The interplay between collective optical response and molecular static and dynamic disorder is studied using simple effective Hamiltonians for an ensemble of two-level emitters inside and outside a single-mode cavity. We model environmental disorder by randomly modulating the molecular transition frequencies and the coupling between the emitters and the electromagnetic field. We also consider the effects of intermolecular interactions and orientational disorder. We investigate how these effects lead to new features in the steady-state absorption (outside the cavity), transmission spectra (inside the cavity), and the yield of local molecular processes such as a unimolecular reaction. Outside the cavity, the collective behavior is manifested in the linewidth of the steady-state absorption, the emission spectrum, and the local chemical yield. Inside the cavity, however, the collective behavior primarily determines the Rabi splitting. The effects of intermolecular interactions under orientational disorder are also studied. For the most part, for all types of disorder, if we increase disorder, we find a reduction in the collective nature of the molecular response (smaller effective $N$) and therefore the Rabi splitting contraction occurs with orientational disorder. Moreover, we find that static disorder is more destructive to collective behavior than dynamic disorder.
The interplay between collective optical response and molecular static and dynamic disorder is studied using simple effective Hamiltonians for an ensemble of two-level emitters inside and outside a single-mode cavity. We model environmental disorder by randomly modulating the molecular transition frequencies and the coupling between the emitters and the electromagnetic field. We also consider the effects of intermolecular interactions and orientational disorder. We investigate how these effects lead to new features in the steady-state absorption (outside the cavity), transmission spectra (inside the cavity), and the yield of local molecular processes such as a unimolecular reaction. Outside the cavity, the collective behavior is manifested in the linewidth of the steady-state absorption, the emission spectrum, and the local chemical yield. Inside the cavity, however, the collective behavior primarily determines the Rabi splitting. The effects of intermolecular interactions under orientational disorder are also studied. For the most part, for all types of disorder, if we increase disorder, we find a reduction in the collective nature of the molecular response (smaller effective N) and therefore the Rabi splitting contraction occurs with orientational disorder. Moreover, we find that static disorder is more destructive to collective behavior than dynamic disorder.
The interplay between collective optical response and molecular static and dynamic disorder is studied using simple effective Hamiltonians for an ensemble of two-level emitters inside and outside a single-mode cavity. We model environmental disorder by randomly modulating the molecular transition frequencies and the coupling between the emitters and the electromagnetic field. We also consider effects of intermolecular interactions and orientational disorder. We investigate how these effects lead to new features in the steady state absorption (outside the cavity), transmission spectra (inside the cavity) and the yield of local molecular processes such as a unimolecular reaction. Outside the cavity, the collective behavior is manifested in the linewidth of the steady state absorption, the emission spectrum, and the local chemical yield. Inside the cavity, however, the collective behavior primarily determines the Rabi splitting. Effects of intermolecular interactions under orientational disorder are also studied. For the most part, for all types of disorder, if we increase disorder, we find a reduction in the collective nature of the molecular response (smaller effective N), and therefore, the Rabi splitting contraction occurs with orientational disorder. Moreover, we find that static disorder is more destructive to collective behavior than dynamic disorder.
We study collective effects in an inhomogeneously broadened ensemble of two-level emitters coupled to an optical cavity with narrow linewidth. Using second-order mean-field theory we find that the emitters within a few times the cavity linewidth exhibit synchronous behavior and undergo collective Rabi oscillations. Under proper conditions, the synchronized oscillations give rise to a modulated intracavity field which can excite emitters detuned by many linewidths from the cavity resonance. To study the synchronization in further detail, we simplify the model and consider two ensembles and study steady-state properties when the emitters are subjected to an incoherent drive.
We study the dependence of the vacuum Rabi splitting (VRS) on frequency disorder, vibrations, near-field effects, and density in molecular polaritonics. In the mesoscopic limit, static frequency disorder alone can already introduce a loss mechanism from polaritonic states into a dark state reservoir, which we quantitatively describe, providing an analytical scaling of the VRS with the level of disorder. Disorder additionally can split a molecular ensemble into donor-type and acceptor-type molecules and the combination of vibronic coupling, dipole-dipole interactions, and vibrational relaxation induces an incoherent FRET (F\"orster resonance energy transfer) migration of excitations within the collective molecular state. This is equivalent to a dissipative disorder and has the effect of saturating and even reducing the VRS in the mesoscopic, high-density limit. Overall, this analysis allows to quantify the crucial role played by dark states in cavity quantum electrodynamics with mesoscopic, disordered ensembles.
Harnessing strong light-matter interactions to control chemical reactions in confined electromagnetic fields offers a promising route toward deepening our understanding of chemical dynamics at the collective quantum-mechanical level, with potential implications for future chemical synthesis paradigms. Achieving this goal, however, requires an in-depth mechanistic understanding of underlying dynamical processes. As a step in this direction, we present a systematic and numerically exact quantum dynamical study of cooperative reaction dynamics inside an optical microcavity. Using a hierarchy of model systems with increasing complexity, we elucidate how cavity-modified reactivity emerges from-and is highly sensitive to-subtle structural and environmental variations. Our models consist of optically dark reactive molecules, each represented by a symmetric double well potential, coupled to infrared-active non-reactive intramolecular or solvent vibrational modes, as well as their respective dissipative environments. Our results demonstrate that cavity-induced rate modifications arise from a delicate interplay among mode hybridization in strong-coupling regimes, the dynamical balance of all participating energy exchange processes, and quantum interference between multiple fluctuation-dissipation-mediated reaction pathways enabled by collective cavity coupling. By continuously tuning a single system parameter or introducing molecular collectivity, we observe qualitatively distinct rate modification profiles as functions of the cavity frequency, including resonant rate enhancement, resonant rate suppression, hybridization-induced peak splitting, and, notably, asymmetric Fano-type line shapes in which enhancement peaks and suppression dips coexist within a narrow resonance window, highlighting the important role of quantum interference in cavity-modified chemical reactivity.
Summary form only given. The interaction strength of light and matter can be greatly influenced by altering the environment of the emitters and the electric field. In a photonic cavity the emitter-field coupling strength may become sufficiently large that the emitters and the field can exchange an excitation multiple times before it decays, giving rise to Rabi oscillations. In a passive cavity with one (several) two-level emitter(s), this manifests itself as a (collective) Rabi splitting of the transmissions spectrum [1-3], and it has recently been shown that incoherently pumped single emitters in cavities may exhibit Rabi splitting of the emission spectrum at large coupling strengths [4,5]. We present a fully analytical model describing a large collection of incoherently pumped two-level emitters in a single-mode cavity (e.g. quantum dots in a nano-cavity) and show that collective Rabi splitting of the emission spectrum can occur in these systems as well [6]. We derive a condition in terms of system parameters for the splitting to occur, and show that this is different from the condition typically associated with strong emitter-field coupling. Moreover, we show that the collective Rabi splitting decreases with increasing pump rate P, giving a transition from the strong-coupling regime to the weak-coupling regime, and possibly lasing at large P (Fig. 1(a)).
Harnessing strong light-matter interactions to control chemical reactions in confined electromagnetic fields offers a promising route toward deepening our understanding of chemical dynamics at the collective quantum-mechanical level, with potential implications for future chemical synthesis paradigms. Achieving this goal, however, requires an in-depth mechanistic understanding of the underlying dynamical processes. As a step in this direction, we present a systematic and numerically exact quantum dynamical study of cooperative reaction dynamics inside an optical microcavity. Using a hierarchy of model systems with increasing complexity, we elucidate how cavity-modified reactivity emerges from-and is highly sensitive to-subtle structural and environmental variations. Our models consist of optically dark reactive molecules, each represented by a symmetric double well potential, coupled to infrared-active non-reactive intramolecular or solvent vibrational modes, as well as their respective dissipative environments. Our results demonstrate that cavity-induced rate modifications arise from a delicate interplay among mode hybridization in strong-coupling regimes, the dynamical balance of all participating energy exchange processes, and quantum interference between multiple fluctuation-dissipation-mediated reaction pathways enabled by collective cavity coupling. By continuously tuning a single system parameter or introducing molecular collectivity, we observe qualitatively distinct rate modification profiles as functions of the cavity frequency, including resonant rate enhancement, resonant rate suppression, hybridization-induced peak splitting, and, notably, asymmetric Fano-type line shapes in which enhancement peaks and suppression dips coexist within a narrow resonance window, highlighting the important role of quantum interference in cavity-modified chemical reactivity.