Abstract
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.
- Received 5 August 2020
- Revised 5 April 2021
- Accepted 17 May 2021
- Corrected 16 September 2021
DOI:https://doi.org/10.1103/PhysRevX.11.031018
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Corrections
16 September 2021
Correction: A proof change request to the first sentence of the abstract was not implemented properly and has now been rectified.
Popular Summary
We extend the celebrated dynamical mean-field theory to solve open quantum many-body systems coupled to Markovian, or memoryless, environments, which model several experimental platforms in quantum optics and atomic physics. We use our approach to study a driven-dissipative Bose-Hubbard model, relevant for ultracold atoms and superconducting circuits experiments.
We show that the combination of drive, dissipation, and interactions between particles gives rise to a phase transition into an exotic quantum time-crystal phase, in which certain properties of the system oscillate in time without decay. This breaks the time-translation symmetry of the system much like a periodic arrangement of atoms in a crystal breaks the perfect symmetry of space. We connect this phenomenon to the physics of quantum synchronization of a large number of quantum oscillators. We show that the quantum fluctuations captured by dynamical mean-field theory are essential to capture most of the physics of this model.
Our new method allows one to investigate a large variety of experimentally relevant models that are not accessible with other theoretical techniques, thus paving the way for new quantum many-body phenomena discoveries.
