Spectral theory of non-Markovian dissipative phase transitions
arXiv:2410.18990 · doi:10.1103/PhysRevA.110.042201
Abstract
Dissipative phase transitions in quantum systems have been largely studied under the so-called Markovian approximation, where the environments to which the systems are coupled are memoryless. Here, we present a generalization of the spectral theory of dissipative phase transitions to non-Markovian systems, encompassing a much broader class of quantum materials and experiments and opening many possibilities for non-Markovian engineering of matter phases such as, as explored in the companion Letter [Debecker et. al., Phys. Rev. Lett. 133, 140403 (2024)], reshaping of phase boundaries and triggering of phase transitions. We first prove several statements about the connections between the spectrum of the generator of the non-Markovian dynamics of general systems and dissipative phase transitions. Then, as a benchmark, we show that our framework can capture all the expected signatures of the superradiant phase transition appearing in a challenging -symmetric two-mode Dicke model from a reduced description of the dynamics of the atoms only, a task for which all other methods have failed so far.
arXiv comment14 pages, 8 figures. Close to published version
References in corpus (64)
- Circuit Quantum Electrodynamics
- Flocks, herds, and schools: A quantitative theory of flocking
- The Dicke Quantum Phase Transition with a Superfluid Gas in an Optical Cavity
- Vacuum Rabi splitting in a plasmonic cavity at the single quantum emitter limit
- Mixed-state dynamics in one-dimensional quantum lattice systems: a time-dependent superoperator renormalization algorithm
- Perspective: Numerically "exact" approach to open quantum dynamics: The hierarchical equations of motion (HEOM)
- Spectral theory of Liouvillians for dissipative phase transitions
- Efficient non-Markovian quantum dynamics using time-evolving matrix product operators
- Dynamical phase transition in the open Dicke model
- Dissipative Phase Transition in Central Spin Systems
- Observation of a dissipative phase transition in a one-dimensional circuit QED lattice
- Circuit QED lattices: towards quantum simulation with superconducting circuits
- Keldysh approach for non-equilibrium phase transitions in quantum optics: beyond the Dicke model in optical cavities
- Tunable-range, photon-mediated atomic interactions in multimode cavity QED
- Hierarchy of stochastic pure states for open quantum system dynamics
- Towards a theory of metastability in open quantum dynamics
- Emergent superfluid crystals, frustration, and topologically defected states in multimode cavity QED
- Non-Markovianity assisted Steady State Entanglement
- Variational Matrix Product Operators for the Steady State of Dissipative Quantum Systems
- Unconventional magnetism via optical pumping of interacting spin systems
- Theory of Pseudomodes in Quantum Optical Processes
- Cluster mean-field approach to the steady-state phase diagram of dissipative spin systems
- Environment-assisted quantum transport in a 10-qubit network
- Frustration and glassiness in spin models with cavity-mediated interactions
- Signatures of a dissipative phase transition in photon correlation measurements
- Genuine quantum trajectories for non-Markovian processes
- Observation of the photon-blockade breakdown phase transition
- Dissipative Phase Transition in the Open Quantum Rabi Model
- Equilibrium and non-equilibrium dynamics of the sub-ohmic spin-boson model
- Pseudomodes as an effective description of memory: Non-Markovian dynamics of two-state systems in structured reservoirs
- A Matrix-Product-Operator Approach to the Nonequilibrium Steady State of Driven-Dissipative Quantum Arrays
- A variational description of the quantum phase transition in the sub-Ohmic spin-boson model
- Non-Markovianity, Loschmidt echo and criticality: a unified picture
- Supermode-Density-Wave-Polariton Condensation
- Corner space renormalization method for driven-dissipative 2D correlated systems
- Atom-light crystallization of BECs in multimode cavities: Nonequilibrium classical and quantum phase transitions, emergent lattices, supersolidity, and frustration
- Analytic Representations of Bath Correlation Functions for Ohmic and Superohmic Spectral Densities Using Simple Poles
- Generalization of the hierarchical equations of motion theory for efficient calculations with arbitrary correlation functions
- QuTiP-BoFiN: A bosonic and fermionic numerical hierarchical-equations-of-motion library with applications in light-harvesting, quantum control, and single-molecule electronics
- Sign-changing photon-mediated atom interactions in multimode cavity QED
- Generalized theory of pseudomodes for exact descriptions of non-Markovian quantum processes
- Atom-only descriptions of the driven-dissipative Dicke model
- An adjustable-length cavity and Bose-Einstein condensate apparatus for multimode cavity QED
- The Open-System Dicke-Model Quantum Phase Transition with a Sub-Ohmic Bath
- Enhancing associative memory recall and storage capacity using confocal cavity QED
- Dissipative phase transitions: Independent versus collective decay and spin squeezing
- Open Quantum System Dynamics from Infinite Tensor Network Contraction
- Many-body quantum state diffusion for non-Markovian dynamics in strongly interacting systems
- Non-equilibrium magnetic phases in spin lattices with gain and loss
- The Hidden Phase of the Spin-Boson Model
- Emergent and broken symmetries of atomic self-organization arising from Gouy phase shifts in multimode cavity QED
- Stochastic Schrödinger equations with coloured noise
- Non-Markovian Quantum Dynamics in Strongly Coupled Multimode Cavities Conditioned on Continuous Measurement
- Signatures of associative memory behavior in a multi-mode spin-boson model
- Critical exponent of quantum phase transitions driven by colored noise
- HierarchicalEOM.jl: An efficient Julia framework for hierarchical equations of motion in open quantum systems
- Non-adiabatic elimination of auxiliary modes in continuous quantum measurements
- Generalized classes of continuous symmetries in two-mode Dicke models
- Atom-only theories for U(1) symmetric cavity-QED models
- A Quantum N-Queens Solver
- Controlling Matter Phases beyond Markov
- Stable bipolarons in open quantum systems
- On the nature of the non-equilibrium phase transition in the non-Markovian driven Dicke model
- Chaos in Optomechanical Systems coupled to a Non-Markovian environment
Cited by in corpus (4)
- Controlling Matter Phases beyond Markov
- Dynamical signatures of discontinuous phase transitions: How phase coexistence determines exponential versus power-law scaling
- Delocalized Excitation Transfer in Open Quantum Systems with Long-Range Interactions
- Beyond mean-field dynamics of the Dicke model with non-Markovian dephasing