Exceptional points and exponential sensitivity for periodically driven Lindblad equations

Abstract

In this contribution to the memorial issue of Göran Lindblad, we investigate the periodically driven Lindblad equation for a two-level system. We analyze the system using both adiabatic diagonalization and numerical simulations of the time-evolution, as well as Floquet theory. Adiabatic diagonalization reveals the presence of exceptional points in the system, which depend on the system parameters. We show how the presence of these exceptional points affects the system evolution, leading to a rapid dephasing at these points and a staircase-like loss of coherence. This phenomenon can be experimentally observed by measuring, for example, the population inversion. We also observe that the presence of exceptional points seems to be related to which underlying Lie algebra the system supports. In the Floquet analysis, we map the time-dependent Liouvillian to a non-Hermitian Floquet Hamiltonian and analyze its spectrum. For weak decay rates, we find a Wannier-Stark ladder spectrum accompanied by corresponding Stark-localized eigenstates. For larger decay rates, the ladders begin to dissolve, and new, less localized states emerge. Additionally, their eigenvalues are exponentially sensitive to perturbations, similar to the skin effect found in certain non-Hermitian Hamiltonians.

arXiv commentThis paper is an invited contribution to the Lindblad memorial volume in Open Systems and Information Dynamics. 19 pages, 4 figures

References in corpus (42)

• Non-Hermitian Physics
• The physics of exceptional points
• Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems
• Topological Origin of Non-Hermitian Skin Effects
• Atomic quantum gases in periodically driven optical lattices
• Observation of bulk boundary correspondence breakdown in topolectrical circuits
• Efficient Light Funneling based on the non-Hermitian Skin Effect
• Non-Hermitian skin effect and chiral damping in open quantum systems
• Biorthogonal Quantum Mechanics
• The Bloch Vector for N-Level Systems
• Quantum exceptional points of non-Hermitian Hamiltonians and Liouvillians: The effects of quantum jumps
• Non-Hermitian Topological Sensors
• Quantum state tomography across the exceptional point in a single dissipative qubit
• Spectral theory of Liouvillians for dissipative phase transitions
• Observation of Non-Hermitian Skin Effect and Topology in Ultracold Atoms
• Observation of hybrid higher-order skin-topological effect in non-Hermitian topolectrical circuits
• Interplay of non-Hermitian skin effects and Anderson localization in non-reciprocal quasiperiodic lattices
• General non-Markovian dynamics of open quantum systems
• Non-stationary coherent quantum many-body dynamics through dissipation
• Stark many-body localization
• A non-Markovian decoherence theory for double dot charge qubit
• Adiabatic approximation in open quantum systems
• Liouvillian Skin Effect: Slowing Down of Relaxation Processes without Gap Closing
• Decoherence in adiabatic quantum computation
• Local PT symmetry violates the no-signaling principle
• Decoherence Induced Exceptional Points in a Dissipative Superconducting Qubit
• A nonequilibrium theory for transient transport dynamics in nanostructures via the Feynman-Vernon influence functional approach
• Time Dependent Markovian Quantum Master Equation
• Geometry of the generalized Bloch sphere for qutrits
• Unraveling the Non-Hermitian Skin Effect in Dissipative Systems
• Increase of entanglement by local PT -symmetric operations
• Liouvillian Skin Effect in an Exactly Solvable Model
• Signatures of Liouvillian exceptional points in a quantum thermal machine
• Fundamentals of Quantum Mechanics in Liouville Space
• Exceptional points for parameter estimation in open quantum systems: Analysis of the Bloch equations
• Sensitivity of non-Hermitian systems
• Exact solution of time-dependent Lindblad equations with closed algebras
• Embedding dissipation and decoherence in unitary evolution schemes
• Time-evolution of nonlinear optomechanical systems: Interplay of mechanical squeezing and non-Gaussianity
• Enhanced continuous generation of non-Gaussianity through optomechanical modulation
• Decoherence-induced geometric phase in a multilevel atomic system
• A view on the open STIRAP problem

Cited by in corpus (5)

• Dephasing-induced mobility edges in quasicrystals
• Chiral Bell-state transfer via dissipative Liouvillian dynamics
• Exploring the impact of fluctuation-induced criticality on non-hermitian skin effect and quantum sensors
• Boundary sensitive Lindbladians and relaxation dynamics
• Liouvillian exceptional points of an open driven two-level system