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Nanophotonics

Ultrastrong coupling effects in molecular cavity QED

Jorge Calvo, David Zueco, Luis Martín-Moreno

Published Dec 27, 2019• 10 citations
Publisher

Abstract

Abstract The spectrum and energy dynamics for a system that comprises a molecule interacting with a cavity photon is analyzed, taking into account the effect of both molecular vibrations and counter‐rotating terms (CR) in the dipole Hamiltonian. The CR terms do not have a strong effect on the spectrum even for moderately large values of the exciton‐photon interaction. However, it is shown that the polariton subspace is governed by an effective Quantum‐Rabi Hamiltonian, where polaritons act as a two‐level system and the phonons play the role of cavity photons. The effect of the CR terms is amplified in the dynamics: as the vibrations reduce the effective photon‐exciton coupling, small Bloch‐Siegert energy shifts can bring the system out of resonance.

DOI
10.1515/nanoph-2019-0403

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Abstract The spectrum and energy dynamics for a system that comprises a molecule interacting with a cavity photon is analyzed, taking into account the effect of both molecular vibrations and counter‐rotating terms (CR) in the dipole Hamiltonian. The CR terms do not have a strong effect on the spectrum even for moderately large values of the exciton‐photon interaction. However, it is shown that the polariton subspace is governed by an effective Quantum‐Rabi Hamiltonian, where polaritons act as a two‐level system and the phonons play the role of cavity photons. The effect of the CR terms is amplified in the dynamics: as the vibrations reduce the effective photon‐exciton coupling, small Bloch‐Siegert energy shifts can bring the system out of resonance.
A dressed-state perturbation theory beyond the rotating waveapproxi-mation (RWA) is presented to investigate the interaction between a two level electronic transition of the polar molecules and a quantized cavity field. Analytical expressions can be explicitly derived for both the ground- and excited-state-energy spectrums and wave functions of the system, where the contribution of permanent dipole moments (PDM) and the counter-rotating wave term (CRT) can be shown separately. The validity of these explicit results is discussed by comparing with the direct numerical simulation. Comparing to CRT coupling, PDM results in the coupling of more dressed states and the energy shift proportional to the square of the normalized permanent dipole difference, and a greater Bloch-Siegert shift could be produced in giant dipole molecule cavity QED. In addition, our method could also be extended to the solution of two-level atom Rabi model Hamiltonian beyond the RWA.
A dressed-state perturbation theory beyond the rotating wave approximation (RWA) is presented to investigate the interaction between a two level electronic transition of the polar molecules and a quantized cavity field.Analytical expressions can be explicitly derived for both the ground-and excited-state-energy spectrums and wave functions of the system, where the contribution of permanent dipole moments (PDM) and the counter-rotating wave term (CRT) can be shown separately.The validity of these explicit results is discussed by comparing with the direct numerical simulation.Comparing to CRT coupling, PDM results in the coupling of more dressed states and the energy shift proportional to the square of the normalized permanent dipole difference, and a greater Bloch-Siegert shift could be produced in giant dipole molecule cavity QED.In addition, our method could also be extended to the solution of two-level atom Rabi model Hamiltonian beyond the RWA.
Molecular polaritons within the mid-infrared regime have emerged as a source for modifying and manipulating molecular and photonic properties. However, the development of new methodologies for photon generation is still a challenge in nanophotonics. We propose a molecular model based on the Holstein-quantum-Rabi Hamiltonian, which also incorporates realistic dipole moments and nonadiabatic couplings among electronic excited states, to study the ultrafast photodynamics of diatomic molecules in confined electromagnetic fields within quantized cavities. In addition to vibronic transitions due to intrinsic nonadiabatic couplings, two types of light-induced crossings emerge: one type is located at molecular nuclear geometries where the rotating wave approximation is fulfilled, and another type appears at different geometries where counter-rotating transitions may occur. We make a comprehensive study of polariton photodynamics within a time window of a few tens of femtoseconds, where dissipative mechanisms do not influence the polariton photodynamics. We stress the dramatic change of the polariton energy spectrum as a function of the Huang-Rhys factor when nonadiabatic couplings are included in the model. We conclude that both the molecular nonadiabatic couplings and, more specifically, the counter-rotating couplings in the cavity-molecule interaction play a crucial role in converting vibronic energy into photons through excited dressed states. We also show that the sign of the Huang-Rhys factor has a significant impact on this photon conversion. Our work paves the way for the development of many-photon generation powered by strong light-matter interaction, along with potential applications using alkaline earth monohydride molecules.
A dressed-state perturbation theory beyond the rotating wave approximation(RWA) is presented to investigate the interaction between a two-level electronic transition of polar molecules and a quantized cavity field. Analytical expressions can be explicitly derived for both the ground- and excited-state-energy spectrums and wave functions of the system, where the contribution of permanent dipole moments(PDM) and the counter-rotating wave term(CRT) can be shown separately.The validity of these explicit results is discussed by comparison with the direct numerical simulation. Compared to the CRT coupling, PDM results in the coupling of more dressed states and the energy shift is proportional to the square of the normalized permanent dipole difference, and a greater Bloch–Siegert shift can be produced in the giant dipole molecule cavity QED. In addition, our method can also be extended to the solution of the two-level atom Rabi model Hamiltonian beyond the RWA.更多还原
We investigate a coherently driven exciton--photon microcavity with Kerr nonlinearity in the ultrastrong-coupling regime. When the lower and upper polariton branches are well separated in energy, the full Hopfield--Rabi--Kerr model reduces to an effective single-mode description of the lower polariton. We analyze the stability of the lower-polariton steady states. We show that the resulting bistability is qualitatively similar to that in the strong-coupling regime. However, in the ultrastrong-coupling regime counter-rotating processes and the diamagnetic A2A^{2}A2 term renormalize the polariton spectrum and composition, changing the effective detuning Δ~1\tildeΔ_{1}Δ~1​ and nonlinearity ULPU_{\mathrm{LP}}ULP​ ggg-dependency beyond the strong-coupling (RWA) picture. As a result, although the semiclassical bistability criterion keeps its standard Kerr--oscillator form, the turning points and hysteresis window are shifted relative to the strong-coupling prediction.
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.