Dynamical Mean-Field Theory for Markovian Open Quantum Many-Body Systems

A number of experimental platforms relevant for quantum simulations, ranging from arrays of superconducting circuits hosting correlated states of light to ultracold atoms in optical lattices in the presence of controlled dissipative processes, are described as open quantum many-body systems. Their t...

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Autores principales:	Orazio Scarlatella, Aashish A. Clerk, Rosario Fazio, Marco Schiró
Formato:	article
Lenguaje:	EN
Publicado:	American Physical Society 2021
Materias:	Physics QC1-999
Acceso en línea:	https://doaj.org/article/d2f2f3f9b571432a8ae236df9261e725
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spelling	oai:doaj.org-article:d2f2f3f9b571432a8ae236df9261e7252021-12-02T19:13:05ZDynamical Mean-Field Theory for Markovian Open Quantum Many-Body Systems10.1103/PhysRevX.11.0310182160-3308https://doaj.org/article/d2f2f3f9b571432a8ae236df9261e7252021-07-01T00:00:00Zhttp://doi.org/10.1103/PhysRevX.11.031018http://doi.org/10.1103/PhysRevX.11.031018https://doaj.org/toc/2160-3308A number of experimental platforms relevant for quantum simulations, ranging from arrays of superconducting circuits hosting correlated states of light to ultracold atoms in optical lattices in the presence of controlled dissipative processes, are described as open quantum many-body systems. Their theoretical understanding is hampered by the exponential scaling of their Hilbert space and by their intrinsic nonequilibrium nature, limiting the applicability of many traditional approaches. In this work, we extend the nonequilibrium bosonic dynamical mean-field theory (DMFT) to Markovian open quantum systems. Within DMFT, a Lindblad master equation describing a lattice of dissipative bosonic particles is mapped onto an impurity problem describing a single site embedded in its Markovian environment and coupled to a self-consistent field and to a non-Markovian bath, where the latter accounts for fluctuations beyond Gutzwiller mean-field theory due to the finite lattice connectivity. We develop a nonperturbative approach to solve this bosonic impurity problem, which dresses the impurity, featuring Markovian dissipative channels, with the non-Markovian bath, in a self-consistent scheme based on a resummation of noncrossing diagrams. As a first application of our approach, we address the steady state of a driven-dissipative Bose-Hubbard model with two-body losses and incoherent pump. We show that DMFT captures hopping-induced dissipative processes, completely missed in Gutzwiller mean-field theory, which crucially determine the properties of the normal phase, including the redistribution of steady-state populations, the suppression of local gain, and the emergence of a stationary quantum-Zeno regime. We argue that these processes compete with coherent hopping to determine the phase transition toward a nonequilibrium superfluid, leading to a strong renormalization of the phase boundary at finite connectivity. We show that this transition occurs as a finite-frequency instability, leading to an oscillating-in-time order parameter, that we connect with a quantum many-body synchronization transition of an array of quantum van der Pol oscillators.Orazio ScarlatellaAashish A. ClerkRosario FazioMarco SchiróAmerican Physical SocietyarticlePhysicsQC1-999ENPhysical Review X, Vol 11, Iss 3, p 031018 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Physics QC1-999
spellingShingle	Physics QC1-999 Orazio Scarlatella Aashish A. Clerk Rosario Fazio Marco Schiró Dynamical Mean-Field Theory for Markovian Open Quantum Many-Body Systems
description	A number of experimental platforms relevant for quantum simulations, ranging from arrays of superconducting circuits hosting correlated states of light to ultracold atoms in optical lattices in the presence of controlled dissipative processes, are described as open quantum many-body systems. Their theoretical understanding is hampered by the exponential scaling of their Hilbert space and by their intrinsic nonequilibrium nature, limiting the applicability of many traditional approaches. In this work, we extend the nonequilibrium bosonic dynamical mean-field theory (DMFT) to Markovian open quantum systems. Within DMFT, a Lindblad master equation describing a lattice of dissipative bosonic particles is mapped onto an impurity problem describing a single site embedded in its Markovian environment and coupled to a self-consistent field and to a non-Markovian bath, where the latter accounts for fluctuations beyond Gutzwiller mean-field theory due to the finite lattice connectivity. We develop a nonperturbative approach to solve this bosonic impurity problem, which dresses the impurity, featuring Markovian dissipative channels, with the non-Markovian bath, in a self-consistent scheme based on a resummation of noncrossing diagrams. As a first application of our approach, we address the steady state of a driven-dissipative Bose-Hubbard model with two-body losses and incoherent pump. We show that DMFT captures hopping-induced dissipative processes, completely missed in Gutzwiller mean-field theory, which crucially determine the properties of the normal phase, including the redistribution of steady-state populations, the suppression of local gain, and the emergence of a stationary quantum-Zeno regime. We argue that these processes compete with coherent hopping to determine the phase transition toward a nonequilibrium superfluid, leading to a strong renormalization of the phase boundary at finite connectivity. We show that this transition occurs as a finite-frequency instability, leading to an oscillating-in-time order parameter, that we connect with a quantum many-body synchronization transition of an array of quantum van der Pol oscillators.
format	article
author	Orazio Scarlatella Aashish A. Clerk Rosario Fazio Marco Schiró
author_facet	Orazio Scarlatella Aashish A. Clerk Rosario Fazio Marco Schiró
author_sort	Orazio Scarlatella
title	Dynamical Mean-Field Theory for Markovian Open Quantum Many-Body Systems
title_short	Dynamical Mean-Field Theory for Markovian Open Quantum Many-Body Systems
title_full	Dynamical Mean-Field Theory for Markovian Open Quantum Many-Body Systems
title_fullStr	Dynamical Mean-Field Theory for Markovian Open Quantum Many-Body Systems
title_full_unstemmed	Dynamical Mean-Field Theory for Markovian Open Quantum Many-Body Systems
title_sort	dynamical mean-field theory for markovian open quantum many-body systems
publisher	American Physical Society
publishDate	2021
url	https://doaj.org/article/d2f2f3f9b571432a8ae236df9261e725
work_keys_str_mv	AT orazioscarlatella dynamicalmeanfieldtheoryformarkovianopenquantummanybodysystems AT aashishaclerk dynamicalmeanfieldtheoryformarkovianopenquantummanybodysystems AT rosariofazio dynamicalmeanfieldtheoryformarkovianopenquantummanybodysystems AT marcoschiro dynamicalmeanfieldtheoryformarkovianopenquantummanybodysystems
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Dynamical Mean-Field Theory for Markovian Open Quantum Many-Body Systems

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