[Paper Review] Tunneling and vibrational relaxation in driven multi-level systems

Michael Thorwart, Milena Grifoni+1 more|arXiv (Cornell University)|Dec 6, 1999

Quantum optics and atomic interactions3 citations

TL;DR

This paper presents a unified theoretical framework for tunneling and vibrational relaxation in driven, dissipative multi-level quantum systems using non-Markovian master equations derived via the discrete variable representation. It analytically describes dynamics valid when friction is below level-broadening or temperature is not too low, validated by real-time path integral simulations.

ABSTRACT

We investigate on a unified basis tunneling and vibrational relaxation in driven dissipative multi-stable systems described by their N lowest lying unperturbed levels. By use of the discrete variable representation} we derive a set of coupled non-Markovian master equations. We present analytical treatments that well describe the dynamics as long as the friction strength does not exceed level-broadening amongst neighbouring doublets or the temperature is not too low. This is corroborated by ``ab-initio'' real-time path integral calculations.

Motivation & Objective

• To develop a unified description of tunneling and vibrational relaxation in driven, dissipative multi-stable quantum systems.
• To model the dynamics of N lowest-lying unperturbed levels in such systems using a non-Markovian approach.
• To identify parameter regimes where analytical treatments remain valid, particularly concerning friction and temperature.
• To validate analytical results against ab-initio real-time path integral calculations.

Proposed method

• Employing the discrete variable representation (DVR) to derive coupled non-Markovian master equations for the system's density matrix.
• Formulating a set of coupled equations that describe both tunneling and energy dissipation processes simultaneously.
• Applying analytical approximations under conditions where friction is below level-broadening or temperature is sufficiently high.
• Validating the analytical results through direct ab-initio real-time path integral simulations.
• Using the non-Markovian formalism to capture memory effects in the system-bath interaction beyond Markovian assumptions.
• Focusing on the dynamics of N-level systems under external driving, with emphasis on relaxation and tunneling pathways.

Experimental results

Research questions

• RQ1 How do tunneling and vibrational relaxation coexist and influence each other in driven multi-level quantum systems?
• RQ2 What are the limits of validity for analytical treatments of non-Markovian dynamics in such systems?
• RQ3 How does the interplay between friction strength and level broadening affect the accuracy of analytical approximations?
• RQ4 Under what conditions does temperature significantly alter the dynamics, and how is this captured in the model?
• RQ5 To what extent do ab-initio path integral simulations confirm the predictions of the analytical framework?

Key findings

• The derived non-Markovian master equations successfully describe both tunneling and vibrational relaxation in driven multi-level systems.
• Analytical solutions are accurate when friction strength remains below the level-broadening of neighboring doublets.
• Analytical treatments remain valid at higher temperatures, where thermal effects dominate over quantum coherence effects.
• Ab-initio real-time path integral calculations confirm the predictions of the analytical framework across the tested parameter regimes.
• The unified approach captures memory effects in dissipation, improving upon Markovian approximations in non-equilibrium dynamics.
• The method enables consistent modeling of both coherent tunneling and incoherent relaxation in complex quantum systems with multiple levels.