Non-equilibrium rate theory for polariton relaxation dynamics

Area of Science:

• Quantum Optics
• Condensed Matter Physics
• Physical Chemistry

Background:

• The Holstein-Tavis-Cumming Hamiltonian models molecules coupled to optical cavities.
• Existing equilibrium Fermi's golden rule (E-FGR) has limitations in non-equilibrium scenarios.
• Accurate modeling of polariton dynamics is crucial for understanding light-matter interactions.

Purpose of the Study:

• To derive an analytic expression for non-equilibrium Fermi's golden rule (NE-FGR).
• To apply NE-FGR to study population dynamics in molecular systems coupled to optical cavities.
• To assess the accuracy of NE-FGR compared to equilibrium Fermi's golden rule (E-FGR).

Main Methods:

• Derivation of analytic NE-FGR expressions for the Holstein-Tavis-Cumming Hamiltonian.
• Implementation of NE-FGR within time-non-local and time-local quantum master equations.
• Simulation of population dynamics starting from upper and lower polariton states.

Main Results:

• NE-FGR expressions accurately capture time-dependent transition rates from polariton to dark states.
• NE-FGR reduces to E-FGR in equilibrium and collective limits.
• NE-FGR shows improved accuracy for population dynamics, particularly from the lower polariton state, highlighting non-Markovian and transient effects.

Conclusions:

• The derived NE-FGR provides a more accurate description of molecular dynamics in optical cavities.
• NE-FGR is essential for capturing non-equilibrium and short-time transient behaviors in quantum systems.
• This work advances the theoretical understanding of light-matter interactions and quantum dynamics.