Unraveling the topology of dissipative quantum systems

Abstract

We discuss topology in dissipative quantum systems from the perspective of quantum trajectories. The latter emerge in the unraveling of Markovian quantum master equations and/or in continuous quantum measurements. Ensemble-averaging quantum trajectories at the occurrence of quantum jumps, i.e., the jump times, gives rise to a discrete, deterministic evolution which is highly sensitive to the presence of dark states. We show for a broad family of translation-invariant collapse models that the set of dark state-inducing Hamiltonians imposes a nontrivial topological structure on the space of Hamiltonians, which is also reflected by the corresponding jumptime dynamics. The topological character of the latter can then be observed, for instance, in the transport behavior, exposing an infinite hierarchy of topological phase transitions. We develop our theory for one- and two-dimensional two-band Hamiltonians and show that the topological behavior is directly manifest for chiral, PT, or time reversal-symmetric Hamiltonians.

arXiv commentCorresponds to published version. 15 pages

References in corpus (42)

• Topological Insulators
• Topological insulators and superconductors
• Berry Phase Effects on Electronic Properties
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Edge states and topological invariants of non-Hermitian systems
• Non-Hermitian Physics
• The Quantum Jump Approach to Dissipative Dynamics in Quantum Optics
• Topological phases of non-Hermitian systems
• Symmetry and Topology in Non-Hermitian Physics
• Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems
• Non-Hermitian Boundary Modes
• Programmable Quantum Simulations of Spin Systems with Trapped Ions
• Edge Modes, Degeneracies, and Topological Numbers in Non-Hermitian Systems
• Quantum jumps of light recording the birth and death of a photon in a cavity
• Non-Hermitian skin effect and chiral damping in open quantum systems
• Real-time quantum feedback prepares and stabilizes photon number states
• Counting statistics of single-electron transport in a quantum dot
• Experimental realization of a symmetry protected topological phase of interacting bosons with Rydberg atoms
• High-fidelity readout and control of a nuclear spin qubit in silicon
• Topological Transition in a Non-Hermitian Quantum Walk
• Spectral signatures of many-body localization with interacting photons
• Quantum exceptional points of non-Hermitian Hamiltonians and Liouvillians: The effects of quantum jumps
• Topologically protected defect states in open photonic systems with non-hermitian charge-conjugation and parity-time symmetry
• Observation of quantum jumps in a superconducting artificial atom
• To catch and reverse a quantum jump mid-flight
• Topology by dissipation
• Tenfold Way for Quadratic Lindbladians
• Environment-assisted quantum transport in a 10-qubit network
• Quantum jumps in the non-Hermitian dynamics of a superconducting qubit
• Probing the topology of density matrices
• Non-Hermitian dynamics without dissipation in quantum systems
• Topological invariants in dissipative extensions of the Su-Schrieffer-Heeger model
• Zeno Hall Effect
• Optical detection of single electron transport dynamics
• Heat and work along individual trajectories of a quantum bit
• Fate of fractional quantum Hall states in open quantum systems: characterization of correlated topological states for the full Liouvillian
• Measurement of spin Chern numbers in quantum simulated topological insulators
• Survival, decay, and topological protection in non-Hermitian quantum transport
• Topological Protection of Coherence in a Dissipative Environment
• Jumptime unraveling of Markovian open quantum systems
• Topological transport in the steady state of a quantum particle with dissipation
• Disorder-dressed quantum evolution

Cited by in corpus (20)

• QuTiP 5: The Quantum Toolbox in Python
• Spectral deformations in non-Hermitian lattices with disorder and skin effect: a solvable model
• Non-Hermitian Pseudomodes for Strongly Coupled Open Quantum Systems: Unravelings, Correlations and Thermodynamics
• A quantum-classical decomposition of Gaussian quantum environments: a stochastic pseudomode model
• Topological optomechanical amplifier with synthetic $\mathcal{P}\mathcal{T}$-symmetry
• Point-gap topology with complete bulk-boundary correspondence in dissipative quantum systems
• Out-of-Time-Order Correlation as a Witness for Topological Phase Transitions
• Topological phase diagrams of exactly solvable non-Hermitian interacting Kitaev chains
• Reviving the Lieb-Schultz-Mattis Theorem in Open Quantum Systems
• Edge modes and symmetry-protected topological states in open quantum systems
• Role of Bath-Induced Many-Body Interactions in the Dissipative Phases of the Su-Schrieffer-Heeger Model
• Observing Parity Time Symmetry Breaking in a Josephson Parametric Amplifier
• Symmetry classes of dissipative topological insulators with edge dark state
• Edge-selective extremal damping from topological heritage of dissipative Chern insulators
• Linear Response for pseudo-Hermitian Hamiltonian Systems: Application to PT-Symmetric Qubits
• Topological extension including quantum jump
• Full counting statistics and first-passage times in quantum Markovian processes: Ensemble relations, metastability, and fluctuation theorems
• Gauge freedoms in unravelled quantum dynamics: When do different continuous measurements yield identical quantum trajectories?
• Replica Keldysh field theory of quantum-jump processes: General formalism and application to imbalanced and inefficient fermion counting
• Simulating monitoring-induced topological phase transitions with small systems