[Paper Review] Non-equilibrium dynamics of many body quantum systems

Loïc Henriet|arXiv (Cornell University)|Apr 14, 2018

Quantum Information and Cryptography6 references3 citations

TL;DR

This thesis develops an exact stochastic approach to model non-equilibrium dynamics in many-body quantum systems, particularly spin-boson models with ohmic and non-ohmic environments. By mapping the bosonic bath to stochastic noise with time-correlated fluctuations derived from spectral properties, the method enables the study of dissipative quantum phase transitions, spontaneous synchronization, and topological transitions, with applications to cavity QED, ultracold atoms, and hybrid quantum dot-resonator systems.

ABSTRACT

This thesis deals with the study of dynamical properties of out-of-equilibrium quantum systems. We introduce in particular a general class of Spin-Boson models, which describe for example light-matter interaction or dissipative phenomena. We contribute to the development of a stochastic approach to describe the spin dynamics in these models. In this context, the effect of the bosonic environment is encapsulated into additional stochastic degrees of freedom whose time-correlations are determined by spectral properties of the bosonic environment. We use this approach to study many-body phenomena such as the dissipative quantum phase transition induced by an ohmic bosonic environment. Synchronization phenomena as well as dissipative topological transitions are identified. We also progress in the study of arrays of interacting light-matter systems. These theoretical developments follow recent experimental achievements, which could ensure a quantitative study of these phenomena. This notably includes ultra-cold atoms, trapped ions and cavity and circuit electrodynamics setups. We finally investigate hybrid systems comprising electronic quantum dots coupled to electromagnetic resonators, which enable us to provide a spectroscopic analysis of many-body phenomena linked to the Kondo effect. We also introduce thermoelectric applications in these devices.

Motivation & Objective

• To develop a general theoretical framework for studying non-equilibrium dynamics in open quantum many-body systems.
• To address the challenge of modeling dissipative effects from bosonic environments in quantum systems with strong correlations.
• To enable quantitative analysis of quantum phase transitions driven by ohmic and non-ohmic baths in spin-boson models.
• To connect theoretical predictions to recent experimental platforms such as ultracold atoms, trapped ions, and circuit quantum electrodynamics.
• To explore thermoelectric and spectroscopic applications in hybrid quantum dot-resonator systems.

Proposed method

• Introduces a stochastic approach where the bosonic environment is represented by additional stochastic degrees of freedom with time-correlation functions determined by the bath's spectral density.
• Uses the convolution theorem to compute the effective $ P(E) $ function for tunneling rates by combining contributions from cold (low-temperature) and hot (thermal) impedance environments.
• Derives the effective $ P_l(E) $ function as a convolution of power-law and Lorentzian components, parameterized by effective $ \tilde{\alpha}_l $, $ \tilde{E}_{c,l} $, and $ \tilde{\Delta}_l $, incorporating capacitive and impedance asymmetries.
• Applies the formalism to calculate tunneling rates $ T_{\pm,l}(\Omega) $ via integrals over Fermi distributions and $ P_l(E) $, enabling analysis of rectified current and efficiency.
• Models left-right asymmetry via different $ \tilde{\alpha}_L \neq \tilde{\alpha}_R $, arising from unequal capacitances or impedances, to break symmetry and enable directional transport.
• Uses the rectified current formula $ I = e \frac{T_{+,L}T_{+,R} - T_{-,L}T_{-,R}}{\sum T} $ to quantify non-equilibrium transport in non-resonant sequential tunneling.

Experimental results

Research questions

• RQ1 How can the non-equilibrium dynamics of many-body quantum systems be accurately described when coupled to a structured bosonic bath?
• RQ2 What are the conditions under which a dissipative quantum phase transition occurs in a spin-boson model with an ohmic bath?
• RQ3 Can spontaneous synchronization and topological transitions emerge in open quantum systems with non-Markovian bath correlations?
• RQ4 How does left-right asymmetry in coupling parameters affect rectified current and thermoelectric efficiency in quantum dot-resonator systems?
• RQ5 To what extent can the stochastic approach accurately model spectroscopic signatures of many-body effects like the Kondo effect in hybrid quantum devices?

Key findings

• The stochastic approach successfully captures non-Markovian bath effects through time-correlated noise, enabling exact treatment of non-equilibrium dynamics in spin-boson models.
• The formalism predicts a dissipative quantum phase transition in the ohmic spin-boson model, with critical behavior governed by the bath spectral density and coupling strength.
• Spontaneous synchronization and topological transitions are identified as emergent phenomena in the presence of structured bath environments.
• The effective $ P_l(E) $ function combines power-law (from cold bath) and Lorentzian (from hot bath) components, enabling finite probability for negative energy transitions via photon absorption.
• Rectified current arises from asymmetry in $ \tilde{\alpha}_L \neq \tilde{\alpha}_R $, with efficiency reduced compared to resonant tunneling due to loss of phase coherence.
• The model enables spectroscopic detection of many-body Kondo-like states via coupling to electromagnetic resonators, offering a pathway to experimental verification.