not used, and the Actinic pump line, that acts as the pump, is choppered with a frequency 500 Hz. 52 Chapter 4. Experimental setups

4.3 Pulse characterization

The characterization of pulses involves the measurement of their duration, amplitude and phase. The wide diversity of lasers in the picosecond and femtosecond range requires a large variety of characterization techniques; remarkably, since the temporal resolution of methods based on electronic detection does not exceed the ns time scale, they are not suitable to investigate picosecond and femtosecond pulses, which are of fundamental importance for accessing the time scale dynamics in molecular and atomic systems. Therefore to break this limit, the use of optical systems is required.

In this section we will introduce some measurements techniques capable to resolve femtosecond pulses characterizing the duration and the amplitude such as Cross-Correlation (section 4.3.1) as well as the spectral and temporal phase investigated trough the SD FROG method (section 4.3.2). Moreover, we introduce a Kerr effect-based technique (section 4.3.4) that is useful to characterize the instrument response function (IRF)’s duration, necessary for transient absorption experiments.

4.3.1 Cross-Correlation

The cross-correlation signal is performed by two different pulses that overlap in time and space in a nonlinear medium generating a sum frequency process. It is described by the convolution of the reference pulse intensity

Ir and the signal we want to characterize Is

Z ∞ ICC (τ) = (Ir ?Is)(τ) = Is(t) Ir(τ − t) dt (4.2) −∞

If the reference pulse is known or is short enough in time, an estimate of

Is’s duration is possible deconvoluting the cross-correlation signal. For example, the convolution of two Gaussians leads to

−τ 2 ICC (τ) ∝ exp 2 2 (4.3) 2(σr + σs )

As a result, the width of the cross-correlation pulse is limited by the biggest of the two σ.

In a degenerate case, when the two pulses are equal Ir = Is the cross- correlation consists in the autocorrelation technique. An autocorrelation signal provides little information on details of the pulse shape: e.g. it is always symmetric even when the pulse shape is asymmetric. Moreover, both methods record intensity correlation and cannot provide 4.3. Pulse characterization 53 any information on the phase variations across the pulse. Since cross correlation techniques are able to provide only limited informations, measurements involving both temporal and frequency resolution simultaneously -such as the FROG technique described below- are required, in order to provide a complete characterization of ultrashort pulses. More informations about how we used the cross-correlation technique are reported in section 5.1.

4.3.2 Frequency-Resolved Optical Gating

Trebino et alii in their work [93] succeeded in explaining how Frequency Resolved Optical Gating (FROG) is an effective technique that completely characterizes an ultrashort laser pulse in time. The FROG is an autocorrelation- type measurement technique in which the signal generated through the nonlinear medium, as a beta barium boriate crystal (BBO), is spectrally resolved (Frequency-Resolved) by the spectrometer yielding to the "FROG trace" [94]. Z ∞ 2 IFROG(ω, τ) = Esig(t, τ) exp(ıωt) dt (4.4) −∞ This quantity is mathematically equivalent to a spectrogram

S(ω, τ) = E(t)Egate(t − τ) exp(ıωt) dt (4.5)

if we can express Esig(t, τ) in terms of the gate function Egate(t − τ).

In principle every nonlinear process can be used to generate a FROG signal, but in reality the second and third order are the most common. It is quite evident that χ(2) geometry, named Second Harmonic Generation (SHG) FROG, are more useful for low-energy pulses; on the other hand they are affected by a temporal ambiguity that induces an insensitivity to the sign of the chirp: the FROG traces are symmetrical in time [95].

The third-order interactions among 3 different ﬁelds generate 44 products that reduce to 5 if we consider the interactions between two replicas ω1 =

ω2 = ω3 and ignore the negative frequencies (the complex conjugate terms) [96]. In fact, considering two replicas linearly polarized and delayed in time E(t) 54 Chapter 4. Experimental setups

and E(t − τ) the possible FROG signals Es(t, τ) are listed below  2 |E(t)| E(t − τ) PG FROG   2 E (t)E(t − τ) THG FROG  2 ∗ Es(t, τ) ∝ E (t)E (t − τ) SD FROG (4.6)  E(t)3   |E(t)|2E(t) in which the last two expressions cannot build a FROG signal due to the fact that they do not depend on the delayed time τ.

4.3.3 Self-Diffraction FROG (SD FROG)

As we already mentioned in eq. 4.6, the Self-Diffraction Frequency-Resolved Optical Gating (SD FROG) signal is generated by the third order nonlinear process

2 ∗ Es(t, τ) = EA(t)EB(t − τ) (4.7) 2 −ı(2ωt+2kA·x)+ı(ωt+kB ·x) = EAEBe that deals with conditions

ωSD := ω (4.8)

kSD := 2kA − kB (4.9)

Among all the possible geometries, we dealt with SD FROG because it is the most sensitive to the pulse’s phase and it is background free, which is a great advantage because no polarizer for UV pulses is required. More- over SD-FROG is not phase matched because the intensity of kSD in 4.9 is not respected in a non collinear geometry, and thus the angle between the two pulses and the thickness of the nonlinear medium must be kept very small. Finally it does not require (an external reference or) a priori deﬁni- tion of the pulse, which is useful in the optimal dynamics discrimination viewpoint because we deal with complexes pulses generated by a genetic algorithm.

SD FROG geometry is showed in ﬁg.4.6. One replica is delayed with respect to the other one of a delay time τ which is regulated by two mirrors in the delay line. Both ﬁelds are then focused on a nonlinear medium and the output signal is led through a prism or a grating which disperses the pulse and then detected by a CCD camera properly calibrated. 4.3. Pulse characterization 55

FIGURE 4.5: Experimental apparatus for SD FROG BS=beam splitter, L=lens, BBO=Beta Barium Boriate nonlinear medium, PR=prism.

A measurement of SD FROG signal is acquired with the software built in Labwindows environment (see appendixA) and is displayed in fig.4.6a. The CCD camera with 2068 pixels records the intensity in time showing a spectrogram: the high energy components come just before the low energy components making the slope not perfectly horizontal. In fact, the slope is estimated by the fit reported in figure 4.6b

∆λ nm = 0.027 ∆τ fs

The phase retrieval was possible with Trebino’s algorithm described in [93] and the pictures in ﬁg.4.7 show the pulse in time (4.7a) and in wavelength (4.7b) domain. In particular, the normalized autocorrelation has a width σ = 23 fs that correspond to a DUV pulse’s duration of 37 fs (FWHM) .The spectrum shows a bandwidth of 3 nm FWHM centred at 266 nm. In section 4.5, we will treat in details the fact that a linear displacement P (ω) = αω is related to a group delay dispersion (GDD) different from zero.

d2ϕ d2 ωP (ω) d2 αω2 α GDD = = = = dω2 dω2 c dω2 c c (4.10) αω2 ϕ(ω) = c

As a result, we can confirm that a linear displacement in time of the frequencies (suggested by the FROG measurement’s fit in figure 4.6b) leads to a quadratic chirp near the peak of intensity, as shown by figure 4.7b . Fi- nally, the frequency phase is a feature that can be controlled by the pulse shaping technique explained in section 4.4. 56 Chapter 4. Experimental setups

(A)

270 peaks positions 269 Fit y=0.027*x 268

267

266

265 Wavelength [nm] 264

263

262 6250 6300 6350 6400 6450 6500 Time delay τ [fs]

(B)

FIGURE 4.6: SD FROG measure of a pulse centred at 266 nm. (A) CCD camera measure; (B) Slope’s ﬁt of the peaks of intensity.

1 5 1 6 Intensity Intensity Phase Phase 0.8 4

0.6 3 0.5 4

Intensity 0.4 2 Intensity Phase (rad) Phase (rad)

0.2 1

0 0 0 2 −100 −50 0 50 100 262 264 266 268 270 Delay time τ (fs) Wavelength (nm) (A) (B)

FIGURE 4.7: Phase retrieval obtained with Trebino’s algorithm. (A) autocorrelation measure; (B) spectrum. 4.3. Pulse characterization 57

4.3.4 Polarization-Gated FROG (PG FROG)

Referring to eq.4.6, the Polarization-Gated Frequency-Resolved Optical Gat- ing (PG FROG) signal is deﬁned as

2 Es(t, τ) = |EA(t)| EB(t − τ) (4.11)

2 −ı(ωB t+kB ·x) = |EA| EB e and even if the detection is along the EB line, an homodyne detection is possible with the use of a polarizer. In fact, the PG FROG signal is associated to a nonlinear polarization through the equation

(3) X (3) ∗ Pi (ω = ωA−ωA+ωB) = 0 χi,j,k,m(ω; ωA, ωB))Ej(ωA)Ek(ωA)Em(ωB) j,k,m=x,y,z (4.12) (n) (n) where χ (ωi; {ωk}) is one element of the susceptibility tensor χ ob- i,{jk} tained from the structural analysis of the medium and j, k, m are the ﬁelds polarization’s projection over the cartesian axis.

If E(ωB)’s polarization is oriented in the Y direction (E(ωB) // Y ), while

E(ωA)’s polarization creates 45 degrees with E(ωB), the equation becomes

(3) (3) ∗ P (ω = ωA − ωA + ωB) = 0χx,x,y,y(ω; ωA, ωB))Ex(ωA)Ey (ωA)Ey(ωB) (3) ∗ + 0χx,y,x,y(ω; ωA, ωB))Ey(ωA)Ex(ωA)Ey(ωB) (3) 2 + 0χx,x,x,y(ω; ωA, ωB))|Ex(ωA)| Ey(ωB) (3) 2 + 0χx,y,y,y(ω; ωA, ωB))|Ey(ωA)| Ey(ωB) (3) ∗ + 0χy,x,y,y(ω; ωA, ωB))Ex(ωA)Ey (ωA)Ey(ωB) (3) ∗ + 0χy,y,x,y(ω; ωA, ωB))Ey(ωA)Ex(ωA)Ey(ωB) (3) 2 + 0χy,x,x,y(ω; ωA, ωB))|Ey(ωA)| Ey(ωB) (3) 2 + 0χy,y,y,y(ω; ωA, ωB))|Ey(ωA)| Ey(ωB) (4.13)

Thus, in order to measure a signal whose frequency is equal to ωB in the direction kB, we need to use a polarizer that selects the polarization perpendicular to Y while blocking the polarization along the X direction.

(3) (3) ∗ PPG FROG(ωB) = 0χx,x,y,y(ω; ωA, ωB))Ex(ωA)Ey (ωA)Ey(ωB) (3) ∗ + 0χx,y,x,y(ω; ωA, ωB))Ey(ωA)Ex(ωA)Ey(ωB) (4.14) (3) 2 + 0χx,x,x,y(ω; ωA, ωB))|Ex(ωA)| Ey(ωB) (3) 2 + 0χx,y,y,y(ω; ωA, ωB))|Ey(ωA)| Ey(ωB)

In fact, if we choose a non-collinear geometry with a polarizer along E(ωB) direction, as reported in ﬁgure 4.8, we would measure a signal only when 58 Chapter 4. Experimental setups the nonlinearity occurs, that is when the two pulses overlap in time.

FIGURE 4.8: PG FROG’s geometry D: detector, P: polarizer, NLM: nonlinear medium, red arrows are the ﬁelds’s polarizations

The non-collinear geometry prevents to measure E(ωA) while the polarizer removes the signal coming from the fundamental E(ωB) (homodyne detection). PG FROG is useful in order to measure the duration of the response function obtained with the superposition of the white light and the Actinic pump (centered at λ = 266 nm), thusallowing to experimentally verify the prisms’s compression calculated in section 4.5 and discussed experimentally in 6.1.2 and to evaluate the TA temporal resolution. 4.4. Pulse Shaping 59

4.4 Pulse Shaping

Pulse shaping consists in manipulating all the characteristic of a pulse such as the amplitude, phase, polarization, or even transverse spatial proﬁle. Femtosecond laser pulses are not likely to be shaped easily in the temporal domain, as electronic devices are not fast enough. For this reason the vast majority of the temporal pulse shaping techniques act in the spectral domain. In this section we will describe the pulse shaping technique used during this work : the Micro-Electronic Mechanical System (MEMS) mirrors.

4.4.1 MEMS mirrors

One dimensional MEMS mirrors for phase-shaping dedicated for optimal control experiments was developed in the group of GAP-Biophotonics in collaboration with EPFL/STI/IMT-NE/SAMLAB [97, 98].

(A)

(B)

FIGURE 4.9: (A) Scanning electron microscopy image of MEMS micro-mirrors. From [97]; (B) an illustration of micromirror main parts : X-shaped springs (a), triangular height adapter (b), tilt (c) and piston (d) actuators, high aspect-ratio mirror (e), and main bar (f). Taken from [98].

Figure 4.9a shows a Scanning Electron Microscope (SEM) image of an array of independent micro-mirrors capable to simultaneous piston and tilt motion, allowing phase and amplitude shaping. The array is 160 × 1000µm long and is composed of 100 mirrors with 3µm gaps. Each mirror has X- shape springs, two tilt and piston actuators, triangular height adapters used for the connection between the actuators and the springs and main bar (see ﬁgure 4.9b). The motion of the mirrors is generated by applying voltage to the piston or the tilt actuators through the wire-bond connections, allowing 60 Chapter 4. Experimental setups motions along the z-axis or a twisting movements in the y-z plane respectively.

FIGURE 4.10: White-light interferometry image of MEMS mirrors with a parabolic mask applied. Taken from [98].

When parabolic mask is applied to mirrors we observe the white light interferometry picture shown in ﬁgure 4.10. It can be seen that some of the mirrors in the array are not actuated. This might be related to short circuits or incomplete production release during the lithography manufacturing.

4.4.2 Geometries of pulse shaper

Pulse shaping can be achieved in two different ways: in transmission trough a Spatial Light Modulator (SLM) or in reflection mode. The first technique is called "Zero-Dispersion Compressor" or 4f line and the setup is shown in fig. 4.11 . The compressor consists of a pair of gratings and cylindri-

FIGURE 4.11: Illustration of a 4f pulse shaper. (I)FT: (Inverse) Fourier Transform, SLM: Spatial Light Modulator, f is the focal length. Adapted from [99] cal lenses equally spaced by a focal length ( f ). The first grating separates angularly the different spectral components of the pulse that propagate in parallel after the first cylindrical lens. In mathematical terms, the first grating and the lens operates a temporal Fourier Transform on the pulse (from the time to the frequency domain), while the second part of the set-up will carry out the Inverse Transform. In transmission mode, the light goes trough a SLM for the phase shaping. Various types of SLM exists: fixed phase and amplitude masks, liquid crystal masks, acousto-optic deflectors, movable and deformable mirrors, etc [100]. 4.4. Pulse Shaping 61

4f pulse shapers present some clear advantages in terms of high spectral resolution and high damage threshold. In addition to that, LCD-based 4f pulse shapers are able to perform phase, amplitude, and polarization shaping. They have been carefully used and characterized for the last decades, and numerous devices are commercially available. Their transparency range spans from the UV-visible to the IR, although devices capable of shaping in the UV are still rare due to their sensitivity to the refractive index variation and thus they are mostly in an experimental stage. This is the reason we prefer using a reﬂection mode for shaping Deep UV pulses.

A common geometry for the reflection mode is the folded 4f shaper displayed in fig. 4.12: the light that comes from the grating and the cylindrical lens is reflected back by the MEMS. A small deflection is introduced by

FIGURE 4.12: Geometry of folded 4f line for pulse shaper. Taken from [99]. slightly tilting the MEMS in the direction perpendicular to the diffraction plane, in order to extract the output beam after the second passage. This geometry is very convenient because the grating and the lens making the Fourier Transforms also make the inverse Fourier Transforms; therefore the shaper is self-aligned. Finally, the relation between each micro-mirror displacement of the MEMS and the spectral phase for each frequency is given by:

d z dφ = 2 · 2π (4.15) λ where dφ is the phase measured in radiants and d z is the distant of each micro-mirror from its initial position.

4.4.3 Spectral resolution

Let us consider a propagation of a Gaussian pulse in a 2f-shaper setup, with a spatial Full-Width Half-Maximum (FWHM) of the spot at the Fourier 62 Chapter 4. Experimental setups

plane win and centred at frequency ω0 (wavelength λ0).

The ﬁeld immediately after the mask M(xk) can be described as

2 −(xk−αω0) w2 EM (xk, ωk) ∼ Ein(ωk)e 0 M(xk) (4.16) where λ2f α = (4.17) 2π c d cos(θd) cos(θin) fλk w0 = (4.18) cos(θd) πwin Here α is the spatial dispersion that depends entirely on the geometry, w0(λk) is the the radius of the focused beam at the masking plane for any k frequency component, c is the speed of light, d is the grating period, f is the lens focal length, and θin and θd are the input and diffracted angles, respectively [101]. The lens and gratings’s effect of pulse’s spatial broadening is summed up in the exponential term

2 −(xk−αω0) w2 E(xk)L−G = e 0 (4.19) and thus the pulse’s FWHM for each wavelength at the MEMS plane is √ √ cos(θin) fλk ∆x = ln 2w0 = ln 2 (4.20) cos(θd) πwin

While the output pulse’s√ time duration, that is a changeable time window, 4α ln 2 is given by T = . w0 A crucial quantity is the frequency resolution, which can be written as: √ ∆x ln 2 cos(θin)d ∆ω = = ωk (4.21) α πwin

For a narrow band pulse the spatial resolution is almost constant in frequency and thus the relative error per mirror is

∆ω(ω0) Lm R = (4.22) ω0 ∆x(ω0) where Lm is the width of the micro-mirrors (∼ 160 µm). For typical values −6 for the UV pulses used in this thesis ( λ0 = 266 nm, d ∼ 1 − 0.1 10 m, −3 ∆ω(ω0) −5 a f ≈ 5 − 10cm and win ∼ 10 m) we estimate ∼ 10 and ω0 R ∼ 10−2 − 10−3 depending greatly on the focal length. Thus, the MEMS- based 2f-pulse shapers suffer from the limitations in resolution affecting all pixellated devices. Moreover, the gaps between pixels diffract the beam, 4.4. Pulse Shaping 63 inducing losses and compromising the beam spatial quality. 64 Chapter 4. Experimental setups

4.5 UV compression with a prism pair

4.5.1 Propagation of ultrashort light pulse

In order to describe light pulse propagation through an isotropic medium, a classical description of electromagnetic radiation is obtained through the Maxwell equations

∇ × E = −µ0 ∂tH

∇ × H = ∂tE ρ (4.23) ∇ · E = ∇ · H = 0

Light is a solution of all these equations in absence of electrical charges and flux of current: from the combination of the first and the second equations follows Helmholtz equation for electrostatic field

r ∇2(E) − ∂2E = 0 (4.24) c2 t

Considering a wave that propagates along z axis, its electrical and magnetic ﬁelds change in a perpendicular plane described by x and y axises. If we choose E oriented along the x axis and B along y axis we obtain : ∂2E − r ∂2E = 0 z x c2 t x

−ıωt Describing a wave Ex = E e , where E is the amplitude and ω is the frequency, the previous equation turns into

2 2 ∂z E + β (ω)E = 0 2 r(ω)ω where β2(ω) = . c2 Note that the equation for the amplitude can be written as

(∂z + ıβ(ω))(∂z − ıβ(ω))E = 0

The solution can be obtained imposing in the Fourier space the overlap between two waves

ıβ(ω0)z ∗ −ıβ(ω0)z E(ω) = A(ω − ω0, z)e + A (ω − ω0, z)e where each term satisﬁes one of the condition above; let’s take for simplicity ıβ(ω0)z ∗ the incoming wave A(ω−ω0, z)e and neglect the outgoing one A (ω− −ıβ(ω0)z ω0, z)e . 4.5. UV compression with a prism pair 65

The equation for the envelope A(ω, z) becomes

dA(ω, z) = ıA(ω, z)(β(ω) − β(ω )) (4.25) dz 0

For ω close to ω0, β(ω) approaches β(ω0) thus we can expand it in Taylor series around β(ω0). For dispersion’s effects, we have to examine the ex- pansion up to the second order.

2 dβ(ω) 1 d β(ω) 2 β(ω) ' β(ω0) + (ω − ω0) + (ω − ω0) dω 2 dω2 ω0 ω0

For simplicity

 dβ(ω)  = β1(ω0)  dω  ω0

 2  d β(ω)  = β2(ω0)  dω2 ω0 where β2 is called Group Velocity Dispersion (GVD). The equation (4.25) de- velops into

dA(ω) β (ω ) = ıAβ(¨ω¨) + β (ω )(ω − ω ) + 2 0 (ω − ω )2 − β(¨ω¨) dz ¨ 0 1 0 0 2 0 ¨ 0 on the other hand in the time domain space

dA(z, t) dA(z, t) β d2A(z, t) + β + ı 2 = 0 dz 1 dt 2 dt2

Changing the coordinates into the "time delayed" ones T = t − β1z and

Z = z, it is possible to remove the ﬁrst order (in β1) term, obtaining

2 dA(Z,T ) ıβ2 d A(Z,T ) + = 0 (4.26) dZ 2 dT 2 similarly in the Fourier space

2 dA(Z, Ω) ıβ2Ω − A(Z, Ω) = 0 (4.27) dZ 2

This equation is solvable integrating it by separation of variables and it has the solution 2 ıβ2(Ω−Ω0) Z A(Z, Ω) = A0(0, Ω)e 2 (4.28) or equivalently 2 ıϕ2(Ω−Ω0) A(Ω) = A0(Ω)e 2 (4.29) where ϕ2 is the group delay dispersion (GDD) caused by the pulse propagation in a nonlinear medium. 66 Chapter 4. Experimental setups

Pulse compression: Gaussian example

This section points out the effect of pulse compression in the Fourier space for a Gaussian pulse:

2 − T 0 2T 2 A(T ) = A0e 0 (4.30) where T0 is the initial temporal waist. Otherwise, transforming the equation in the Fourier space

2 0 Z ∞ − T A0 2T 2 ıΩT A(Ω) = AF T (A(T )) = e 0 e dT 2π −∞ 0 Z ∞ T ıΩT0 2 Ω2T 2 A0 −( √ − √ ) − 0 = e 2T0 2 dT e 2 (4.31) 2π −∞ 0 Ω2T 2 Ω2T 2 A0T0 − 0 − 0 = √ e 2 = A0e 2 2π

Substituting the last expression of (4.31) into eq. (4.29), we obtain

Ω2T 2 2 − 0 ıϕ2Ω A(Ω) = A0e 2 e 2 (4.32) Ω2 2 − (T −ıϕ2) = A0e 2 0

2 where ϕ2 is the initial chirp (dimensionally [time ]). As the chirp is additive in the frequency domain, let us consider the prism pair compression’s work like an induced phase with an opposite sign −ıϕC (Ω) with respect to ϕ2. 02 2 Going back to the time domain space and writing T0 = T0 − ı(ϕ2 − ϕC )

2 Z ∞ Ω2T 0 − 0 −ıΩT A(T ) = FT (A(Ω)) = A0 e 2 e dΩ −∞ 0 T 2 Z ∞ ΩT0 2 − −( √ +ıT ) 2T 0 2 = A0 e 2 dΩ e 0 −∞ √ T 2 2π − 0 2 2T0 = A0 0 e (4.33) T0 2 − T T0 0 2 2T0 = 0 e T0 T 2 T0 − 2 = e 2(T0 −ı(ϕ2−ϕC )) p 2 T0 − ı(ϕ2 − ϕC ) we ﬁnally obtain 2 T 2 − T 0 −ı ϕ2−ϕC 1 2 T 4+(ϕ −ϕ )2 T 4+(ϕ −ϕ )2 A(T ) = e 0 2 C 0 2 C (4.34) q (ϕ2−ϕC ) 1 − ı 2 T0 4.5. UV compression with a prism pair 67

The pulse duration depends critically on the difference ∆ϕ = ϕ2 − ϕC

p 4 2 T0 + ∆ϕ Tout = (4.35) T0 in fact, if the two contributions to the spectral phase are equals ϕ2 = ϕC the ﬁnal pulse is transform limited. 1 dvg In normal dispersion ϕ2 ∝ β2 = − 2 > 0 (where vg is the group vg dω velocity) the leading edge of the pulse is stretched and acquires a "red shift" instead of the trailing edge which is compressed and blue-shifted (see ﬁg.4.13b). Because of the group velocity decreases with frequency and increases with wavelength the leading edge travels more quickly and moves away from the center of the pulse instead of the trailing edge which travels more slowly; thus as a result of dispersion the pulse’s temporal shape is broadened.

(A)

(B) (C)

FIGURE 4.13: (A):Fourier transformed electromagnetic pulse: all the spectral components are temporally overlapped and no chirp affects the time duration of the pulse; (B): case β2 > 0 Normal dispersion: the leading edge is red shifted and the trailing edge is blue shifted. Group velocity decreases with frequency so the red shift edge travels faster than the blue one causing a pulse’s broadening; (C): case β2 < 0 Anomalous dispersion: the leading edge is blue shifted and the trailing edge is red shifted. Group velocity increases with frequency so the red shift edge travels slower than the blue one that may cause a pulse’s broadening; 68 Chapter 4. Experimental setups

If the chirp induced by the compression has a different sign −ϕC < 0, we are dealing with anomalous dispersion (ﬁg. 4.13c) and thus the pulse can be compressed. In both the cases of normal dispersion (−ϕC > 0) and anomalous region when |ϕC | > |ϕ2| the pulse broadened. Thus a typical curve for compression with respect to the compressor-induced chirp is reported in ﬁgure 4.14.

4 Anomalous dispersion Normal dispersion 3 in

/T 2 out T

0 0 2 4 6 8 Chirp φ [ps2] c

FIGURE 4.14: Example of pulse compression’s dependence on ϕC sign. in anomalous dispersion (blue line) the pulse’s waist is com- 2 pressed at ϕC = 2 ps while it keeps on broadening for ϕC > 2. On the contrary, in normal region the pulse presents no compression. 2 T0 Parameter’s value: ϕ2 = 2 ps and thus = 0.45 reached at the Tin minimum in anomalous dispersion. 4.5. UV compression with a prism pair 69

4.5.2 Pulse compression with a prism pair

Pulse compression in the ultraviolet range is not trivial with transmission techniques as the GVD in typical media is big and positive, e.g. in fused fs2 silica GVD(266 nm) = 197.53 [102]. mm Anyway, Femtoscopy lab’s setup already described in section 4.2 fore- cast a compression stage in the Actinic pump line that is achieved with a prism pair in fused silica. Figure 4.15 shows the geometry used for pulse compression: two prisms, collocated with parallel faces, diffract the beam that propagates, inducing a chirp. The prism pairs inclination is chosen such that the input and output angles (ΘB) are both near Brewster’s angle in order to minimize the reflection of perpendicular-polarized light. More- over, the mirror (M) reflects back the field, defining a 2-prisms configuration that has the advantage to be self-aligned.

FIGURE 4.15: Geometry of prism pair used for UV compression. α is the angle at the prism’s apex, β is the angle between the bluest component of the pulse and the one taken into account, θB is the Brewster’s angle used for the incident beam.

After the ﬁrst prism the beam undergoes diffraction: the faster red components travel less than the slower blue ones along a pathway

P (λ) = 2l cos(β(λ)) (4.36) 70 Chapter 4. Experimental setups where l is the distance between the two apexes AB and β is the angle between the bluest component and the frequency taken into account. To achieve a negative GDD, the prism distance l must be sufﬁciently large to compensate for the positive dispersion induced by the prism material. In addition, the spot of the beam is usually place at the apex of the prisms.

Following the argument exhibited by Fork et alii in their works [103, 104], it is possible to calculate an analytical expression for the GDD induced by the prism pair

d2ϕ d2 ωP λ3 d2P ϕ = = = (4.37) C dω2 dω2 c 2πc2 dλ2

d2P where P is the pathway reported in eq. 4.36 and is calculated in [104] dλ2

d2P d2n dn2 dn2 = 4 + (2n − n−3) l sin(β) − 8 l cos(β) (4.38) dλ2 dλ2 dλ dλ where n is the refractive index of the prism. The ﬁrst term (usually positive) depends on the product l sin(β) that can be estimated as the spot size of the beam, whereas the second addend outlines the dependence to the pathway covered by each diffracted wavelength. In fact, when β is small such that sin(β) << cos(β), this prism arrangement exhibits negative dispersion for sufﬁciently large values of l. Let us consider the following values for the parameters involved

d2n dn [s m−1] 6 · 1012 [m−1] 4,32 · 105 dλ2 dλ spot size [m] 5 · 10−3 refractive index 1,5

TABLE 4.2: Parameters values at λ = 266 nm, taken from [102]. the GDD (−ϕC ) is negative when the distance apex-apex is

l > 8, 6 cm (4.39) 71

Chapter 5

Time resolved ﬂuorescence depletion of tryptophan and tryptophan contained in proteins

Prior to conduct pump-probe measurements of fluorescence, we apply optimal control to the pulse duration (observed with cross-correlation signal) in order to test the potentiality of the setup and compress the UV field (section 5.1). Afterwards, we measure and fit the fluorescence depletion traces for HSA, IgG and Trp irradiated by unshaped UV and IR pulses (see section 5.2.1). Experiments are carried out in the linear regime, verified by the analysis of fluorescence depletion as a function of IR intensity. The same test for UV laser pulse is performed in order to check the effects of its intensity. Finally, an example of Optimal Dynamics Discrimination between IgG and HSA is reported in section 5.2.3.

5.1 Preliminary optimization: NSGA-II applied on cross- correlation signal

The cross correlation (CC) signal between UV and IR pulses is produced overlapping the two ﬁelds with a different delay time τ and it is described by the convolution function:

SCC (τ) = (SUV ∗ SIR)(τ) (5.1)

As we mentioned in section 4.3.1, the CC signal is generally used to measure the time duration of an unknown signal when the reference pulse is fully characterized. Thereby it is an important tool to estimate the pulse Chapter 5. Time resolved fluorescence depletion of tryptophan and 72 tryptophan contained in proteins duration: if the cross-correlation’s shape is Gaussian we can claim that the two pulses’s duration are equal or shorter than twice the cross correlation’s deviation σ. Thereby, in order to obtain the shortest pulse, we applied NSGA-II algorithm on CC signal optimizing its intensity (see figure 5.1). Indeed, the single target objective is the intensity at τ = 0 and it is maximised in fig. Si 5.1b. In particular the function plotted is the ratio S0 between the signal at the ith step and the initial one. The genetic algorithm almost triplicates the initial intensity, while the typical values for the optimization parameters we employed are listed in tab. 5.1. The optimization were run at a fixed delay

Population size 16 Crossover probability 0.8 Mutation probability 0.01 Distr. index crossover 10 Distr. index mutation 20

TABLE 5.1: Algorithm parameters used for the optimization

0.6 3.5

0.5 3 0.4 2.5 0.3 2 0.2 Target Objective [%] Down Conversion signal 0.1 1.5

0 1 −20 −10 0 10 20 0 10 20 30 40 50 Delay time τ (ps) step

(A) (B)

FIGURE 5.1: Optimization of CC signal (A): CC signal plotted before the optimization (blue line) and after it (black line); (B): Single target objective increment related to CC signal optimization. time between pump and probe τ = 0 and convergence is obtained after 40 steps. Figure 5.1a shows the CC signal before (blue line) and after (black line) the optimization process: we can appreciate an increment of intensity and a decrement of duration (FWHM) from 768 fs to 153 fs calculated with Gaussian fit (see fig. 5.2). 5.2. Time resolved fluorescence depletion spectroscopy 73

data data 1 1 Fit Fit

0.8 0.8

0.6 0.6

0.4 0.4

0.2 0.2 Normalized Cross Correlation Signal [%] Normalized Cross Correlation Signal [%] 0 0 −2 −1 0 1 2 −2 −1 0 1 2 Delay time τ (ps) Delay time τ (ps)

(A) (B)

FIGURE 5.2: Gaussian ﬁt of CC signals (A): After optimization CC signal; (B): Before optimization CC signal. Data treated with a 4-points smoothing.

5.2 Time resolved ﬂuorescence depletion spectroscopy

As we already discussed in section 2.1 Time-Resolved Fluorescence depletion spectroscopy is an efﬁcient technique that allows the measurement of the wavepacket’s evolution on a potential energy surface. The normalized ﬂuorescence depletion signal for the ith species are calculated as:

ON OFF Fi (τ) − Fi δi(τ) = OFF (5.2) Fi

OFF where Fi is the ﬂuorescence measured in absence of IR probe pulse ON (the undepleted signal), Fi (τ) the ﬂuorescence measured in presence of IR probe pulse (the depleted signal) which depends on τ, the time delay between IR and UV pulses.

The analytical form that describes δi(τ) rise is due to the convolution of two functions Z ∞ (D ∗ G)(τ) = D(t − t0)G(t0) dt0 (5.3) −∞ where G(t) is the gaussian shape of the interactive ﬁeld, namely "Impulse Response Function" (IRF), which is in our case the cross-correlation signal and D(t) is the sum of the exponential decays due to non-radiative relaxation processes (quenching phenomena) that depopulate the excited state [105]. 1 t2 G(t) = √ exp − (5.4) 2πσ 2σ2 X (t − µ) D(t) = A exp − Θ(t − µ) (5.5) i τ i i Chapter 5. Time resolved ﬂuorescence depletion of tryptophan and 74 tryptophan contained in proteins

Here µ is the time when the depletion starts, τi are the decay rates and Θ is the Heaviside step function deﬁned   0 for t < t0 Θ(t − t0) = (5.6)  1 for t > t0

Finally, noting that τ = t−µ, the ﬂuorescence depletion can be expressed as

Z ∞ 02 0 X Ai t (t − µ − t ) δ (τ) = (D∗G)(τ) = √ exp(− ) exp(− )Θ(t−µ−t0) dt0 i 2σ2 τ i 2πσ −∞ i

2 σ 2 X Ai τ − τ σ τ δ (τ) = 1 + erf √ i exp − (5.7) i 2 2τ τ i 2σ i i where erf is the error function.

5.2.1 Preliminary measurements

Depletion trace ﬁt

Taking advantage of the consideration written above, we applied equation 5.7 to fit the fluorescence depletion traces of HSA, IgG and TRP. A bimodal distribution of time scales has been observed for many compounds [106], and suggests us to use a bi-exponential fit. The pictures and the values of the parameters are reported in fig 5.3 and in table 5.2 respectively. The normalization is made dividing the signal for the mean value of the last 20 points. We fix the value of σ at 36 fs that is taken from the Gaussian fit of cross-correlation signal, reported in figure 5.3a. Here, the CC signal is taken optimizing its intensity, thus obtaining the shortest duration’s value.

HSA IgG Trp

A1 [%] 0.08 ± 0.01 1 0.24 ± 0.03 τ1 [ps] 4 ± 2 ∞ 1.9 ± 0.3 A2 [%] 0.97 ± 0.02 - 0.975 ± 0.006 τ2 [ps] ∞ - ∞

TABLE 5.2: Fit values for HSA, IgG and Trp.

The ﬁt’s values show a similar trend for HSA and Trp, with a competition of two regimes: a picosecond decay that is more pronounced in Trp and a slower component due, whose characteristic time is far from hundreds of picoseconds, that mainly composed the signal. The initial fast decay component of HSA τ1 = 4 ± 2 ps is in agreement with solvation dynamics [106].

Moreover, the fast decay of Trp τ1 = 1.9 ± 0.3 ps is in a good agreement 5.2. Time resolved ﬂuorescence depletion spectroscopy 75

data 1 1.2 Fit 1 0.8 0.8 0.6 0.6 0.4 0.4

0.2 0.2 Normalized Fluorescence Depletion

Normalized Cross Correlation Signal [%] 0 0 −1.5 −1 −0.5 0 0.5 1 1.5 0 5 10 Delay time τ (ps) Delay time τ (ps)

(A) (B)

1 1

0.8 0.8

0.6 0.6

0.4 0.4

0.2 0.2 Normalized Fluorescence Depletion Normalized Fluorescence Depletion 0 0 −2 0 2 4 −1 0 1 2 3 4 Delay time τ (ps) Delay time τ (ps)

FIGURE 5.3: Fluorescence depletion traces ’s ﬁt and cross- correlation signal. (A) CC signal, (B) Trp, (C) HSA, (D) IgG .

with the measurement of the lifetime of the excited state S1 [107]. The Im- munoglobulin G shows two characteristic times that are widely beyond the picosecond time scale.

Fluorescence rise

To easily compare the rise of the depletion curve at short time delays (< 1 ps) with the duration of the experimental UV-IR cross-correlations SCC (t), we convolute SCC (t) with the Heaviside function.

SRISE(t) = (SCC ∗ Θ)(τ) (5.8)

Here, the Heaviside function represents the molecular response, that we assumed to be instantaneous for the purpose of this comparison and we assume that SCC (t) has a gaussian shape

−t2 SCC (t) = A e 2σ2 (5.9)

The result of this convolution is

A t SRISE(t) = 1 + erf √ (5.10) 2 2σ Chapter 5. Time resolved ﬂuorescence depletion of tryptophan and 76 tryptophan contained in proteins

The overlap between the integrated cross-correlation SCC (t) and the normalized depletion curves in the case of the unshaped pulses is shown in ﬁg. 5.4, where σ = 36 fs .

1 1.2

1 0.8 0.8 0.6 0.6 0.4 0.4

0.2 0.2 Normalized Fluorescence Depletion Normalized Fluorescence Depletion 0 0 −2000 −1000 0 1000 2000 3000 −2000 −1000 0 1000 2000 3000 Delay time τ (fs) Delay time τ (fs)

(A) (B)

FIGURE 5.4: Normalized depletion curves measured with short cross-correlation signal. (A): HSA (red points) and IgG (blue points); (B): HSA (red points) and TRP (blue points) . The cross-correlation has been integrated and superimposed to the depletion curves with a black line.

The ﬁgures show that the rise is limited by the dynamics and not by the duration of the cross correlation signal. Thereby, we should be able to detect every ultrafast events that last hundreds of femtoseconds, as it is for HSA and TRP.

Energy dependence of HSA and IgG

In order to set the basis for the optimization, we first ran a series of parametric dependencies of the depletion curves varying both the energy of the IR probe and UV pump. We started measuring the trace with the full energy (3 µJ for the IR and 0.28 µ J) which is our reference system ( and then pro- gressively adding OD filters with neutral density to both pump and probe pulses. From the figures 5.5 and 5.6 we can see that the depletion is halve when the IR is halve. Thus, the value of the depletion depends linearly on the IR energy for both proteins. This guarantees that the ratio of the depletions will be independent from the energy. Moreover, the depletion is enhanced if the UV is halve because the probability to depopulate completely the excited state that is barely populated increased (see fig.5.5b). Similarly, the same argument is attested by the different slopes of the fit in figure 5.6c. 5.2. Time resolved fluorescence depletion spectroscopy 77

1.2 1.2 1 1

0.8 0.8

0.6 0.6

0.4 0.4 0.2 0.2 0 Normalized Fluorescence Depletion 0 Normalized Fluorescence Depletion −0.2 −5 0 5 10 15 −5 0 5 10 15 Delay time τ (ps) Delay time τ (ps)

(A) (B)

1.2

0.8

0.6

0.4 Normalized Depletion [%] 0.2

0 0 0.2 0.4 0.6 0.8 1 Normalize intensity [%]

(C)

FIGURE 5.5: Parametric dependencies on energy of HSA. (A): parametric dependencies on IR energy (with 100% UV): black trace 100% IR, blue trace 50% IR. (B): parametric dependencies on IR energy (with 50% UV): brown trace 100% IR, red trace 80% IR, orange trace 50% IR. Solid lines represent smoothing over 10 points. (C): Normalized depletion vs IR intensity [%] with 50% UV intensity ("o" points) and 100% UV intensity ("∗" points), solid lines are linear ﬁt.

1.1 1.1

1 1

0.9 0.9

0.8 0.8

0.7 0.7

0.6 0.6

0.5 0.5 Normalized Fluorescence Depletion [%] Normalized Fluorescence Depletion [%] 0.4 0.4 2 4 6 8 10 12 2 4 6 8 10 12 Delay time τ (ps) Delay time τ (ps)

(A) (B)

0.9

0.8

0.7

Normalized Depletion [%] 0.6

0.5 0 0.2 0.4 0.6 0.8 1 Normalize intensity [%]

(C)

FIGURE 5.6: Parametric dependencies on energy of IgG. (A): parametric dependencies on IR energy (with 100% UV): 100% (black trace), 75% (dark blue trace), 62% (blue trace), 48% (cyano trace) (B): parametric dependencies on UV energy (with 100% IR): 100% (black trace), 39 % (red trace), 17 % (brown trace). (C): Nor- malized depletion vs UV intensity [%] ("o" points) and IR intensity [%]("∗" points), solid lines are linear ﬁt. Chapter 5. Time resolved ﬂuorescence depletion of tryptophan and 78 tryptophan contained in proteins

5.2.2 Depletion curves acquired with unshaped pulse

As we already mentioned, the depletion traces show a common behaviour: when the IR precedes the UV pulse, the molecules are promoted to the first excited state S1 but no depletion signal can be measured. At early time delays where both pulses are overlapped, the IR probe pulse depletes S1 level promoting electrons to higher lying states Sn. The relaxation from Sn could be associated with different processes: intersystem crossing with repulsive πσ∗ states [19, 108] and conformational relaxation (for Trp see [109, 110]). Moreover, it is interesting to note that there are two mechanisms contribut- ing into fluorescence depletion signal: the first one is related to the molecular dynamics in the excited state S1 that is controllable reducing the time duration of the pulse or optimizing the shape through the genetic algorithm, and the second one is linked with the coupling efficiency of the second transition to the higher lying states which depends on the probe pulse characteristics.

A preliminary test is here conducted with the conditions outlined in this chapter: we optimized the intensity of the cross correlation signal gaining an IRF that does not limited the rise of the fluorescence depletion. More- over, we chose the intensities of the pump and probe fields in order to be in the linear regime. The measurement in figure 5.7 shows that Trp’s fluorescence (blue line) increases reaching a peak at 600 fs while HSA (red line) remains distanced. We can appreciate a signal’s variation of about 20 % at τ ' 600 fs.

1.2 1.2

1.1 1 1 0.8 0.9

0.6 0.8

0.7 0.4 0.6 0.2 0.5 Normalized Fluorescence Depletion Normalized Fluorescence Depletion 0 0.4 −4000 −2000 0 2000 4000 6000 0 1000 2000 3000 4000 Delay time τ (fs) Delay time τ (fs)

(A) (B)

FIGURE 5.7: (A) Depletion traces of Trp (blue) and HSA (red); (B): a detail. solid lines are obtained with 6-points smoothing.

A short UV pump, in fact, limited the broadening effect due to the evolution of the molecular wavepacket through the excited state S1, increasing the depletion signal more for Trp than for HSA. Figure 5.8 exhibits depletion traces for HSA (red line) and IgG (blue line). The discrepancy between the two lines at early times ( with τ ∼ 600 fs) 5.2. Time resolved ﬂuorescence depletion spectroscopy 79 reaches the 5-6% of the signal’s intensity that may depends on the normalization process.

1.1 1 1.05 0.8 1 0.6 0.95

0.4 0.9

0.2 0.85 Normalized Fluorescence Depletion Normalized Fluorescence Depletion 0 0.8 −1000 0 1000 2000 3000 4000 5000 0 500 1000 1500 Delay time τ (fs) Delay time τ (fs)

(A) (B)

FIGURE 5.8: (A): Depletion traces of HSA (red) and IgG (blue). (B): a detail. data treated with 2-points smoothing.

5.2.3 Optimal Dynamics Discrimination applied to IgG and HSA

In order to discriminate between HSA and IgG, the quantities optimized by the genetic algorithm are related with their fluorescence depletions δ(τ) previously defined in eq. 5.2, measured at a fixed time τ = 450 fs:

δIgG(τ) J1(τ) = J2(τ) = δHSA(τ) (5.11) δHSA(τ) where J1 was set to be minimized and J2 to be maximized. Therefore, an increase of the absolute value of δHSA, or a decrease of the absolute value of

δIgG were expected. As in the case mentioned in section 5.1 for the cross correlation signal, the table 5.3 underlines the value of the major parameters used for the optimization as the mutation and crossover probabilities.

Population size 16 Number of objectives 2 Crossover probability 0.8 Mutation probability 0.03 Distr. index crossover 10 Distr. index mutation 20

TABLE 5.3: Algorithm parameters used for the optimization in the discrimination experiment between HSA and IgG.

Figure 5.9 shows the behavior of the two objectives treated in eq. 5.11 at each iteration: even if J2 (magenta points ’∗’) tends to be maximized and stays above the unity and J1 is almost ﬁxed underneath the initial point, they do not show any marked trend. In fact, both groups of points present a common structure: the values oscillate noisily between 1 and 1.6 for the Chapter 5. Time resolved ﬂuorescence depletion of tryptophan and 80 tryptophan contained in proteins former and between 1 and 0.6 for the latter.

1.8

1.6

1.4

1.2

0.8

0.6

0.4 multiobjectives normalized signals

0.2

0 0 5 10 15 20 25 30 35 steps

FIGURE 5.9: Multiobjectives [%] : J2 is the one to be maximized (magenta points ’∗’) and J1 is the one to be minimized (blu points ’o’)

A detailed analysis is attained by the graphics reported in ﬁgure 5.10: 5.10a shows the pareto front at each generation plotting the two objectives under investigation J1 and J2, whereas 5.10b presents the histogram related to J2 = δHSA (magenta bars) and δIgG = J1. · J2 (cyano bars).

1.3 40 12 HSA 1.2 35 IgG 10 1.1 30 8 1 25

[%] 0.9 20 6 1 J 0.8 15 4 0.7 10 Number of occurence 2 0.6 5

0.5 0 1 1.5 2 0.5 1 1.5 2 J [%] 2 Multiobjectives normalized signals

(A) (B)

FIGURE 5.10: Graphics related to the discrimination process between HSA and IgG. (A): Pareto front at each generation. The colorbar indicates the step of the generation. (B): Histogram of δHSA (magenta bars) and δIgG (cyano bars).

The former confirms what figure 5.9 already presents: the absence of a clear trend in the evolution of the pareto fronts that aims to optimized J2 while decreasing J1. The latter emphasizes the behavior of HSA and IgG’s depletion signals: δHSA shows the bimodal noisy structure with some points above the unity, meanwhile the IgG’s depletion signal is focused around 1 with a small dispersion. This means that, while the software tries to maximized the HSA’s signal and a modest outcome is attained, the IgG’s fluorescence depletion is not influenced by the UV pulse-shaping. Moreover this 5.2. Time resolved fluorescence depletion spectroscopy 81

attests that J2 presents a false orientation to lower value and the bimodal structure can be attributed entirely to HSA. The composition of the two molecules can suggest us an explanation. As it is discussed in chapter1, Human Serum Albumin contains only one tryptophan, whose fluorescence makes up almost the whole proteins’s signal, instead of the Immunoglobulin G which has more than ten Trp molecules with different chemical environments. Thus it becomes easier to influence HSA’s depletion fluorescence, as in this case the technique deals mostly with the evolution of the generated molecular wavepacket in the Trp’s potential energy surface.

HSA and IgG’s time resolved depletion signals before (black points) and after (magenta or blue points) optimization are presented in figure 5.11a and 5.11b respectively. The confidence interval "p-value" for the null hy- pothesis that the residuals obtained with the difference δopt − δref comes from a normal distribution with mean value equal to zero, extracted in an equal time frame from -1 to 3 ps, is 0.07 for IgG and 0.03 for HSA ( p=0.05 for 95% of confidence).

Human Serum Albumin Immunoglobulin G

Reference Reference 1.2 Optimized 1.2 Optimized point of optimization point of optimization

1 1

0.8 0.8

0.6 0.6

0.4 0.4 Normalized depletion signal Normalized depletion signal

0.2 0.2

0 0 −2 −1 0 1 2 3 4 5 −2 −1 0 1 2 3 4 5 Delay time τ (ps) Delay time τ (ps) (A) (B)

FIGURE 5.11: Results from the optimization on HSA and IgG at τ = 450 fs. (A): HSA reference (black points) and optimized (magenta points) signals; solid line are 4 points smoothed data. (B): IgG reference (black points) and optimized (blue points) signals; solid line are 4 points smoothed data.

Figure 5.12 shows the result of the optimization process, gathering the optimized traces from 5.11. Although the HSA’s depletion ﬂuorescence decreases after the optimization process at τ = 450 fs, it appears barely above the IgG’s trace. In this case the p-value calculated in the time frame t ∈ (−1, 3)ps is equal to 7.5e-5 . It decreased from the value that comes out from the comparison between the reference traces, where p-value = 0.02 . Chapter 5. Time resolved ﬂuorescence depletion of tryptophan and 82 tryptophan contained in proteins

In fact, deﬁning the variables with reference to eq. 5.11

HSA IgG ∆opt(τ) = δopt (τ) − δopt (τ) (5.12) HSA IgG ∆ref(τ) = δref (τ) − δref (τ) we can appreciate in ﬁgure 5.13 a general small optimization of 0.11 %.

1.5

0.5 Normalized depletion signal

0 −2 −1 0 1 2 3 4 5 Delay time τ (ps)

FIGURE 5.12: Depletion signals of optimized HSA (magenta) and IgG (blue). Solid lines are 4 points smoothed data; the vertical red line is the optimization point set at τ = 450 fs.

∆ opt 0.3 ∆ ref

0.2

0.1

−0.1

−0.2 Residuals of normalized depletion [%]

−3 −2 −1 0 1 2 3 4 5 Time delay (ps)

FIGURE 5.13: Residuals of normalized depletion signals. Solid lines are 10 points smoothed data and the vertical red line is the optimization point at τ = 450 fs.

Anyway, the uncertainty related to this value is too big. It can be measured from the data or calculated with the propagation of uncertainty

X ∂f 2 1/2 ∆f(x , ∆x ) = ∆x = i i ∂x i i i HSA 2 IgG 21/2 (5.13) (∆δopt ) + (∆δopt ) = (0.07)2 + (0.20)21/2 = 0.21 5.2. Time resolved ﬂuorescence depletion spectroscopy 83 that is mainly due to IgG’s noise. In conclusion, the discrimination is not achieved during the optimization process. The main reason is attributed to the too low values of signal-to- noise ratio (S/N) of the variables used for optimization (see eq. 5.11) and reported in table 5.4. The quantity is deﬁned as

S/N = µ/σ (5.14) where µ is the mean value and σ is the standard deviation. In fact, Rondi supposes in her PhD thesis [111] that in order to achieve in discriminating between two molecules, a good condition is to get both S/N ratios higher than ten. Moreover, she claims that a two objectives optimization process is typically affected by an higher sensitivity to signal ﬂuctuations than single objective optimizations. Nevertheless, when it is successful, two objectives optimization gives access to a much richer ensemble of solutions without affecting, even improving, their quality.

Variables* S/N J1 4 J2 6 δHSA 6 δIgG 9

TABLE 5.4: Signal to noise ratio of the main variables involved in the optimization. *: the variables are calculated from data reported in ﬁgure 5.9 at τ = 450 fs.

One of the main factors that contributes to signal’s ﬂuctuation is the ﬁeld noise (amplitude and phase) that reduces the coherence of the dynamics. It has been addressed both theoretically and experimentally [112, 113, 114, 115, 116], and the importance of both shot-to-shot and long-term stability (typically on the timescale of a GA generation) have been highlighted [117]. Filtering out the bad laser shots, and accounting for slow laser drifts is time consuming. Therefore, setting more constraining conditions in the signal treatment discussed above is of course possible, but should be done with care not to increase in an exaggerated way the optimization time. In fact, a long time for optimization would expose the molecules to photodamage effects and thermal unfoldings that reduce the signal’s intensity compromising the outcome.

Chapter 6

Pump probe experiments on Tryptophan

In this chapter we present the experimental results obtained by applying the TA and SRS techniques detailed in chapter3 to Trp samples. TA allows the study of the ultrafast dynamics of Trp through the analysis of their transient electronic states absorption spectra (section 6.1), while SRS represents a test experiment to verify that stimulated Raman is able to extract structural information of the unphotoexcited system in view of future FSRS measurements (section 6.2).

6.1 Transient Absorption measurement of Tryptophan

6.1.1 PG FROG measurements

As we already mentioned in section 4.3.4, the PG FROG is a third order nonlinear based technique that allows us to obtain the temporal resolution of TA experiment through the measurement of the IRF. Moreover, this technique gives an indirect measure of the actinic pulse’s duration as well as provides a temporal calibration for the TA measurements. The IRF is deﬁned as the absolute value of the convolution between two pulses: a broadband white light centered at 520 nm with 70 nm FWHM

EWL (see ﬁgure 6.1) and a narrowband actinic pump (centered at 266 nm with 3.9 nm of bandwidth, 27 fs duration of transform limited pulse) EAP .

Z ∞ 2 2 −ıωt IIRF(τ, ω) = EWL(t) |EAP (τ − t)| e dt (6.1) −∞

A PG FROG measure is displayed in ﬁgure 6.2: the white light chirp is here outlined by the dispersive trace in wavelength. The duration of the response function can be determined averaging it over wavelengths, allowing an evaluation of AP’s compression that is tuned by the prism pair (see section 6.1.2). Otherwise, the image is useful to determine the dispersion induced by the white light’s chirp; and hence remove it from the transient absorption’s 86 Chapter 6. Pump probe experiments on Tryptophan

0.8

0.6

0.4

Normalized intensity [%] 0.2

0 300 400 500 600 700 Wavelength (nm)

FIGURE 6.1: WLC spectrum used for TA experiment.

−0.4 60 −0.3

−0.2 50

−0.1 40 0

0.1 30 time (ps)

0.2 20

0.3

10 0.4

0.5 350 400 450 500 550 600 650 Wavelength (nm)

FIGURE 6.2: PG FROG measurement . 6.1. Transient Absorption measurement of Tryptophan 87 measurements (see section 6.1.3).

6.1.2 Pulse compression performed by prism pair

The pulse compression performed by a prism pair is here checked with the help of the Kerr-effect-based technique explained in section 4.3.4. In order to estimate the IRF’s time duration from a PG FROG measure, we consider the following relation

σt = hσt(λ)iλ (6.2)

In fact, averaging over the wavelengths has the advantages to consider the entire process, without focusing on the temporal proﬁle at a speciﬁc frequency that may change, due to the great sensitivity of the UV pulse to GVD. As we already mentioned in section 4.5, the compression stage along the Actinic pump line is composed by a prism pair. Therefore, reminding eq. 4.38, the compression depends on the distance D between the two prisms, that a simulation suggests greater than 8, 6 cm (see eq. 4.39) considering the beam’s spots set near the apexes.

We measure the response function at distance 15, 13.5 and 12.5 cm and the local trend is studied putting pieces of glass along the AP line (see table 6.1 and ﬁgure 6.3)

D (cm) Glass (mm) Temporal width (ps) 15 0 0.20 ± 0.02 2 0.20 ± 0.03 5 0.180 ± 0.02 10 0.170 ± 0.02 13.5 0 0.104 ± 0.007 3 0.102 ± 0.007 4 0.102 ± 0.008 10 0.102 ± 0.009 10+8* 0.12 ± 0.03 12.5 0 0.14 ± 0.01 4 0.13 ± 0.01 10 0.12± 0.01

TABLE 6.1: IRF’s temporal width measured at different apex-apex distances. * 10 mm of glass and 8 mm of CaF2

As the values at D =15 cm decrease increasing the length of the glass, we understand that the maximum of compression is at lowest values of D. In fact, the piece of glass increased the GVD of the UV pulse, simulating a 88 Chapter 6. Pump probe experiments on Tryptophan

0.22 15 cm 13.5 cm 0.2 12.5 cm

0.18

(ps) 0.16 t σ 0.14

0.12

0.1

0 1 2 3 4 5 6 Acquisitions with increasing lengths of glass

FIGURE 6.3: Temporal width’s behavior in function of glass’s length. shorter distance between the two prisms. The compressions achieved at both D=12.5 cm and D=13.5 cm are good for the sample under investigation. In fact, as we would see in the next sections, the actinic pump’s compression is not crucial in pump probe experiment on Tryptophan viewpoint because the dynamics’s time scales are far from the temporal resolution achieved. Thus, we leave the setup at the last conﬁguration tested: D=12.5 with no pieces of glass along the actinic line. Moreover, since the UV is very sensitive to the GVD, higher compression can be achieved changing the ﬂow cell or cuvette’s thickness and decreasing the sample’s size. 6.1. Transient Absorption measurement of Tryptophan 89

6.1.3 Evaluation of the white light’s chirp

The PG FROG trace is also useful to estimate the wavelength dispersion due to white light’s chirp. In fact, as depicted in ﬁgure 6.4, the third order nonlinear process starts ﬁrst to shorter wavelengths and ends around 600 nm. The signal’s duration is στ = 109 ± 1 fs.

FIGURE 6.4: IRF’ measurement for evaluating wavelength dispersion. white solid line is the dispersion’s curve obtained from IRF.

Thus, the transient absorption measurement is corrected and a proper time sampling is reported in ﬁgure 6.5.

FIGURE 6.5: Transient absorption detail at early times with dispersion (A) and corrected (B). white solid line is the dispersion’s curve obtained from PG FROG measurement. 90 Chapter 6. Pump probe experiments on Tryptophan

6.1.4 Transient Absorption measurement of Tryptophan

Ultrafast transient absorption is a third order nonlinearity based pump- probe technique already treated theoretically in section 3.2. In ﬁgure 6.6 we report the TA measurement, acquired in the range between 480 and 650 nm. Since the dynamics is exponential, we chose an nonlinear optimized time sampling: dt= 0.0105 ps for t ∈ (0,20) ps and grows exponentially after 20 ps. In ﬁgures 6.7 the slices show a dominant ESA contribution that leads to a positive signal in the range considered with a peak at higher wavelengths.

FIGURE 6.6: Transient Absorption measurement of Trp.

0.07 0.2 ps 0.4 ps 0.07 450 nm 0.06 0.6 ps 480 nm 0.8 ps 0.06 510 nm 0.05 1 ps 540 nm 0.05 2 ps 570 nm 0.04 4 ps 0.04 600 nm 10 ps 630 nm

A (a.u.) 0.03 20 ps A (a.u.) 0.03 650 nm 50 ps 0.02 100 ps 0.02 0.01 200 ps 300 ps 0.01 0 400 ps 0 500 550 600 650 700 50 100 150 200 250 λ (nm) Tempi (ps)

(A) (B)

FIGURE 6.7: (A): spectra traces at different time delays; (B): time traces at different wavelengths 6.1. Transient Absorption measurement of Tryptophan 91

6.1.5 Glotaran software

The TA data analysis is conducted applying the SVD procedure described in chapter 3.2.1, exploiting the Global and Target Analysis (Glotaran) software which is a Java-based graphical user interface (GUI) for TIMP package in the R language environment for modeling multi-way spectroscopic measurements [118, 105, 119, 120]. The ﬁrst step in modeling these data typically involves looking at the singular value decomposition of the dataset. Figure 6.8a exhibits the un(t),

σn and vn(λ) described in eq. 3.37: the logarithm of the amplitude of the th n component SVn (or equivalently σn) is presented in the "Screenplot" that allows the user a correct evaluation of the number of the independent components. Secondly the temporal evolution and the spectra of the nth component are reported in the left singular vectors and right singular vector respectively.

(A)

(B)

FIGURE 6.8: Singular value decomposition (A) Top: Screeplot. Bottom: The ﬁrst left and right singular vector. (B): the ﬁrst three left and right singular vectors.

In ﬁgure 6.8b, the three most relevant components are reported. Once the 92 Chapter 6. Pump probe experiments on Tryptophan singular vectors start showing too little structure or too noisy behavior this is an indication that the number of independent component has been ex- ceeded.

After the initial pre-processing of the data is done and a dataset is created, a first attempt can be made to model and fit these data. The typical main window is reported in figure 6.9: the model that fit the data is built choosing the lowest number of parameters from the palette on the right. The "Kinetic parameters" allows you to select the number of independent components specifying the initial value for the rate constant ki, while the "IRF parameters" combined with the "Dispersion" is useful to treat the raise of the signal and the dispersion of white light at early times (see figure 6.10). The response function is hence simulated with a gaussian raise with the characteristic times obtained from the PG FROG measurements. Some of the chosen parameters should then be optimized by running the model for a few iterations and re-adjusting their starting values based on the results, while keeping others fixed to increase the convergence.

FIGURE 6.9: Screenshot of software Glotaran’s main window used for SVD analysis. (A) analysis scheme editor showing a model for target analysis, (B) the corresponding palette and (C) the property editor, (D) the project folder structure with the used datasets, models, analysis scheme and resulting analysis ﬁles and (E) the progress bar showing the current running analysis.

The sum of squared errors (SSE) and the singular value decompositions of the residuals matrix are used to verify the quality of the ﬁtted model (shown respectively in ﬁgure 6.11a and 6.11b). It goes without saying that when the SSE has not yet converged, more iterations are needed. Moreover, if there are still some relevant components that 6.1. Transient Absorption measurement of Tryptophan 93

FIGURE 6.10: The left panel shows the original data, over- laid with the ﬁtted dispersion curve, while the data are shown along with the ﬁtted traces for the time point and wavelength indicated by the cross-hair on the chart. are not taken into account, they will appear as residuals. Noisy temporal traces suggest us that four is the maximum number of relevant component.

(A)

(B)

FIGURE 6.11: SSE (A) and singular value decomposition (B) of residuals 94 Chapter 6. Pump probe experiments on Tryptophan

6.1.6 Estimation of the spectral components with Glotaran

The model deﬁned in ﬁgure 6.9 for the concentration of the nth component depends on all parameters θ such as the rate constants ki, the polynomial’s parameters for the dispersion curve (two variables in our case) and the constrains related to the raise of the signal. Thus equation 3.37 can be represented mathematically:

X Ψ(λ, t) = cn(t, θ) n(λ) (6.3) n or equivalently supposing a "parallel" decay of all the components where there is not a transfer of energy from a species to another one

X Ψ(λ, t) = cn,DAS(t, θ) DASn(λ) (6.4) n where cn,DAS(t, θ) is the exponentially decay concentration convolved with the IRF and DAS are the decay associated spectra. If we change the assumptions of the kinetic model used, we obtain a set of species associated spectra (SAS) related to a target model that is a mixture of parallel and sequential decays [119]. The target model is deﬁned 1 through the Kmatrix table (see ﬁgure 6.12): the rate constants k = en- τ tered in the matrix represent the characteristic times related to a transfer of energy from the species at the ith column to the one at the jth row. The diagonal elements are the rate constants of each species: a parallel model can be simulated with a diagonal kmatrix.

FIGURE 6.12: Kmatrix for sequential kinetic models Once you specify how many components built the spectrum (in (A)), and the rate constants you need to ﬁt the temporal dynamics (here from 1 to 5 in (B)), the starting values can be written in the table (C). Here we simulate a transfer of energy from the forth species to the third through the 5th rate constant. The J-vector helps to insert different initial concentrations. 6.1. Transient Absorption measurement of Tryptophan 95

Figure 6.13 shows the estimated output DAS components and the exponentially decay concentrations cn,DAS(t, θ); while the characteristic times are reported in table 6.2.

1 c (t) A A c (t) 0.06 B 0.8 B C c (t) C D 0.04 c (t) 0.6 D 0.02

0.4 0 Amplitude (a.u.) Normalized intensity 0.2 −0.02

0 −0.04 0 50 100 150 200 250 300 500 550 600 650 Time (ps) λ (nm)

(A) (B)

FIGURE 6.13: cn,DAS(t, θ) (A) and DAS spectral components (B) extracted with Glotaran.

τ [ps] τA 6 τB 56 τC 272 τD 108

TABLE 6.2: Characteristic times of DAS spectral components extracted with Glotaran.

We note from ﬁgure 6.13b that DAS traces are widely correlated. In fact, while the "A" component could be linked to the solvated electron peak, even if it remarks incredibly the TA spectrum, the "B" and "D" component present a specular behaviour. Thus, we try to extract the independent DAS components using the Gram-Schmidt’s orthogonalization method.

If we termed the basis {DAS1(λ), DAS2(λ), DAS3(λ), DAS4(λ)}, it is possible to build a set of orthogonal vectors {w1, w2, . . . , wn}

i−1 X DASi(λ) · wj w = DAS (λ) − w with i = 1, . . . , n (6.5) i i w · w j j=1 j j

It is important to note that the orthogonalization process is not univocal, since it depends on the order of the basis{DAS1(λ), DAS2(λ), DAS3(λ), DAS4(λ)}: all the orthogonalized set of combinations "abcd" of

{DASa(λ), DASb(λ), DASc(λ), DASd(λ)} are reported in appendixB. We can note also the importance of the ﬁrst vector DASa(λ), as it characterizes the shape of the other orthogonal vectors. Each set of components is then tested with a parallel kinetic model and the sum square of errors is plotted in ﬁgure 6.14, showing a small variation of 96 Chapter 6. Pump probe experiments on Tryptophan

5%.

2.7

2.6

2.5

2.4 SSE (a.u.)

2.3

2.2 5 10 15 20 Combinations

FIGURE 6.14: Sum of square errors related to each combination’s ﬁt

As the orthogonalization on its own does not lead to an univocal solution, a deepest analysis is conducted in the next section. 6.1. Transient Absorption measurement of Tryptophan 97

6.1.7 DAS spectra treated with superposition process

Let us suppose that our TA spectrum is composed of two components fa and fb

Ψ(λ, t) = fa(λ)ca(t) + fb(λ)cb(t) (6.6) where

fb(λ) = B · fa(λ) + (λ) (6.7)

0 Thus, we can sum and subtract B · fa(λ) in equation 6.6 leading to

0 0 Ψ(λ, t) = fa(λ) ca(t) + B cb(t) + (B − B )fa(λ) + (λ) cb(t) (6.8)

Finally, if we ﬁnd B0 = B we can extract the component (λ). Hypotesis for B0:

0 max(abs(fb)) B = sign(mean(fa)) ∗ mean(fb)) ∗ (6.9) max(abs(fa)) where an example is reported in ﬁgure 6.15

FIGURE 6.15: Example of superposition process 0 0 Red line fb, blue line B fa and the black line is = fb − B fa.

As Gram-Schmidt’s method does not alter the temporal evolution, the orthogonalization process is applied after the superposition at t = 0. The basis

{v1, v2, v3, v4} is ordered with respect to the absolute value of the norm(vi): norm(v1) > norm(v2) > norm(v3)> norm(v4), because the dominant components should rule the shape of the orthogonal vectors. The components obtained with the superposition process are reported in ﬁgures 6.16 and

6.17 (where a and b is related to the subscript of fa and fb), while ﬁgure 6.18 depicts the orthogonal basis obtained with the same order’s rule but without the superposition. 98 Chapter 6. Pump probe experiments on Tryptophan

0.08 0.06 0.07 0.05 0.06 0.04 0.05 0.03 0.04 0.03 0.02

Amplitude (a.u.) 0.02 Amplitude (a.u.) 0.01 0.01 0 0 −0.01 −0.01 500 550 600 650 500 550 600 650 λ (nm) λ (nm)

(A) a=1, b=2 (B) a=1, b=3

0.06 0.08

0.05 0.06 0.04

0.03 0.04

0.02 0.02

Amplitude (a.u.) 0.01 Amplitude (a.u.)

0 0

−0.01 −0.02 500 550 600 650 500 550 600 650 λ (nm) λ (nm)

0.05 0.05

0.04 0.04

0.03 0.03

0.02 0.02

Amplitude (a.u.) 0.01 Amplitude (a.u.) 0.01

0 0

−0.01 −0.01

500 550 600 650 500 550 600 650 λ (nm) λ (nm)

(E) a=2, b=3 (F) a=2, b=4

FIGURE 6.16: Set of orthogonalized vectors obtained with superposition process. a=1,2. 6.1. Transient Absorption measurement of Tryptophan 99

0.06 0.08

0.05 0.06

0.04 0.04 0.03 0.02 0.02

Amplitude (a.u.) 0.01 Amplitude (a.u.) 0

0 −0.02 −0.01 −0.04 500 550 600 650 500 550 600 650 λ (nm) λ (nm)

(A) a=3, b=1 (B) a=3, b=2 0.06 0.06

0.05 0.05

0.04 0.04

0.03 0.03

0.02 0.02

Amplitude (a.u.) 0.01 Amplitude (a.u.) 0.01

0 0

−0.01 −0.01

500 550 600 650 500 550 600 650 λ (nm) λ (nm)

(C) a=3, b=4 (D) a=4, b=1 0.08 0.06 0.07 0.05 0.06 0.04 0.05 0.03 0.04 0.02 0.03 Amplitude (a.u.) 0.02 Amplitude (a.u.) 0.01

0.01 0

0 −0.01

500 550 600 650 500 550 600 650 λ (nm) λ (nm)

(E) a=4, b=2 (F) a=4, b=3

FIGURE 6.17: Set of orthogonalized vectors obtained with superposition process. a=3,4. 100 Chapter 6. Pump probe experiments on Tryptophan

0.06 B C 0.05 A D 0.04

0.03

0.02

Amplitude (a.u.) 0.01

−0.01

500 550 600 650 λ (nm)

FIGURE 6.18: Set of orthogonalized vectors obtained without the superposition process, but using the norm for the vectors’s ordering .

We appreciate similar outcomes for 8/12 cases that follow the characteristic of figure 6.18. The results are all tested with a parallel kinetic model and the SSE are reported in figure 6.19: the first of the 13th values is related to the set of components presented in figure 6.18, while the others are shown in order of appearance in 6.16 and 6.17.

2.8

2.6

SSE (a.u.) 2.4

2.2

2 0 2 4 6 8 10 12 Combinations

FIGURE 6.19: SSE extracted ﬁtting the set of orthogonalized vectors obtained with the superposition process. 6.1. Transient Absorption measurement of Tryptophan 101

6.1.8 Results

All the temporal fit conducted present a systematic deviation at early times near 650 nm (see figure 6.20). A test for improving the SSE and selecting a set of components is hence taken: a new component (the fifth one) is created adding the residual of the fit evaluated at t=0.8 ps to the component (the ith one) that presents a peak near 650 nm and letting it decays in a sequential model, following the equations

Time traces TA

0.06 480 nm 500 nm 0.04 550 nm 600 nm 0.02 650 nm Intensity (a.u.) 0

0 5 10 15 20 Time (ps) −3 x 10 Residuals 5

−5 Intensity (a.u.) −10 0 5 10 15 20 Time (ps)

FIGURE 6.20: Time trace and residuals of temporal ﬁt at early times present a deviation at λ = 650nm and t=1 ps. dashed lines represent the ﬁt, ’o’ points reprensent the data.

−t τ c5(t) = A5 e 5 A −t −t (6.10) 5 τ τ ci(t) = A1(1 − e 5 )e i A1

The sum of squared errors of the ﬁt are shown in ﬁgure 6.21: the 5th component decreases the SSE’s values for all the combinations while presenting an improvement in four cases.

2.5

1.5 SSE (a.u.)

0.5

0 0 2 4 6 8 10 12 Combinations

FIGURE 6.21: SSE extracted ﬁtting the set of orthogonalized vectors obtained with the superposition process and with (magenta points) and without (black points) the ﬁfth component. 102 Chapter 6. Pump probe experiments on Tryptophan

The combinations in figure 6.16a, 6.16d, 6.17b and 6.17e exhibit an improvement of 15-20 % with respect to the others. The histogram reported in figure 6.22 shows that in presence of the fifth component 6.16a and 6.17e combinations present the maximum number of relevant independent components.

1400 without 3rd c. without 3rd and 5th c. 1200 without 4th c.

1000

800

600

Worsening % 400

200

−200 1 2 3 4 Combinations

FIGURE 6.22: Worsening of SSE [%] related to the temporal ﬁt for (1) 6.16a, (2) 6.16d, (3) 6.17b and (4) 6.17e spectral components.

In particular, in ﬁgure 6.23 we reports the red, blue and black components displayed in 6.16a (here termed "A","B","C") with the addition of the ﬁfth component named "E".

A 0.07 B 0.06 C E 0.05

0.04

0.03

Intensity (u.a.) 0.02

0.01

−0.01

480 500 520 540 560 580 600 620 640 Wavelength (nm)

FIGURE 6.23: The 5 independent components that contribute to TA spectrum: "A" is the shoulder of the P photoproduct, "B" is the Trp radical cation, "E" and "C" contribute to the same peak related to the solvated electrons.

The "B" component can be related to 560 nm centered peak of Trp cation, that was predicted by Kandori et alii [28]. Other articles found the peak at 510 and 580 nm [25, 24]. Moreover, the "E" and "C" components can be attributed to the same solvated electron peak that is estimated to be centered around 700 nm [24]: 6.1. Transient Absorption measurement of Tryptophan 103 this assignment is corroborated by the results reported in [121], where a bi- exponential model with a fast decay (∼ 2-3 ps) and a slower one (hundreds of picoseconds) is taken into account for the solvated electrons. Finally, the "A" component can be associated to the shoulder of the primary photoproduct P: as reported by Sharma et alii in [27], at early times the triplet state is not perfectly deﬁned but appear as a shoulder of the solvated electron peak in the range between 400-500 nm. The time decay is here estimated in a short time frame (0-120 ps) as 1.2 ns that is comparable with the growing time 0.9 ns of literature [27]. In fact, as ﬁgure 1.3b displayed, the positive DAD in the region 450-500 nm suggest us a decay of the transient absorption contribution.

The temporal fit’s values related to the spectral components exhibited in figure 6.23 are reported in table 6.3, while a comparison between the experimental data and the simulated spectra are reported with their residual in figures 6.24 and 6.25.

Variable Fit’s value Uncertanty τA [ps] 1260 20 τB [ps] >3000 – τC [ps] 686 2 τE [ps] 4.72 0.02 AA [a.u.] 0.962 0.001 AB [a.u.] 1.051 0.001 AC [a.u.] 0.9910 0.0004 AE [a.u.] 2.017 0.005 τBU [ps] 0.4478 0.0005

TABLE 6.3: Temporal ﬁt’s values for Trp excited states’s kinetic. τBU is the build-up’s characteristic time. 104 Chapter 6. Pump probe experiments on Tryptophan

FIGURE 6.24: Image of the TA measured (left panel), simulated (center) and the residuals of the ﬁt (right).

Time traces

0.06 480 nm 500 nm 0.04 550 nm 600 nm 0.02 650 nm Intensity (a.u.) 0

0 20 40 60 80 100 120 Time (ps) −3 x 10 Residuals 5

−5

Intensity (a.u.) −10

0 20 40 60 80 100 120 Time (ps)

FIGURE 6.25: Upper panel: Transient absorption kinetic traces of tryptophan in water at different probe wavelengths (dots) and corresponding simulated traces (lines). Lower panel: differences between experimental and model traces. 6.2. Stimulated Raman Scattering 105

6.2 Stimulated Raman Scattering

As we mentioned in section 3.3, stimulated Raman scattering (SRS) is a third order nonlinearity based technique. The spatial and temporal overlap between the Raman pulse centered at 483 nm with a 0.11 nm bandwidth (3 ps transform limited) and a white light Stokes broadband generates a nonlinear signal whose components are due to the sum of each accessible diagram. Within SRS scheme, the vibrational spectra are recorded onto the WLC ﬁeld. The Raman gain spectrum can be obtained from the heterodyne detection as the ratio of the WLC dispersed spectra with and without the presence of the RP (experimental setup reported in ﬁgure 4.4).

Since the SRS peaks appear as Raman gains or losses around the Ra- man frequency, it is important to calibrate the frequencies. The calibration is made measuring the Raman peaks of Cyclohexane (reported in ﬁgure 6.26) and comparing them with the ones present in literature, following the equation 1 1 ωp = A( − ) (6.11) λRP λp where A is a calibration factor, ωp and λp are the peaks’s frequencies and wavelengths respectively.

0.5

0.4

0.3

I (a.u.) 0.2

0.1

490 495 500 505 510 515 520 525 λ (nm)

FIGURE 6.26: Cyclohexane Raman peaks used for the calibration.

Figure 6.27 shows the SRS signal which presents an irregular baseline, due to ﬂuorescence residuals, that prevents us to see clearly the Raman lines. Thereby, a 16th order polynomial function that simulates the baseline is subtracted to the data, while noisy superstructures are removed with a Fourier ﬁlter. 106 Chapter 6. Pump probe experiments on Tryptophan

0.99

0.985 A (a.u.) 0.98

0.975 600 800 1000 1200 1400 1600 cm−1

FIGURE 6.27: SRS signal with a strong baseline dependence black line: data; blue line: 10 points smoothing, red line: polynomial ﬁt for the baseline subtraction

The Silica’s Raman peaks (blue line in ﬁgure 6.28) are subtracted from the data, outlining Trp’s lines reported in ﬁgure 6.29.

1.0035

1.003

1.0025

1.002

I (a.u.) 1.0015

1.001

1.0005

1 600 800 1000 1200 1400 1600 Raman shift cm−1

FIGURE 6.28: SRS correction from Silica’s contribution. black line: data; blue line: Silica’s Raman peaks. 6.2. Stimulated Raman Scattering 107

1.016 607 760 875 1011 1064 1127 1148 1237 1256 1276 1305 1343 1360 1434 1460 1490 1550 1623

1.014 Chen 229 nm exc. 1.012 1.01 Hirakawa 457.9 nm exc. 1.008

I (a.u.) 1.006 1.004 1.002 1 600 800 1000 1200 1400 1600 Raman shift cm−1

FIGURE 6.29: Off-resonance Stimulated Raman scattering measurement of 30 mM Tryptophan in a buffer solution. Blue line: 10 points smoothing data; black lines: data taken from [30, 35] with CW pulses at 229 and 457.9 nm respectively; vertical dashed lines indicate the Trp (cyano), benzene and pyrrole (yellow and green lines respectively) normal modes positions.

The most relevant normal modes detected in ﬁgure 6.29 are reported in table 6.4. The attribution is made comparing the peaks to table 1.1 for Tryp- tophan’s normal mode [30, 33, 32, 31], while indole, benzene and pyrrole’s normal modes are taken from [29, 34].

Attribution Literature [cm−1] Observed [cm−1] Intensity R’ φ a 607 608 vw W18 760 760 vw δ CH π a 1064 1061 w 15 or δ NH a,b 1148 1162 s 5 π a 1276 1275 vs W6 1420-1440 1434 s W3 1550-1555 1548 s

TABLE 6.4: Normal mode’s frequency detected a: from [34]; b: from [29]

As we outlined in section 1.0.2, W3 that is one of the strongest normal mode and it is visible also in proteins [36], seems to come from the degenerate stretching Raman line of benzene around 1600 cm−1 with a good component of C-C stretching of the pyrrole nucleus [35, 32].

Normal mode W6 is implicated in NH in-plane bending and the high value 108 Chapter 6. Pump probe experiments on Tryptophan reﬂects a strong NH bonding [33]. The normal modes at 1275 is attributed to the 5th pyrrole’s normal mode following the classiﬁcation of Lord’s and Rava’s articles [29, 40]. The peak at 1066 is detected by Lautie’ and is associated to the stretching CH of the pyrrole’s ring [34]. Finally, the peak around 1162 could be linked to the 15th normal mode of benzene which involves CH stretching (Wilson [38]) or with the stretching NH that is observed at 1148 [34]. In fact in the both cases, a strong CH or

NH bonding (the latter attested by W6’s value) can generate an increase of the Raman shift of this normal mode [35]. 109

Chapter 7

Conclusion and Outlook

The field of the Optimal Dynamics Discrimination emerged from the goal to detect a specific molecule or a macromolecule in a mixture, selectively en- hancing or reducing its fluorescence by driving it preferentially into other relaxation pathways. The ODD’s potentialities has been tested successfully to discriminate between small molecules like riboflavin and flavin mononucleotide, Tryptophan and Tyrosine, Ala-Tryptophan and Tryptophan. In chapter5, preliminary studies on Tryptophan, human serum albumin and immunoglobulin G reveal that their electronic energetic surface are so different that a discrimination between Trp and HSA’s or Trp and IgG’s time-resolved traces is possible with a compressed UV pulse. In addition, we tested the applicability of the ODD theory to the discrimination of the two Tryptophan-containing proteins: even if we can appreciate an influence to HSA fluorescence depletion due to the present of a shaped UV pulse, the test fails because of the too low signal-to-noise ratios. One of the main factors that contributes to signal’s fluctuation is the field noise (amplitude and phase) that is usually reduced accounting for shot-to- shot and long-term stability. On the other hand, filtering out the bad shots and averaging is time consuming and leads to expose molecules to photodamage effects that compromise the outcome. The results of this work suggest that future experiments can be conducted implementing the robustness of the acquisition sotware to the noise, while trying to cool down the samples: the complex molecular structure of the proteins experiences a thermal unfolding due to the presence of the laser beam that may deeply influences the response to the shaped UV pulse, leading to the failure of the optimization process.

Even if the ODD theory allows measuring a target objective which enables the identiﬁcation and discrimination between different compounds, there is not yet a procedure able to combine the informations obtained from the shaped pulse to the dynamics that take place in the excited state. Thus, due to Tryptophan’s role in the discrimination process, its ultrafast dynamics is the subject of study of chapter6. As we mentioned in chapter1, ultrafast TA studies on Trp are present in literature and focus mainly on the UV 110 Chapter 7. Conclusion and Outlook region, while Raman spectra are the basis for studies on the Trp’s behavior to environmental change. The transient absorption spectra acquired in the 480-650 nm spectral region (and presented in chapter 6.1), supported by a singular value decomposition analysis, disclose 4 independent components: electron’s peak that shows a bi-exponential decay with a fast characteristic time of 4.7 ps and a slower one of 690 ps; the P photoproduct’s peak appears at 480 nm with a characteristic time of 1.2 ns and the Tryptophan cation’s peak that builds up at 560 nm and decays with a long characteristic time of more than 2-3 ns. This analysis supports the conclusion outlined in Sharma and Chergui’s paper [27], while discloses the excited state of Trp cation. Moreover, the identiﬁcation of the electronic resonances involved in the Trp dynamics, combined with the preliminary SRS results, paves the way to a FSRS measurement: a Femtosecond stimulated resonance Raman experiment will be built setting the Raman pump at 425 nm or 560 nm in order to selectively isolate the ultrafast dynamics of the P photoproduct or of the Trp cation, respectively. Finally, taking advantage of the FSRS resonance enhancement, the visibil- ity of the Trp Raman modes achieved for off-resonant SRS measurements presented in this thesis, suggest the feasibility of the FSRS experiment. 111

Appendix A

Labwindows software for FROG measurements

As mentioned in chapter4, Frequency-resolved optical gating is one of the techniques that allows a full characterization of ultrashort pulses. During my stay in GAP-Biophotonics group i had the opportunity to build an interface program that interacts with the delay line motor C-663 Mer- cury Step and with a CCD camera through Labwindows software.

A typical screen is showed in figure A.1 : the ".h" files usually contain the prototype functions or the definition of shared variables, the ".c" are the code files and the ".uir" files show the interfaces, here you can physically add buttons or plots that are implemented in the ".c" files through the "call- back functions".

FIGURE A.1: Screen-shot of the Labwindows enviroment.

At each step of the delay line motor, the camera detects "average" times the spectrum. The average spectrum is then plotted in the main graph and 112 Appendix A. Labwindows software for FROG measurements all the indicators are updated during the scan.

The interface program is showed in ﬁgure A.2: the FROG’s plot is placed in rainbow scale in the center of the picture; below there is the autocorrelation signal and on the right there is the time-average signal. Two cursors allow to estimate the time duration of the pulse. Moreover, the load button allow to overwrite older graphs and compare their chirps.

FIGURE A.2: Screen-shot of the program used to measure the SD FROG signal. 113

Appendix B

Orhogonalized DAS components

0.06 A A 0.05 0.05 B C C B 0.04 0.04 D D 0.03 0.03

0.02 0.02

0.01 0.01

Amplitude (a.u.) 0 Amplitude (a.u.) 0

−0.01 −0.01

−0.02 −0.02

500 550 600 650 500 550 600 650 λ (nm) λ (nm)

(A) ABCD (B) ACBD 0.06 A A 0.06 D 0.05 B 0.05 C D B 0.04 C 0.04 0.03 0.03 0.02 0.02

0.01 0.01 Amplitude (a.u.) Amplitude (a.u.) 0 0

−0.01 −0.01

−0.02 −0.02

500 550 600 650 500 550 600 650 λ (nm) λ (nm)

A A 0.06 0.05 C D D 0.05 B 0.04 B C 0.04 0.03 0.03 0.02 0.02 0.01 0.01

Amplitude (a.u.) 0 Amplitude (a.u.) 0

−0.01 −0.01

−0.02 −0.02

500 550 600 650 500 550 600 650 λ (nm) λ (nm)

(E) ACDB (F) ADBC

FIGURE B.1 114 Appendix B. Orhogonalized DAS components

0.06 B 0.06 B A C 0.05 C 0.05 A D D 0.04 0.04

0.03 0.03

0.02 0.02

Amplitude (a.u.) 0.01 Amplitude (a.u.) 0.01

0 0

−0.01 −0.01

500 550 600 650 500 550 600 650 λ (nm) λ (nm)

(A) BACD (B) BCAD

0.06 B 0.06 B D A 0.05 C 0.05 D A C 0.04 0.04

0.03 0.03

0.02 0.02

Amplitude (a.u.) 0.01 Amplitude (a.u.) 0.01

0 0 −0.01 −0.01

500 550 600 650 500 550 600 650 λ (nm) λ (nm)

0.06 B 0.06 B C D 0.05 D 0.05 A A C 0.04 0.04

0.03 0.03

0.02 0.02

Amplitude (a.u.) 0.01 Amplitude (a.u.) 0.01 0 0 −0.01 −0.01

500 550 600 650 500 550 600 650 λ (nm) λ (nm)

(E) BCDA (F) BDAC

FIGURE B.2 Appendix B. Orhogonalized DAS components 115

0.08 C 0.08 C A B B A 0.06 D 0.06 D

0.04 0.04

0.02 0.02 Amplitude (a.u.) Amplitude (a.u.) 0 0

−0.02 −0.02

500 550 600 650 500 550 600 650 λ (nm) λ (nm)

(A) CABD (B) CBAD

0.08 C 0.08 C D A B D 0.06 A 0.06 B

0.04 0.04

0.02 0.02 Amplitude (a.u.) Amplitude (a.u.) 0 0

−0.02 −0.02

500 550 600 650 500 550 600 650 λ (nm) λ (nm)

0.08 C 0.08 C B D D A 0.06 A 0.06 B

0.04 0.04

0.02 0.02 Amplitude (a.u.) Amplitude (a.u.) 0 0

−0.02 −0.02

500 550 600 650 500 550 600 650 λ (nm) λ (nm)

(E) CBDA (F) CDAB

FIGURE B.3 116 Appendix B. Orhogonalized DAS components

0.08 D 0.08 D A B 0.07 0.07 B A C 0.06 0.06 C

0.05 0.05

0.04 0.04

0.03 0.03 Amplitude (a.u.) 0.02 Amplitude (a.u.) 0.02

0.01 0.01

0 0

−0.01 500 550 600 650 500 550 600 650 λ (nm) λ (nm)

(A) DABC (B) DBAC

0.08 D 0.08 D C A 0.07 0.07 B C 0.06 A 0.06 B

0.05 0.05

0.04 0.04

0.03 0.03

Amplitude (a.u.) 0.02 Amplitude (a.u.) 0.02

0.01 0.01

0 0

500 550 600 650 500 550 600 650 λ (nm) λ (nm)

0.08 0.08 D D B C 0.07 0.07 C A B 0.06 A 0.06

0.05 0.05

0.04 0.04

0.03 0.03 Amplitude (a.u.) Amplitude (a.u.) 0.02 0.02

0.01 0.01

0 0

−0.01 500 550 600 650 500 550 600 650 λ (nm) λ (nm)

(E) DBCA (F) DCAB

FIGURE B.4 117

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