Instability of the engineered dark state in two-band fermions under number-conserving dissipative dynamics
arXiv:2408.04987 · doi:10.1103/PhysRevB.111.094302
Abstract
Correlated quantum many-body states can be created and controlled by the dissipative protocols. Among these, particle number-conserving protocols are particularly appealing due to their ability to stabilize topologically nontrivial phases. Is there any fundamental limitation to their performance? We address this question by examining a general class of models involving a two-band fermion system subjected to dissipation designed to transfer fermions from the upper band to the lower band. By construction, these models have a guaranteed steady state - a dark state - with a completely filled lower band and an empty upper band. In the limit of weak dissipation, we derive equations governing the long-wavelength and long-time dynamics of the fermion densities and analyze them numerically. These equations belong to the Fisher-Kolmogorov-Petrovsky-Piskunov reaction-diffusion universality class. Our analysis reveals that the engineered dark state is generically unstable, giving way to a new steady state with a finite density of particles in the upper band. We also estimate the minimum system sizes required to observe this instability in finite systems. Our results suggest that number-conserving dissipative protocols may not be a reliable universal tool for stabilizing dark states.
arXiv commentv2, 18 pages, 14 figures
References in corpus (67)
- Quantum States and Phases in Driven Open Quantum Systems with Cold Atoms
- A Rydberg Quantum Simulator
- Preparation of Entangled States by Quantum Markov Processes
- Measurement-Induced Phase Transitions in the Dynamics of Entanglement
- Quantum Zeno Effect and the Many-body Entanglement Transition
- Quasiparticle Lifetime in a Finite System: A Non--Perturbative Approach
- Measurement-driven entanglement transition in hybrid quantum circuits
- Keldysh Field Theory for Driven Open Quantum Systems
- Confining the state of light to a quantum manifold by engineered two-photon loss
- Topology by Dissipation in Atomic Quantum Wires
- Third quantization: a general method to solve master equations for quadratic open Fermi systems
- Symmetries and conserved quantities in Lindblad master equations
- Keldysh technique and non-linear sigma-model: basic principles and applications
- A note on symmetry reductions of the Lindblad equation: transport in constrained open spin chains
- Topology by dissipation
- Theory of Branching and Annihilating Random Walks
- Coulomb drag
- Microscopic model of quantum butterfly effect: out-of-time-order correlators and traveling combustion waves
- Field Theory of Branching and Annihilating Random Walks
- Spectral theorem for the Lindblad equation for quadratic open fermionic systems
- Fermionic Superradiance in a Transversely Pumped Optical Cavity
- Umklapp Superradiance from a Collisionless Quantum Degenerate Fermi Gas
- Dissipative preparation of Chern insulators
- Super-Radiant Dynamics, Doorways, and Resonances in Nuclei and Other Open Mesoscopic Systems
- Nonequilibrium Phase Diagram of a Driven-Dissipative Many-Body System
- Theory of free fermions under random projective measurements
- Ultracold fermions in a cavity-induced artificial magnetic field
- Non Perturbative Renormalization Group study of reaction-diffusion processes and directed percolation
- Inelastic Electron Lifetime in Disordered Mesoscopic Systems
- Majorana Modes in Driven-Dissipative Atomic Superfluids With Zero Chern Number
- Symmetry classes of open fermionic quantum matter
- Localization and fluctuations of local spectral density on tree-like structures with large connectivity: Application to the quasiparticle line shape in quantum dots
- Nonlinear sigma models for monitored dynamics of free fermions
- Measurement-induced phase transition for free fermions above one dimension
- Zeno Hall Effect
- Dissipative topological superconductors in number-conserving systems
- Driven dissipative dynamics and topology of quantum impurity systems
- Fate of fractional quantum Hall states in open quantum systems: characterization of correlated topological states for the full Liouvillian
- From Classical to Quantum Glasses with Ultracold Polar Molecules
- Field Theory of Many-Body Lindbladian Dynamics
- Topological Field Theory far from Equilibrium
- Dissipation-induced topological insulators: A no-go theorem and a recipe
- Lindblad master equation approach to the topological phase transition in the disordered Su-Schrieffer-Heeger model
- Exploring quantum phases by driven dissipation
- Decay of Quasi-Particle in a Quantum Dot: the role of Energy Resolution
- Topology by Dissipation: Transport properties
- Lieb-Schultz-Mattis Theorem in Open Quantum Systems
- Reaction-limited quantum reaction-diffusion dynamics
- Many-body delocalization transition and relaxation in a quantum dot
- Driven Dissipative Majorana Dark Spaces
- Absence of many-body localization in a continuum
- Generating topological order: no speedup by dissipation
- Towards dark space stabilization and manipulation in driven dissipative Majorana platforms
- Symmetry-protected dissipative preparation of matrix product states
- Dissipative Preparation of Spatial Order in Rydberg-Dressed Bose-Einstein Condensates
- Reaction-diffusion processes and non-perturbative renormalisation group
- Disorder in dissipation-induced topological states: Evidence for a different type of localization transition
- An exactly solvable travelling wave equation in the Fisher-KPP class
- Multidimensional dark space and its underlying symmetries: towards dissipation-protected qubits
- Dissipative preparation of many-body Floquet Chern insulators
- Uniqueness of steady states of Gorini-Kossakowski-Sudarshan-Lindblad equations: a simple proof
- Stretched Exponential Decay of a Quasiparticle in a Quantum Dot
- Measurement induced criticality in quasiperiodic modulated random hybrid circuits
- Reaction-diffusive dynamics of number-conserving dissipative quantum state preparation
- Hydrodynamic theory of scrambling in chaotic long-range interacting systems
- Quantum reaction-limited reaction-diffusion dynamics of noninteracting Bose gases
- Diffusive modes of two-band fermions under number-conserving dissipative dynamics