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arXiv:2006.08519 · Physical Review A

Enhanced optical nonlinearities under collective strong light-matter coupling

Raphael F. Ribeiro, Jorge A. Campos-Gonzalez-Angulo, Noel C. Giebink, Wei Xiong, Joel Y. Yuen-Zhou

Published Jun 17, 2021• 48 citations
arXivHTMLPDF

Abstract

Optical microcavities and metallic nanostructures have been shown to significantly modulate the dynamics and spectroscopic response of molecular systems. We present a study of the nonlinear optics of a model consisting of $N$ anharmonic multilevel systems (e.g., Morse oscillators) undergoing collective strong coupling with a resonant infrared microcavity. We find that, under experimentally accessible conditions, molecular systems in microcavities may have nonlinear phenomena significantly intensified due to the high quality of polariton resonances and the enhanced microcavity electromagnetic energy density relative to free space. Particularly large enhancement of multiphoton absorption happens when multipolariton states are resonant with bare molecule multiphoton transitions. In particular, our model predicts two-photon absorption cross-section enhancements by several orders of magnitude relative to free space when the Rabi splitting ${\mathrm{\ensuremath{\Omega}}}_{R}$ is approximately equal to the molecular anharmonic shift $2\mathrm{\ensuremath{\Delta}}$. Our results provide rough upper bounds to resonant nonlinear-response enhancement factors as relaxation to dark states is treated phenomenologically. Notably, ensembles of two-level systems undergoing strong coupling with a cavity (described by the Tavis-Cummings model) show no such optical nonlinearity enhancements, highlighting the rich phenomenology afforded by multilevel anharmonic systems. Similar conclusions are expected to hold for excitonic systems that share features with our model (e.g., molecular dyes with accessible ${S}_{0}\ensuremath{\rightarrow}{S}_{1}\ensuremath{\rightarrow}{S}_{2}$ transitions) and strongly interact with a UV-visible cavity.

DOI
10.1103/physreva.103.063111

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Optical microcavities and metallic nanostructures have been shown to significantly modulate the dynamics and spectroscopic response of molecular systems. We present a study of the nonlinear optics of a model consisting of NNN anharmonic multilevel systems (e.g., Morse oscillators) undergoing collective strong coupling with a resonant infrared microcavity. We find that, under experimentally accessible conditions, molecular systems in microcavities may have nonlinear phenomena significantly intensified due to the high quality of polariton resonances and the enhanced microcavity electromagnetic energy density relative to free space. Particularly large enhancement of multiphoton absorption happens when multipolariton states are resonant with bare molecule multiphoton transitions. In particular, our model predicts two-photon absorption cross-section enhancements by several orders of magnitude relative to free space when the Rabi splitting \ensuremathΩR{\mathrm{\ensuremath{\Omega}}}_{R}\ensuremathΩR​ is approximately equal to the molecular anharmonic shift 2\ensuremathΔ2\mathrm{\ensuremath{\Delta}}2\ensuremathΔ. Our results provide rough upper bounds to resonant nonlinear-response enhancement factors as relaxation to dark states is treated phenomenologically. Notably, ensembles of two-level systems undergoing strong coupling with a cavity (described by the Tavis-Cummings model) show no such optical nonlinearity enhancements, highlighting the rich phenomenology afforded by multilevel anharmonic systems. Similar conclusions are expected to hold for excitonic systems that share features with our model (e.g., molecular dyes with accessible S0\ensuremath→S1\ensuremath→S2{S}_{0}\ensuremath{\rightarrow}{S}_{1}\ensuremath{\rightarrow}{S}_{2}S0​\ensuremath→S1​\ensuremath→S2​ transitions) and strongly interact with a UV-visible cavity.
Confined electromagnetic modes strongly couple to collective excitations in ensembles of quantum emitters, producing light–matter hybrid states known as polaritons. Under such conditions, the discrete multilevel spectrum of molecular systems offers an appealing playground for exploring multiphoton processes. This work contrasts predictions from the Tavis–Cummings model in which the material is a collection of two-level systems, with the implications of considering additional energy levels with harmonic and anharmonic structures. We discuss the exact eigenspectrum, up to the second excitation manifold, of an arbitrary number N of oscillators collectively coupled to a single cavity mode in the rotating-wave approximation. Elaborating on our group-theoretic approach [New J. Phys. 23, 063081 (2021)], we simplify the brute-force diagonalization of N2 × N2 Hamiltonians to the eigendecomposition of, at most, 4 × 4 matrices for arbitrary N. We thoroughly discuss the eigenstates and the consequences of weak and strong anharmonicities. Furthermore, we find resonant conditions between bipolaritons and anharmonic transitions where two-photon absorption can be enhanced. Finally, we conclude that energy shifts in the polaritonic states induced by anharmonicities become negligible for large N. Thus, calculations with a single or few quantum emitters qualitatively fail to represent the nonlinear optical response of the collective strong coupling regime. Our work highlights the rich physics of multilevel anharmonic systems coupled to cavities absent in standard models of quantum optics. We also provide concise tabulated expressions for eigenfrequencies and transition amplitudes, which should serve as a reference for future spectroscopic studies of molecular polaritons.
Molecular complexes are held together via a variety of bonds, but they all share the common feature that their individual entities are in contact. In this work, we introduce and demonstrate the concept of a \textit{molecular optical bond}, resulting from the far-field electromagnetic coupling of several molecules via a shared mode of an optical microcavity. We discuss a collective enhancement of the vacuum Rabi splitting and study super- and sub-radiant states that arise from the cavity-mediated coupling both in the resonant and dispersive regimes. Moreover, we demonstrate a two-photon transition that emerges between the ground and excited states of the new optical compound. Our experimental data are in excellent agreement with the predictions of the Tavis-Cummings Hamiltonian and open the door to the realization of hybrid light-matter materials.
We predict that an ensemble of organic dye molecules with permanent electric dipole moments embedded in a microcavity can lead to strong optical nonlinearities at the single-photon level. The strong long-range electrostatic interaction between chromophores due to their permanent dipoles introduces the desired nonlinearity of the light-matter coupling in the microcavity. We develop a semiclassical model to obtain the absorption spectra of a weak probe field under the influence of strong exciton-photon coupling with the cavity field. Using realistic parameters, we demonstrate that a cavity field with an average photon number near unity can significantly modify the absorptive and dispersive response of the medium to a weak probe field at a different frequency. Finally, we show that the system is in the regime of cavity-induced transparency with a broad transparency window for dye dimers. We illustrate our findings using pseudoisocyanine chloride (PIC) J-aggregates in currently available optical microcavities.
We investigate the effect of a cavity on nonlinear two-photon transitions of a molecular system and we analyze how such an effect depends on the cavity quality factor, the field enhancement, and the possibility of dephasing. We find that the molecular response to strong light fields in a cavity with a variable quality factor can be understood as arising from a balance between (i) the ability of the cavity to enhance the field of an external probe and promote multiphoton transitions more easily and (ii) the fact that the strict selection rules on multiphoton transitions in a cavity support only one resonant frequency within the excitation range. Although our simulations use a classical level description of the radiation field (i.e., we solve Maxwell-Bloch or Maxwell-Liouville equations within the Ehrenfest approximation for the field-molecule interaction), based on experience with this level of approximation in the past studies of plasmonic and polaritonic systems, we believe that our results are valid over a wide range of external probing.
Light and matter can be unified under the strong coupling regime, creating superpositions of both, called dressed states or polaritons. After initially being demonstrated in bulk semiconductors and atomic systems ,strong coupling phenomena have been realized in solid state optical microcavities. They form an essential ingredient in the exciting physics spanning from many-body quantum coherence phenomena, like Bose-Einstein condensation and superfluidity, to cavity quantum electrodynamics (cQED). A widely used approach within cQED is the Jaynes-Cummings (JC) model that describes the interaction of a single fermionic two-level system with a single bosonic photon mode. For a photon number larger than one, known as quantum strong coupling (QSC), a significant anharmonicity is predicted for the ladder-like spectrum of dressed states. For optical transitions in semiconductor nanostructures, first signatures of the quantum strong coupling were recently published. In our latest report we applied advanced coherent nonlinear spectroscopy to explore a strongly coupled exciton-cavity system. Specifically, we measured and simulated its four-wave mixing (FWM) response, granting direct access to the first two rungs of the JC ladder. This paper summarizes the main results of Ref. 15 and adds FWM experiments obtained on a micropillar cavity in which a doublet of quantum dot (QD) excitons interacts with the cavity mode in the limit of weak to strong coupling.
The field of Polaritonic Chemistry studies molecules strongly coupled to the light field of optical cavities. The resulting modification of the potential energy landscape has been demonstrated to enable control over the chemical and physical properties of materials and molecular ensembles. This thesis extends the Tavis–Cummings model to describe molecules under strong light–matter coupling, incorporating static dipole moments and dipole self-energy contributions derived from the Pauli–Fierz Hamiltonian. These additional terms are shown to be essential for reproducing cavity-modified molecular dynamics and spectra. Simulations on the nuclear wavefunction propagation of MgH+ molecules demonstrate the impact of these terms, while an effective two-level system model accurately captures the behavior of large ensembles. Beyond single excitations, the thesis also explores the higher excitation manifolds of the Tavis-Cummings model, which reveals that allowing for more than a single excitation makes the reaction of the involved polaritons entropically more favorable. Open-system simulations highlight how the coherence of the system's initial state governs decay pathways and enables long-lived energy storage. Finally, a multilevel vibrational model coupled to a two-mode cavity is introduced, where a Raman scheme enables selective mixing of vibrational states. The simulation results show that continuous pumping can drive molecules into specific vibrational states while suppressing electronic excitation, both for single molecules and small ensembles. Together, these results provide new theoretical insights into the mechanisms by which optical cavities reshape molecular energy landscapes. The results suggest approaches for controlling photonic, electronic, and vibrational dynamics in strongly coupled systems, contributing to the theoretical foundation of polariton chemistry.