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Vacuum-Enhanced Optical Nonlinearities with Organic Molecular Photoswitches

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Vacuum-Enhanced Optical Nonlinearities with Organic Molecular Photoswitches Vacuum-enhanced optical nonlinearities with organic molecular photoswitches Marina Litinskaya1, ∗ and Felipe Herrera2, 3, y 1Department of Physics & Astronomy and Department of Chemistry, University of British Columbia, Vancouver, Canada, V6T 1Z1 2Department of Physics, Universidad de Santiago de Chile, Av. Ecuador 3493, Santiago, Chile. 3Millenium Institute for Research in Optics MIRO, Chile. (Dated: April 6, 2018) We propose a cavity QED scheme to enable cross-phase modulation between two arbitrarily weak classical fields in the optical domain, using organic molecular photoswitches as a disordered intracavity nonlinear medium. We show that a long-lived vibrational Raman coherence between the cis and trans isomer states of the photoswitch can be exploited to establish the phenomenon of vacuum-induced transparency (VIT) in high-quality microcavities. We exploit this result to derive an expression for the cross-phase modulation signal and demonstrate that it is possible to surpass the detection limit imposed by absorption losses, even in the presence of strong natural energetic and orientational disorder in the medium. Possible applications of the scheme include the development of organic nanophotonic devices for all-optical switching with low photon numbers. Organic chromophores and semiconducting polymers ulation between the probe and signal fields can reach are known for having very large optical nonlinearities [1], values that are orders of magnitude larger than without with applications in lasing [2], frequency conversion [3], the cavity, exceeding the detection limit imposed by ab- nonlinear microscopy [4], and all-optical switching [5]. sorption losses. Replacing the control laser by a strongly However, the typical magnitude of the nonlinear suscep- coupled vacuum represents a clear advantage for organic tibility in organic materials is still orders of magnitude materials with low laser damage thresholds [2]. Although below those needed to enable nonlinear optical effects at EIT has been measured at low temperatures in solid state the level of single photons, an important prerequisite in systems with negligible inhomogeneous broadening [34{ photonic quantum technologies [6]. In recent years, the 37], condensed-phase VIT has yet to be demonstrated in demonstration of strong and ultrastrong coupling of or- systems with strong inhomogeneously broadening, such ganic molecules with the quantized electromagnetic vac- as organic molecular ensembles. uum in optical and infrared cavities [7{10] has stimulated The envisioned light-matter scheme is shown in Fig.1. the study of single-photon control of chemical reactiv- The ground electronic potential of the photoswitch (S0) ity [11{13], energy transport [14, 15], charge transport has two deep wells in the isomerization coordinate corre- [16, 17], and spectroscopy [18{21]. However, the manip- sponding to the cis and trans molecular isomers [25]. The ulation of polariton coherences to enhance the natural lowest vibrational state of the trans isomer, is the stable optical nonlinearities of organic materials still remains a ground state of the system 1 . The meta-stable ground largely unexplored topic [22{24]. state 2 corresponds to the lowestj i vibrational level of the j i We propose a scheme to observe cross-phase modula- cis isomer potential well. Thermal isomerization of state tion between two arbitrarily weak classical fields within a nanoscale cavity, using disordered organic molecu- lar photoswitches as the intracavity medium. Molec- (a) S (a) 2 4 ular photoswitches are commonly used in photochem- | i istry due to their ability to undergo spectrally-resolved ΓIVR (b) S1 3 photoisomerization processes [25], for applications such | i as optical information storage and controlled cataly- Γ31 Γ32 ! arXiv:1804.01816v1 [quant-ph] 5 Apr 2018 s sis [26{28]. In this work, we suggest that natural ! features in the vibrational structure of organic photo- !p c switches can be exploited to enable the observation of S0 vacuum-induced transparency (VIT [29{32]), a variation 2 1 | i of electromagnetically-induced transparency (EIT [33]) | i Cis in which a cavity vacuum{rather than a strong control Trans laser{ is used to drive an internal coherence in the ma- terial. We further demonstrate that under conditions of FIG. 1: Light-matter coupling scheme. (a) Energy level struc- VIT, the figure-of-merit for intracavity cross-phase mod- ture of molecular photoswitches. Straight arrows indicate near-resonant light-matter couplings at the cavity (!c), probe (!p) and signal (!s) frequencies. Curly arrows indicate non- radiative molecular decay processes. (b) Representative ab- sorption spectrum of the molecular photoswitch. The highest ∗Electronic address: [email protected] yElectronic address: [email protected] trans absorption peak corresponds to the transition S0 ! S2. 2 2 is strongly suppressed [25], resulting in lifetimes for statej i 2 of up to a few days at room-temperature [38, 39]. We associatej i the lowest two excited electronic potentials of the molecular photoswitch, S1 and S2 [40, 41], with the states 3 and 4 , respectively. The vibrational struc- ture of thej excitedi j potentialsi is not resolved in condensed phase, but S0 has well-defined torsional modes with fre- quencies in the range !v 160 190 meV/~ [42{44]. The level structure in Fig.1 generalizes∼ − the atomic scheme introduced in Refs. [45, 46] to molecular systems with multiple ground state isomers. Our model does not require an exact knowledge of the molecular potentials. Instead, we impose a set of VIT FIG. 2: Disorder-averaged absorptive (Imhχp i) and dis- constraints on the inhomogeneously-broadened photo- VIT persive response (Rehχp i) of molecular photoswitches as a switch absorption spectrum outside the cavity, which function of the probe detuning ∆p = !p − h!31i, for a res- we illustrate in Fig.1b. We assume that the photo- onant cavity field !c = h!32i. (a)-(b) Uniform orientational switch spectrum has: (i) a well-resolved band associ- disorder on the vacuum Rabi frequency with mean amplitude ated with the cis transition 2 3 , resonant with Ω0 = 1:2γ. The disorder-free lineshape is shown for compari- j i ! j i the cavity frequency !c;(ii) a well-resolved band asso- son (dashed line). (c)-(d) Gaussian disorder on !31 for σ = 6γ ciated with the trans transition 1 3 , near resonant and Ωc = 1:2γ. The VIT linewidth ΓVIT is graphically de- j i ! j i fined. γ is the homogeneous absorption linewidth. with the probe frequency !p > !c;(iii) a well-resolved high-frequency band associated with the cis transition 2 4 , weakly driven by a blue-detuned signal field j i ! j i at frequency !s > !p. These spectral requirements can cavity field polarization. be met using so-called orthogonal molecular photoswiches Although in general the dissipative dynamics of photoi- [47{49]. somerization involves a complex interplay between non- For a single molecular emitter, the light-matter cou- adiabatic dynamics and non-secular relaxation [51, 52], pling scheme in Fig.1 can be modelled using the Hamil- in this work we adopt a simpler Lindblad quantum mas- tonian ter equation approach to describe dissipation. We ac- count for empty cavity decay with bare photon lifetimes H^ = ! a^ya^ + ! 2 2 + ! 3 3 + ! 4 4 S c 21 j i h j 31 j i h j 41 j i h j assumed in the range 1/κ 1 100 ps, which can y −i!pt ∼ − +Ωc( 3 2 a^ + 2 3 a^ ) + Ωp( 3 1 e (1) be achieved using high-Q dielectric cavities [53]. Non- j i h j j i h j j i h j i!pt −i!st i!st + 1 3 e ) + Ωs( 4 2 e + 2 4 e ); radiative decay of the excited state S2 S1 by in- j i h j j i h j j i h j tramolecular vibrational relaxation (IVR)! is also taken where Ω and Ω are the probe and signal semiclassi- into account, with decay lifetime 1=ΓIVR 0:1 ps [43], p s ∼ cal Rabi frequencies, respectively. Ω is the cavity vac- as well as non-radiative decay S1 S0 into the trans c ! uum Rabi frequency, anda ^ is annihilation operator of and cis ground states, at rates Γ31 and Γ32, respectively. the cavity field. In a dressed-state picture, our elec- The homogeneous probe absorption linewidth is defined tronic basis must be supplemented with the cavity states as γ = Γ31+Γ32, with typical excited state lifetimes in the to read: 1~ 1; 0 , 2~ 2; 1 , 3~ 3; 0 , and range 1/γ 0:1 0:5 ps [50, 54]. Finally, we account for c c c ∼ − 4~ 4;j 1i. ≡ The j probei j i ≡ field j thusi j drivesi ≡ j thei mate- pure dephasing of the coherence between the vibrational j i ≡ j ci rial transition 1~ 3~ , the signal field the transition ground states 1 and 2 at the rate Γpd, with typical j i $ j i j i j i 2~ 4~ , and the cavity field strongly admixes the dephasing times in range 1=Γpd 1 100 ps [55{58], ∼ − nearly-degeneratej i $ j i dressed states 2~ and 3~ . depending on the molecular species, solvent and temper- j i j i We model energy disorder in the Hamiltonain H^S by ature. Having defined a master equation for the problem, defining the random transition frequencies !31 = !31 + we solve for the stationary reduced density matrix of the δ , ! = ! + δ and ! = ! + δ ,h wherei system to obtain an expression for disorder-free medium 31 32 h 32i 32 42 h 42i 42 !ji corresponds to the band center frequency and δji susceptibility at the probe frequency, denoted χp, to first ish ai random static fluctuation that gives rise to the in- order in Ωp. The derivation can be found in the Sup- homogeneous linewidths σji. Inhomogeneous linewidths plemental Material (SM).
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