Accelerating relaxation through Liouvillian exceptional point

Abstract

We investigate speeding up of relaxation of Markovian open quantum systems with the Liouvillian exceptional point (LEP), where the slowest decay mode degenerate with a faster decay mode. The degeneracy significantly increases the gap of the Liouvillian operator, which determines the timescale of such systems in converging to stationarity, and hence accelerates the relaxation process. We explore an experimentally relevant three level atomic system, whose eigenmatrices and eigenspectra are obtained completely analytically. This allows us to gain insights in the LEP and examine respective dynamics with details. We illustrate that the gap can be further widened through Floquet engineering, which further accelerates the relaxation process. Finally, we extend this approach to analyze laser cooling of trapped ions, where vibrations (phonons) couple to the electronic states. An optimal cooling condition is obtained analytically, which agrees with both existing experiments and numerical simulations. Our study provides analytical insights in understanding LEP, as well as in controlling and optimizing dissipative dynamics of atoms and trapped ions.

References in corpus (62)

• The physics of exceptional points
• Preparation of Entangled States by Quantum Markov Processes
• Observation of parity-time symmetry breaking transitions in a dissipative Floquet system of ultracold atoms
• Observation of the Quantum Zeno and Anti-Zeno effects in an unstable system
• Symmetries and conserved quantities in Lindblad master equations
• Quantum exceptional points of non-Hermitian Hamiltonians and Liouvillians: The effects of quantum jumps
• Quantum state tomography across the exceptional point in a single dissipative qubit
• Spectral theory of Liouvillians for dissipative phase transitions
• Dissipative production of a maximally entangled steady state
• Quantum state engineering on an optical transition and decoherence in a Paul trap
• From the quantum Zeno to the inverse quantum Zeno effect
• Effective operator formalism for open quantum systems
• Ground state laser cooling using electromagnetically induced transparency
• Inverse design of third-order Dirac exceptional points in photonic crystals
• Engineered Dissipation for Quantum Information Science
• Anomalous cooling and heating - the Mpemba effect and its inverse
• Cavity-assisted quantum bath engineering
• Towards a theory of metastability in open quantum dynamics
• Relaxation times of dissipative many-body quantum systems
• Liouvillian Skin Effect: Slowing Down of Relaxation Processes without Gap Closing
• High-order exceptional points in optomechanics
• Exponentially faster cooling in a colloidal system
• Quantum jumps in the non-Hermitian dynamics of a superconducting qubit
• Exponentially accelerated approach to stationarity in Markovian open quantum systems through the Mpemba effect
• The Mpemba index and anomalous relaxation
• Artificial atoms can do more than atoms: Deterministic single photon subtraction from arbitrary light fields
• Universal stabilization of a parametrically coupled qubit
• Dynamical Control of Quantum Heat Engines Using Exceptional Points
• Decoherence Induced Exceptional Points in a Dissipative Superconducting Qubit
• Quantum Mpemba effect in a quantum dot with reservoirs
• Unraveling the Non-Hermitian Skin Effect in Dissipative Systems
• Faster uphill relaxation in thermodynamically equidistant temperature quenches
• Observation of $\mathcal{P}\mathcal{T}$-symmetric quantum coherence in a single ion system
• Spectral gaps and mid-gap states in random quantum master equations
• Comparing and combining measurement-based and driven-dissipative entanglement stabilization
• Asymptotic Floquet states of open quantum systems: The role of interaction
• Robustness of exceptional-point-based sensors against parametric noise: The role of Hamiltonian and Liouvillian degeneracies
• Liouvillian exceptional points of any order in dissipative linear bosonic systems: Coherence functions and switching between $\mathcal{P}\mathcal{T}$ and anti-$\mathcal{P}\mathcal{T}$ symmetries
• Topological quantum state control through exceptional-point proximity
• Efficient ground-state cooling of large trapped-ion chains with an EIT tripod scheme
• Signatures of Liouvillian exceptional points in a quantum thermal machine
• Single-photon absorber based on strongly interacting Rydberg atoms
• Optimized heat transfer at exceptional points in quantum circuits
• Mean-field validity in a dissipative critical system: Liouvillian gap, $\mathbb{PT}$-symmetric antigap, and permutational symmetry in the $XYZ$ model
• Free-Space Quantum Electrodynamics with a single Rydberg superatom
• Dissipative Topological Phase Transition with Strong System-Environment Coupling
• Geometry, robustness, and emerging unitarity in dissipation-projected dynamics
• Double-EIT Ground-State Cooling of Stationary Two-Dimensional Ion Lattices
• Eigenvalue crossing as a phase transition in relaxation dynamics
• Toward relaxation asymmetry: Heating is faster than cooling
• Superfast Cooling
• On the application of Floquet theorem in development of time-dependent Lindbladians
• Quantum Zeno effects across a parity-time symmetry breaking transition in atomic momentum space
• Optimized Steering: Quantum State Engineering and Exceptional Points
• Observation of collective decay dynamics of a single Rydberg superatom
• High-frequency expansions for time-periodic Lindblad generators
• Floquet exceptional contours in Lindblad dynamics with time-periodic drive and dissipation
• Unification of quantum Zeno-anti Zeno effects and parity-time symmetry breaking transitions
• Fast Cooling of Trapped Ion in Strong Sideband Coupling Regime
• Solvable BCS-Hubbard Liouvillians in arbitrary dimensions
• Liouvillian exceptional points in continuous variable system
• Fast Laser Cooling Using Optimal Quantum Control

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• Observation of quantum strong Mpemba effect
• Multiple quantum Mpemba effect: exceptional points and oscillations
• The quantum Mpemba effects
• Non-Markovian Quantum Exceptional Points
• Speedups in nonequilibrium thermal relaxation: Mpemba and related effects
• Chiral Bell-state transfer via dissipative Liouvillian dynamics
• Bosonic Mpemba effect with non-classical states of light
• Quantum Mpemba effect without global symmetries
• Mpemba effect and super-accelerated thermalization in the damped quantum harmonic oscillator
• Enhanced Quantum Metrology with Non-Phase-Covariant Noise
• Tuning the Quantum Mpemba Effect in Isolated System by Initial State Engineering
• Accelerating Quantum Relaxation via Temporary Reset: A Mpemba-Inspired Approach
• Quantum Mpemba effect from initial system-reservoir entanglement
• Asymmetries of thermal processes in open quantum systems
• Laser Mpemba effect
• Quantum Mpemba effect in parity-time symmetric systems
• Skin Effect Induced Anomalous Dynamics from Charge-Fluctuating Initial States
• Solution of the Metropolis dynamics on a complete graph with application to the Markov chain Mpemba effect
• Many-excitation removal of a transmon qubit using a single-junction quantum-circuit refrigerator and a two-tone microwave drive
• Family of Exact and Inexact Quantum Speed Limits for Completely Positive and Trace-Preserving Dynamics
• Quantum Pontus-Mpemba Effect Enabled by the Liouvillian Skin Effect
• Quantum Mpemba Effect Induced by Non-Markovian Exceptional Points
• Emergent Liouvillian exceptional points from exact principles
• Asymptotic Exceptional Steady States in Dissipative Dynamics
• Separation of relaxation timescales via strong system-bath coupling: Dissipative three-level system as a case study
• Non-Hermiticity induced thermal entanglement phase transition
• Engineering the non-Hermitian Su-Schrieffer-Heeger model with skin effects in Rydberg atom arrays