DOCSLIB.ORG

Durham E-Theses

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Durham E-Theses Durham E-Theses Steady-State and Ultrafast Fluorescence Depolarisation in Rigid-Rod Conjugated Polymers VAUGHAN, HELEN,LOUISE How to cite: VAUGHAN, HELEN,LOUISE (2010) Steady-State and Ultrafast Fluorescence Depolarisation in Rigid-Rod Conjugated Polymers, Durham theses, Durham University. Available at Durham E-Theses Online: http://etheses.dur.ac.uk/223/ Use policy The full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that: • a full bibliographic reference is made to the original source • a link is made to the metadata record in Durham E-Theses • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders. Please consult the full Durham E-Theses policy for further details. Academic Support Oce, Durham University, University Oce, Old Elvet, Durham DH1 3HP e-mail: [email protected] Tel: +44 0191 334 6107 http://etheses.dur.ac.uk 2 Abstract Steady-State and Ultrafast Fluorescence Depolarisation in Rigid-Rod Conjugated Polymers Helen Louise Vaughan Polarised spectroscopic techniques were used to investigate the underlying physics of steady- state and ultrafast fluorescence depolarisation in conjugated polymers. Depolarisation is due to fluorescence anisotropy: the angular difference between the absorption and emission transition dipole moments of a molecule. Polarised spectroscopy results from a polymer with a flexible backbone, poly (9,9-di(ethylhexyl)fluorene) were compared with those from two rigid backbone polymers: methyl-substituted ladder-type poly (para-phenylene) and the newly synthesised naphthylene ladder-type polymer (2,6-NLP). This revealed that there is an intrinsic anisotropy directly associated with the molecular backbone. This work is the first reported on 2,6-NLP. Fluorescence anisotropy was shown to be dependent upon the conjugation length; the tran- sition dipole moments show larger angles for short lengths, tending to a minimum as the length increases. For rigid-rod polymers, this behaviour is replicated at each vibronic posi- tion. In the flexible polymer, planarisation of the backbone elongates the excited state over more conjugated bonds, changing the angle between the transition dipole moments, whereas in rigid-rod polymers, such elongation can only be electronic. Linear dichroism results obtained for all the polymers has shown the angle between the ab- sorption transition dipole moment and the molecular backbone is large and that the emission transition dipole moment is aligned with the backbone. Off-chain to on-chain transition dipole moments arise from transitions from localised to delocalised states suggesting that the excited state in conjugated polymers is delocalised. Time-dependent measurements show that the main fluorescence depolarisation mechanism occurs in under 5 ps for both flexible and rigid polymers. The ultrafast timescale and the similarity of the two systems requires the process to be electronic in origin and not linked to a physical deformation. This work proposes that ultrafast fluorescence depolarisation is a result of the delocalisation of the electronic state as the conjugation length extends over more of the polymer. 1 Steady-State and Ultrafast Fluorescence Depolarisation in Rigid-Rod Conjugated Polymers by Helen Louise Vaughan A thesis submitted to the Faculty of Science, University of Durham for the degree of Doctor of Philosophy Department of Physics University of Durham December 2009 Overview - A comprehensive abstract Steady-State and Ultrafast Fluorescence Depolarisation in Rigid-Rod Conjugated Polymers Helen Louise Vaughan This thesis contains experimental results of the photophysical behaviour of blue emitting conjugated polymers and discusses how these can be used to further the understanding of the fundamental processes involved. In particular, an answer for the problem of ultrafast fluorescence depolarisation has been sought. Fluorescence depolarisation is the result of an angular difference between the absorption and emission transition dipole moments on a molecule. This is also referred to as the fluorescence anisotropy and the angles can be measured by polarised spectroscopies. By monitoring the change in angle and how it relates to the conjugated backbone, the intra-chain processes governing excitation energy transfer can be categorised. These processes are linked to the photoluminescence efficiency of the molecule and evaluating the processes assists in the man- ufacture of efficient light emitting devices. Two families of blue emitting conjugated polymers, both used in light emitting devices, were studied. In particular, a polymer with a flexible backbone, poly (9,9-di(ethylhexyl) fluo- rene) (PF2/6), and two with rigid backbones, ladder-type polymers poly (para-phenylene)s (MeLPPP and 2,6-NLP), were investigated via fluorescence anisotropy. This thesis contains the first photophysical results published about 2,6-NLP. The flexible polymer, PF2/6 presented a large anisotropy loss that was dependent upon the excitation wavelength except at low energy excitation wavelengths. Therefore depolarisation is thought to occur as a result of excitation migration from higher energy states to lower energy states. A smaller fluorescence anisotropy loss was observed in shorter versions of this polymer. The short oligomers are unable to support excitation energy migration and the anisotropy loss was explained as a change in dipole orientation associated with the elongation of the excited state as a result of planarisation of the backbone. It is postulated that, in longer chains, both processes take place. The rigid polymers, MeLPPP and 2,6-NLP, were investigated to further understand the effect of structural motion on fluorescence depolarisation. The fluorescence anisotropy was once again dependent upon the excitation wavelength, therefore fluorescence depolarisation is a result of an electronic process. It was observed that the angle of the absorption transition dipole moment is dependent upon the conjugation length. As the conjugation length increases the angle of absorption transition dipole tends to the same angle as the emission transition dipole moment. It was hypothesised that as the excited state elongates, it encompasses more covalent bonds and the state, and its associated transition dipole moment, becomes more aligned with the backbone. i The natural anisotropy of the three polymers was also found: 0.32 ± 0.04 for PF2/6 and 0.36 ± 0.05 for the ladder polymers. These values, which are less than the maximum for parallel dipole moments, show that there was an intrinsic anisotropy loss associated with the structure of the polymer. An angle between the two transition dipole moments also means that at least one of them lies at an angle to the molecular backbone. The molecular backbones of the three polymers were oriented in stretched polyethylene films and the degree of orientation was measured by three different methods. The methods used, x-ray diffraction; polarised Raman spectroscopy and a polarised fluorescence anisotropy tech- nique, were in good agreement and the angle of the backbones relative to the stretch orien- tation was found. Using the aligned films and the polarised absorption technique, linear dichroism, the angle between the absorption transition dipole moments and the backbone was found. The ab- sorption transition dipole was found to be off-axis for short conjugation lengths and that the angle between the backbone and the transition dipole moment decreased as the conjugation length increased. The data were used to show that the emission transition dipole, associated with longer conjugation lengths, was parallel the backbone. The off-axis transition dipole moments are thought to arise from transitions from localised states to delocalised states, sug- gesting that the absorption transition dipole moment is localised and the emission transition moment is delocalised. The polymers were also investigated by time-resolved fluorescence anisotropy which allows a study of the intrinsic anisotropy loss. It was found that the anisotropy loss evolves on the same time scale for both the flexible polymer and the rigid polymer, further confirming the presence of a similar process in both systems. The results of these experiments were limited by the detection system's resolution, but it was confirmed that the intrinsic loss must occur in under 5 ps. The ultrafast timescale for this depolarisation strongly suggests that it must be electronic in origin and not linked to a physical deformation of the polymer. From the results in this thesis, it is proposed that the ultrafast depolarisation observed in these, and other conjugated polymers, is a result of the delocalisation of the electronic state as the conjugation length extends over more of the polymer. ii Preface The work contained in this thesis was carried out in the Organic Electroactive Materials Group and with its collaborators between 2003-2008. The following publications result from the work contained within this thesis. Chapter 4 An investigation into the excitation migration in polyfluorene solutions via tem- perature dependent fluorescence anisotropy. H. L. Vaughan, F. B. Dias and A. P. Monkman Journal of Chemical Physics 122(1) 014902 (2005) Chapter 5 On the angular dependence of the optical polarisation anisotropy in ladder-type polymers. H. L. Vaughan, L.-O. P˚alsson,B. S. Nehls, A. Farrell,
Load more

Recommended publications
  • Magnetism, Angular Momentum, and Spin
    Chapter 19 Magnetism, Angular Momentum, and Spin P. J. Grandinetti Chem. 4300 P. J. Grandinetti Chapter 19: Magnetism, Angular Momentum, and Spin In 1820 Hans Christian Ørsted discovered that electric current produces a magnetic field that deflects compass needle from magnetic north, establishing first direct connection between fields of electricity and magnetism. P. J. Grandinetti Chapter 19: Magnetism, Angular Momentum, and Spin Biot-Savart Law Jean-Baptiste Biot and Félix Savart worked out that magnetic field, B⃗, produced at distance r away from section of wire of length dl carrying steady current I is 휇 I d⃗l × ⃗r dB⃗ = 0 Biot-Savart law 4휋 r3 Direction of magnetic field vector is given by “right-hand” rule: if you point thumb of your right hand along direction of current then your fingers will curl in direction of magnetic field. current P. J. Grandinetti Chapter 19: Magnetism, Angular Momentum, and Spin Microscopic Origins of Magnetism Shortly after Biot and Savart, Ampére suggested that magnetism in matter arises from a multitude of ring currents circulating at atomic and molecular scale. André-Marie Ampére 1775 - 1836 P. J. Grandinetti Chapter 19: Magnetism, Angular Momentum, and Spin Magnetic dipole moment from current loop Current flowing in flat loop of wire with area A will generate magnetic field magnetic which, at distance much larger than radius, r, appears identical to field dipole produced by point magnetic dipole with strength of radius 휇 = | ⃗휇| = I ⋅ A current Example What is magnetic dipole moment induced by e* in circular orbit of radius r with linear velocity v? * 휋 Solution: For e with linear velocity of v the time for one orbit is torbit = 2 r_v.
    [Show full text]
  • Oscillator Strength ( F ): Quantum Mechanical Model
    Oscillator strength ( f ): quantum mechanical model • For an electronic transition to occur an oscillating dipole must be induced by interaction of the molecules electric field with electromagnetic radiation. 0 • In fact both ε and k can be related to the transition dipole moment (µµµge ) • If two equal and opposite electrical charges (e) are separated by a vectorial distance (r), a dipole moment (µµµ ) of magnitude equal to er is created. µµµ = e r (e = electron charge, r = extent of charge displacement) • The magnitude of charge separation, as the electron density is redistributed in an electronically excited state, is determined by the polarizability (αααα) of the electron cloud which is defined by the transition dipole moment (µµµge ) α = µµµge / E (E = electrical force) µµµge = e r • The magnitude of the oscillator strength ( f ) for an electronic transition is proportional to the square of the transition dipole moment produced by the action of electromagnetic radiation on an electric dipole. 2 2 f ∝ µµµge = ( e r) fobs = fmax ( fe fv fs ) 2 f ∝ µµµge fobs = observed oscillator strength f ∝ ΛΏΦ ∆̅ !2#( fmax = ideal oscillator strength ( ∼1) f = orbital configuration factor ͯͥ e f ∝ ͤ͟ ̅ ͦ Γ fv = vibrational configuration factor fs = spin configuration factor • There are two major contributions to the electronic factor fe : Poor overlap: weak mixing of electronic wavefunctions, e.g. <nπ*>, due to poor spatial overlap of orbitals involved in the electronic transition, e.g. HOMO→LUMO. Symmetry forbidden: even if significant spatial overlap of orbitals exists, the resonant photon needs to induce a large transition dipole moment.
    [Show full text]
  • Spontaneous Rotational Symmetry Breaking in a Kramers Two- Level System
    Spontaneous Rotational Symmetry Breaking in a Kramers Two- Level System Mário G. Silveirinha* (1) University of Lisbon–Instituto Superior Técnico and Instituto de Telecomunicações, Avenida Rovisco Pais, 1, 1049-001 Lisboa, Portugal, [email protected] Abstract Here, I develop a model for a two-level system that respects the time-reversal symmetry of the atom Hamiltonian and the Kramers theorem. The two-level system is formed by two Kramers pairs of excited and ground states. It is shown that due to the spin-orbit interaction it is in general impossible to find a basis of atomic states for which the crossed transition dipole moment vanishes. The parametric electric polarizability of the Kramers two-level system for a definite ground-state is generically nonreciprocal. I apply the developed formalism to study Casimir-Polder forces and torques when the two-level system is placed nearby either a reciprocal or a nonreciprocal substrate. In particular, I investigate the stable equilibrium orientation of the two-level system when both the atom and the reciprocal substrate have symmetry of revolution about some axis. Surprisingly, it is found that when chiral-type dipole transitions are dominant the stable ground state is not the one in which the symmetry axes of the atom and substrate are aligned. The reason is that the rotational symmetry may be spontaneously broken by the quantum vacuum fluctuations, so that the ground state has less symmetry than the system itself. * To whom correspondence should be addressed: E-mail: [email protected] -1- I. Introduction At the microscopic level, physical systems are generically ruled by time-reversal invariant Hamiltonians [1].
    [Show full text]
  • PHYSICAL SPECTROSCOPY) MODULE No. : 5 (TRANSITION PROBABILITIES and TRANSITION DIPOLE MOMENT. OVERVIEW of SELECTION RULES
    ____________________________________________________________________________________________________ Subject Chemistry Paper No and Title 8 and Physical Spectroscopy Module No and Title 5 and Transition probabilities and transition dipole moment, Overview of selection rules Module Tag CHE_P8_M5 CHEMISTRY PAPER No. : 8 (PHYSICAL SPECTROSCOPY) MODULE No. : 5 (TRANSITION PROBABILITIES AND TRANSITION DIPOLE MOMENT. OVERVIEW OF SELECTION RULES) ____________________________________________________________________________________________________ TABLE OF CONTENTS 1. Learning Outcomes 2. Introduction 3. Transition Moment Integral 4. Overview of Selection Rules 5. Summary CHEMISTRY PAPER No. : 8 (PHYSICAL SPECTROSCOPY) MODULE No. : 5 (TRANSITION PROBABILITIES AND TRANSITION DIPOLE MOMENT. OVERVIEW OF SELECTION RULES) ____________________________________________________________________________________________________ 1. Learning Outcomes After studying this module, • you shall be able to understand the basis of selection rules in spectroscopy • Get an idea about how they are deduced. 2. Introduction The intensity of a transition is proportional to the difference in the populations of the initial and final levels, the transition probabilities given by Einstein’s coefficients of induced absorption and emission and to the energy density of the incident radiation. We now examine the Einstein’s coefficients in some detail. 3. Transition Dipole Moment Detailed algebra involving the time-dependent perturbation theory allows us to derive a theoretical expression for the Einstein coefficient of induced absorption ! 2 3 M ij 8π ! 2 B M ij = 2 = 2 ij 6ε 0" 3h (4πε 0 ) where the radiation density is expressed in units of Hz. ! The quantity M ij is known as the transition moment integral, having the same unit as dipole moment, i.e. C m. Apparently, if this quantity is zero for a particular transition, the transition probability will be zero, or, in other words, the transition is forbidden.
    [Show full text]
  • Chapter 14 Radiating Dipoles in Quantum Mechanics
    Chapter 14 Radiating Dipoles in Quantum Mechanics P. J. Grandinetti Chem. 4300 P. J. Grandinetti Chapter 14: Radiating Dipoles in Quantum Mechanics P. J. Grandinetti Chapter 14: Radiating Dipoles in Quantum Mechanics Electric dipole moment vector operator Electric dipole moment vector operator for collection of charges is ∑N ⃗̂휇 ⃗̂ = qkr k=1 Single charged quantum particle bound in some potential well, e.g., a negatively charged electron bound to a positively charged nucleus, would be [ ] ⃗̂휇 ⃗̂ ̂⃗ ̂⃗ ̂⃗ = *qer = *qe xex + yey + zez Expectation value for electric dipole moment vector in Ψ(⃗r; t/ state is ( ) ê ⃗휇 ë < ⃗; ⃗̂휇 ⃗; 휏 < ⃗; ⃗̂ ⃗; 휏 .t/ = Ê Ψ .r t/ Ψ(r t/d = Ê Ψ .r t/ *qer Ψ(r t/d V V Here, d휏 = dx dy dz P. J. Grandinetti Chapter 14: Radiating Dipoles in Quantum Mechanics Time dependence of electric dipole moment Energy Eigenstate Starting with ( ) ê ⃗휇 ë < ⃗; ⃗̂ ⃗; 휏 .t/ = Ê Ψ .r t/ *qer Ψ(r t/d V For a system in eigenstate of Hamiltonian, where wave function has the form, ` ⃗; ⃗ *iEnt_ Ψn.r t/ = n.r/e Electric dipole moment expectation value is ( ) ` ` ê ⃗휇 ë < ⃗ iEnt_ ⃗̂ ⃗ *iEnt_ 휏 .t/ = Ê n .r/e *qer n.r/e d V Time dependent exponential terms cancel out leaving us with ( ) ê ⃗휇 ë < ⃗ ⃗̂ ⃗ 휏 .t/ = Ê n .r/ *qer n.r/d No time dependence!! V No bound charged quantum particle in energy eigenstate can radiate away energy as light or at least it appears that way – Good news for Rutherford’s atomic model.
    [Show full text]
  • Decoupling Light and Matter: Permanent Dipole Moment Induced Collapse of Rabi Oscillations
    Decoupling light and matter: permanent dipole moment induced collapse of Rabi oscillations Denis G. Baranov,1, 2, ∗ Mihail I. Petrov,3 and Alexander E. Krasnok3, 4 1Department of Physics, Chalmers University of Technology, 412 96 Gothenburg, Sweden 2Moscow Institute of Physics and Technology, 9 Institutskiy per., Dolgoprudny 141700, Russia 3ITMO University, St. Petersburg 197101, Russia 4Department of Electrical and Computer Engineering, The University of Texas at Austin, Austin, Texas 78712, USA (Dated: June 29, 2018) Rabi oscillations is a key phenomenon among the variety of quantum optical effects that manifests itself in the periodic oscillations of a two-level system between the ground and excited states when interacting with electromagnetic field. Commonly, the rate of these oscillations scales proportionally with the magnitude of the electric field probed by the two-level system. Here, we investigate the interaction of light with a two-level quantum emitter possessing permanent dipole moments. The semi-classical approach to this problem predicts slowing down and even full suppression of Rabi oscillations due to asymmetry in diagonal components of the dipole moment operator of the two- level system. We consider behavior of the system in the fully quantized picture and establish the analytical condition of Rabi oscillations collapse. These results for the first time emphasize the behavior of two-level systems with permanent dipole moments in the few photon regime, and suggest observation of novel quantum optical effects. I. INTRODUCTION ment modifies multi-photon absorption rates. Emission spectrum features of quantum systems possessing perma- Theory of a two-level system (TLS) interacting with nent dipole moments were studied in Refs.
    [Show full text]
  • Lecture 13 Page 1 Note That Polarizability of Classical Conductive Sphere of Radius a Is
    Lectures 13 - 14 Hydrogen atom in electric field. Quadratic Stark effect. Atomic polarizability. Emission and Absorption of Electromagnetic Radiation by Atoms Transition probabilities and selection rules. Lifetimes of atomic states. Hydrogen atom in electric field. Quadratic Stark effect. We consider a hydrogen atom in the ground state in the uniform electric field The Hamiltonian of the system is [using CGS units] orienting the quantization axis (z) along the electric field. Since d is odd operator under the parity transformation r → -r even function product Therefore, need second-order correction to the energy We will use the approximation Note that we included 100 term to make use of the completeness relation since it is zero anyway. Lecture 13 Page 1 Note that polarizability of classical conductive sphere of radius a is Lecture 13 Page 2 Emission and Absorption of Electromagnetic Radiation by Atoms (follows W. Demtr öder, chapter 7) During the past few lectures, we have discussed stationary atomic states that are described by a stationary wave function and by the corresponding quantum numbers. We also discussed the atoms can undergo transitions between different states with energies E i and E , when a photon with energy k (1) is emitted or absorbed. We know from the experiments, however, that the absorption or emission spectrum of an atom does not contain all possible frequencies ω according to the formula above . Therefore, t here must be “selection rules” that select the possible radiative transitions from all combinations of E i and E k. These selection rules strongly affect the lifetimes of the atomic excited states.
    [Show full text]
  • Chapter 15 the Tools of Time-Dependent Perturbation Theory Can Be Applied to Transitions Among Electronic, Vibrational, and Rotational States of Molecules
    Chapter 15 The tools of time-dependent perturbation theory can be applied to transitions among electronic, vibrational, and rotational states of molecules. I. Rotational Transitions Within the approximation that the electronic, vibrational, and rotational states of a molecule can be treated as independent, the total molecular wavefunction of the "initial" state is a product F i = y ei c vi f ri of an electronic function y ei, a vibrational function c vi, and a rotational function f ri. A similar product expression holds for the "final" wavefunction F f. In microwave spectroscopy, the energy of the radiation lies in the range of fractions of a cm-1 through several cm-1; such energies are adequate to excite rotational motions of molecules but are not high enough to excite any but the weakest vibrations (e.g., those of weakly bound Van der Waals complexes). In rotational transitions, the electronic and vibrational states are thus left unchanged by the excitation process; hence y ei = y ef and c vi = c vf. Applying the first-order electric dipole transition rate expressions Ri,f = 2 p g(wf,i) |a f,i|2 obtained in Chapter 14 to this case requires that the E1 approximation Ri,f = (2p/h2) g(wf,i) | E0 · <F f | m | F i> |2 be examined in further detail. Specifically, the electric dipole matrix elements <F f | m | F i> with m = S j e rj + S a Za e Ra must be analyzed for F i and F f being of the product form shown above. The integrations over the electronic coordinates contained in <F f | m | F i>, as well as the integrations over vibrational degrees of freedom yield "expectation values" of the electric dipole moment operator because the electronic and vibrational components of F i and F f are identical: <y ei | m | y ei> = m (R) is the dipole moment of the initial electronic state (which is a function of the internal geometrical degrees of freedom of the molecule, denoted R); and <c vi | m(R) | c vi> = mave is the vibrationally averaged dipole moment for the particular vibrational state labeled c vi.
    [Show full text]
  • Electric Dipole Moment and Therefore Can Be Excited by Either a Photon Or an Electron
    Chem 253, UC, Berkeley Fermi Surface E 2k 2 F E(k) x 2m K KF a2 r 2 2 r 0.4a Chem 253, UC, Berkeley With periodic boundary conditions: ik L eikx Lx e y y eikz Lz 1 2nx kx Lx 2n k y 2 2 y 2D k space: Ly Area per k point: L L 2nz x y kz Lz 2 2 2 8 3 3D k space: Area per k point: Lx Ly Lz V V A region of k space of volume will contain: allowed 8 3 8 3 k values. ( ) V 1 Chem 253, UC, Berkeley For divalent elements: free –electron model a2 r 2 r 0.56a Chem 253, UC, Berkeley 2 Chem 253, UC, Berkeley For nearly free electron: 1. Interaction of electron with periodic potential opens gap at zone boundary 2. Almost always Fermi surface will intersect zone Boundaries perpendicularly. 3. The total volume enclosed by the Fermi surface depends only on total electron concentration, not on interaction Chem 253, UC, Berkeley Alkali Metal Na, Cs: spherical Fermi surface a2 r 2 2 r 0.4a Alk. Earth metal: Be, Mg:: nearly spherical Fermi surface a2 r 2 r 0.56a 2D case 3 Chem 253, UC, Berkeley Chem 253, UC, Berkeley 4 Chem 253, UC, Berkeley Chem 253, UC, Berkeley 5 Chem 253, UC, Berkeley Chem 253, UC, Berkeley 6 Chem 253, UC, Berkeley Chem 253, UC, Berkeley 7 Chem 253, UC, Berkeley Brillouin Zone of Diamond and Zincblende Structure (FCC Lattice) Sign Convention Zone Edge or surface : Latin alphabets Interior of Zone: Greek alphabets Center of Zone or origin: Chem 253, UC, Berkeley Band Structure of 3D Free Electron in FCC in reduced zone scheme Notation: <=>[100] direction X<=>BZ edge along [100] direction <=>[111] direction E(k)=( 2/2m)
    [Show full text]
  • Ultracold Rare-Earth Magnetic Atoms with an Electric Dipole Moment
    Ultracold rare-earth magnetic atoms with an electric dipole moment Maxence Lepers1,2, Hui Li1, Jean-Fran¸cois Wyart1,3, Goulven Qu´em´ener1 and Olivier Dulieu1 1Laboratoire Aim´eCotton, CNRS, Universit´eParis-Sud, ENS Paris-Saclay, Universit´eParis-Saclay, 91405 Orsay, France 2Laboratoire Interdisciplinaire Carnot de Bourgogne, CNRS, Universit´ede Bourgogne Franche-Comt´e, 21078 Dijon, France∗ and 3LERMA, Observatoire de Paris-Meudon, PSL Research University, Sorbonne Universit´es, UPMC Univ. Paris 6, CNRS UMR8112, 92195 Meudon, France (Dated: March 13, 2018) We propose a new method to produce an electric and magnetic dipolar gas of ultracold dysprosium − atoms. The pair of nearly degenerate energy levels of opposite parity, at 17513.33 cm 1 with − electronic angular momentum J = 10, and at 17514.50 cm 1 with J = 9, can be mixed with an external electric field, thus inducing an electric dipole moment in the laboratory frame. For field amplitudes relevant to current-day experiments, we predict a magnetic dipole moment up to 13 Bohr magnetons, and an electric dipole moment up to 0.22 Debye, which is similar to the values obtained for alkali-metal diatomics. When a magnetic field is present, we show that the electric dipole moment is strongly dependent on the angle between the fields. The lifetime of the field- mixed levels is found in the millisecond range, thus allowing for suitable experimental detection and manipulation. Introduction. In a classical neutral charge distribu- with an electric and a magnetic dipole moment, which up tion, a dipole moment appears with a separation be- to now consist of paramagnetic polar diatomics [23–32].
    [Show full text]
  • CHAPTER 12 Molecular Spectroscopy 1: Rotational and Vibrational Spectra
    CHAPTER 12 Molecular Spectroscopy 1: Rotational and Vibrational Spectra I. General Features of Spectroscopy. A. Overview. 1. Bohr frequency rule: hc Ephoton = hν = = hcν˜ = Eupper −Elower λ 1 Also remember ν˜ = (usually in cm-1) λ € 2. Types of spectroscopy (three broad types): -emission € -absorption -scattering Rayleigh Stokes Anti-Stokes CHAPTER 12 1 3. The electromagnetic spectrum: Region λ Processes gamma <10 pm nuclear state changes x-ray 10 pm – 10 nm inner shell e- transition UV 10 nm – 400 nm electronic trans in valence shell VIS 400 – 750 nm electronic trans in valence shell IR 750 nm – 1 mm Vibrational state changes microwave 1 mm – 10 cm Rotational state changes radio 10 cm – 10 km NMR - spin state changes 4. Classical picture of light absorption – since light is oscillating electric and magnetic field, interaction with matter depends on interaction with fluctuating dipole moments, either permanent or temporary. Discuss vibrational, rotational, electronic 5. Quantum picture: Einstein identified three contributions to transitions between states: a. stimulated absorption b. stimulated emission c. spontaneous emission Stimulated absorption transition probability w is proportional to the energy density ρ of radiation through a proportionality constant B w=B ρ The total rate of absorption W depends on how many molecules N in the light path, so: W = w N = N B ρ CHAPTER 12 2 Now what is B? Consider plane-polarized light (along z-axis), can cause transition if the Q.M. transition dipole moment is non-zero. µ = ψ *µˆ ψdτ ij ∫ j z i Where µˆ z = z-component of electric dipole operator of atom or molecule Example: H-atom € € - e r + µˆ z = −er Coefficient of absorption B (intrinsic ability to absorb light) 2 µij B = 6ε 2€ Einstein B-coefficient of stimulated absorption o if 0, transition i j is allowed µ ij ≠ → µ = 0 forbidden € ij € 6.
    [Show full text]
  • Coherent Optical Spectroscopy of a Single Semi- Conductor Quantum Dot
    COHERENT OPTICAL SPECTROSCOPY OF A SINGLE SEMI- CONDUCTOR QUANTUM DOT by Xiaodong Xu A dissertation submitted in partial ful¯llment of the requirements for the degree of Doctor of Philosophy (Physics) in The University of Michigan 2008 Doctoral Commitee: Professor Duncan G. Steel, Chair Professor Roberto D. Merlin Professor Theodore B. Norris Professor Georg A. Raithel Associate Professor Luming Duan Xiaodong Xu °c 2008 All Rights Reserved ACKNOWLEDGEMENTS 6 years ago when I joined the group, Elaine gave me a lab tour. I saw Jun and Yanwen sitting in the dark and taking data. At that time there was a big chiller in the time domain lab and making huge noise. Frankly, I was a bit scared since I had never been in a real lab before graduate school. I was wondering whether I could do well in such a lab as an experimental physicist. Now it is 6 years later and I am so happy to say that I made it. During the entire graduate school, there are so many people I would like to thank. The ¯rst and the most important person I would like to thank is my advisor Professor Duncan Steel. I am so lucky to have Duncan as my advisor. He is such a smart scientist with great personality. His working ethics and conscientious attitudes inspired me a lot in research. He always tries to create the best education and research support for me. One of the greatest things is that he tried to develop my weakness, exploit my strength, and carefully shape me to be a good physicist.
    [Show full text]