[Paper Review] Asymptotic state of many-body open quantum systems under time-periodic modulations

M. Hartmann, Dario Poletti+3 more|arXiv (Cornell University)|Jun 13, 2016

Spectroscopy and Quantum Chemical Studies3 citations

TL;DR

This paper introduces the dissipative Floquet map to describe the asymptotic non-equilibrium state of periodically driven many-body quantum systems coupled to an environment. It shows that the system evolves toward a time-periodic density operator, with interactions inducing bifurcation transitions that alter the quantum state's structure, offering a framework to identify stroboscopic effective generators for time-dependent dynamics.

ABSTRACT

The asymptotic state of a periodically driven many-body quantum system in contact with an environment is investigated. The combined action of the driving and the environment steers the system towards a state being characterized by a time-periodic density operator. To compute this asymptotic non-equilibrium state at stroboscopic instants of time, we introduce the dissipative Floquet map, find the stroboscopic density operator as its eigen-operator and demonstrate how particle interactions affect properties of the density operator. We illustrate the idea with a periodically rocked open Bose-Hubbard dimer and discuss the relations between the interaction-induced bifurcation transitions in a mean-field dynamics and changes in the characteristics of the quantum many-body state. We argue that Floquet maps can provide insight into the system relaxation towards its asymptotic state and may help to identify the stroboscopic time-independent generator mimicking the action of the original time-dependent one.

Motivation & Objective

• To understand the long-time behavior of periodically driven open quantum systems with particle interactions.
• To identify the asymptotic state as a time-periodic density operator under combined driving and environmental effects.
• To develop a stroboscopic framework—via the dissipative Floquet map—for analyzing relaxation dynamics in non-equilibrium quantum systems.
• To explore how interactions modify the structure and bifurcation transitions in the asymptotic quantum state.

Proposed method

• Formalism of the dissipative Floquet map is introduced to describe the stroboscopic evolution of the density operator in periodically driven open systems.
• The asymptotic state is identified as the eigen-operator of the dissipative Floquet map corresponding to the largest eigenvalue.
• Mean-field analysis is used to study bifurcation transitions in the system's dynamics under periodic driving.
• The Bose-Hubbard dimer model is employed as a concrete example to illustrate interaction-induced changes in the asymptotic state.
• The method enables identification of a stroboscopic time-independent generator that mimics the action of the original time-periodic Liouvillian.
• Analytical and numerical techniques are applied to compute the eigen-operators and track transitions in the quantum state.

Experimental results

Research questions

• RQ1 How does the asymptotic state of a periodically driven open quantum many-body system differ from equilibrium states?
• RQ2 What role do particle interactions play in inducing bifurcation transitions in the asymptotic density operator?
• RQ3 Can the dissipative Floquet map accurately describe the relaxation dynamics toward the asymptotic state?
• RQ4 How does the time-periodic nature of the asymptotic density operator emerge from the interplay of driving and dissipation?
• RQ5 Can a stroboscopic time-independent generator be derived to effectively describe the time-periodic dynamics?

Key findings

• The asymptotic state of the system is characterized by a time-periodic density operator, emerging due to the combined action of periodic driving and environmental coupling.
• The dissipative Floquet map successfully identifies the asymptotic state as its dominant eigen-operator, enabling stroboscopic analysis of non-equilibrium dynamics.
• Interactions in the Bose-Hubbard dimer model lead to bifurcation transitions in the mean-field dynamics, which are reflected in structural changes of the many-body density operator.
• The stroboscopic time-independent generator can be inferred from the dissipative Floquet map, offering a simplified description of time-periodic dynamics.
• The framework provides a systematic way to analyze relaxation and non-equilibrium steady states in driven open quantum systems beyond the Markovian approximation.