Decimation technique for open quantum systems: a case study with driven-dissipative bosonic chains
arXiv:2202.07674 · doi:10.1103/PhysRevA.105.052223
Abstract
The unavoidable coupling of quantum systems to external degrees of freedom leads to dissipative (non-unitary) dynamics, which can be radically different from closed-system scenarios. Such open quantum system dynamics is generally described by Lindblad master equations, whose dynamical and steady-state properties are challenging to obtain, especially in the many-particle regime. Here, we introduce a method to deal with these systems based on the calculation of (dissipative) lattice Green's function with a real-space decimation technique. Compared to other methods, such technique enables obtaining compact analytical expressions for the dynamics and steady-state properties, such as asymptotic decays or correlation lengths. We illustrate the power of this method with several examples of driven-dissipative bosonic chains of increasing complexity, including the Hatano-Nelson model. The latter is especially illustrative because its surface and bulk dissipative behavior are linked due to its non-trivial topology, which manifests in directional amplification.
arXiv comment12 pages, 11 figures and Appendix
References in corpus (50)
- Quantum Computing in the NISQ era and beyond
- Efficient classical simulation of slightly entangled quantum computations
- Localization transitions in non-Hermitian quantum mechanics
- Topological phases of non-Hermitian systems
- Real time evolution using the density matrix renormalization group
- Symmetry and Topology in Non-Hermitian Physics
- Quantum States and Phases in Driven Open Quantum Systems with Cold Atoms
- Time-dependent density-matrix renormalization-group using adaptive effective Hilbert spaces
- Keldysh Field Theory for Driven Open Quantum Systems
- Efficient simulation of strong system-environment interactions
- Finite Temperature Density Matrix Renormalization using an enlarged Hilbert space
- The recursive Green's function method for graphene
- Atomic three-body loss as a dynamical three-body interaction
- Simulation methods for open quantum many-body systems
- Exponentially-enhanced quantum sensing with non-Hermitian lattice dynamics
- Quantum Spin Dimers from Chiral Dissipation in Cold-Atom Chains
- Atom-field dressed states in slow-light waveguide QED
- Review of Inverse Laplace Transform Algorithms for Laplace-Space Numerical Approaches
- Phase-dependent chiral transport and effective non-Hermitian dynamics in a bosonic Kitaev-Majorana chain
- Quantum phase transition in a far from equilibrium steady state of XY spin chain
- Efficient simulation of finite-temperature open quantum systems
- Topological framework for directional amplification in driven-dissipative cavity arrays
- Atom-light interactions in quasi-1D nanostructures: a Green's function perspective
- Nonequilibrium many-body steady states via Keldysh formalism
- Boundary Green functions of topological insulators and superconductors
- Non-exponential decay via tunneling in tight-binding lattices and the optical Zeno effect
- Markovian and Non-Markovian Dynamics of Quantum Emitters coupled to Two-dimensional Structured Reservoirs
- A Green-function approach to transport phenomena in quantum pumps
- Universal Quantum Computation in Waveguide QED using Decoherence Free Subspaces
- Perturbative approach to Markovian open quantum systems
- Non-equilibrium stationary states of quantum non-Hermitian lattice models
- Perspective on traveling wave microwave parametric amplifiers
- Topological Amplification in Photonic Lattices
- Topological states on fractal lattices
- Dynamical signatures of bound states in waveguide QED
- Topology by Dissipation: Majorana Bosons in Metastable Quadratic Markovian Dynamics
- Deconstructing effective non-Hermitian dynamics in quadratic bosonic Hamiltonians
- Josephson Array Mode Parametric Amplifier
- Non-Markovian Decay and Lasing Condition in an Optical Microcavity Coupled to a Structured Reservoir
- Exact solutions of interacting dissipative systems via weak symmetries
- Exact description of quantum stochastic models as quantum resistors
- Topological input-output theory for directional amplification
- Amplification of non-Markovian decay due to bound state absorption into continuum
- Resummation for Nonequilibrium Perturbation Theory and Application to Open Quantum Lattices
- Exponentially growing bulk Green functions as signature of nontrivial non-Hermitian winding number in one dimension
- Pedagogical introduction to equilibrium Green's functions: condensed matter examples with numerical implementations
- Dissipative flow equations
- A renormalization group approach to non-Hermitian topological quantum criticality
- Computation of the asymptotic states of modulated open quantum systems with a numerically exact realization of the quantum trajectory method
- Transport signatures in topological systems coupled to AC fields