Lindblad dynamics of open multi-mode bosonic systems: Algebra of bilinear superoperators, exceptional points and speed of evolution
arXiv:2412.13890 · doi:10.1103/2lgr-34qp
Abstract
We develop the algebraic method based on the Lie algebra of quadratic combinations of left and right superoperators associated with matrices to study the Lindblad dynamics of multimode bosonic systems coupled a thermal bath and described by the Liouvillian superoperator that takes into account both dynamical (coherent) and environment mediated (incoherent) interactions between the modes. Our algebraic technique is applied to transform the Liouvillian into the diagonalized form by eliminating jump superoperators and solve the spectral problem. The temperature independent effective non-Hermitian Hamiltonian, , is found to govern both the diagonalized Liouvillian and the spectral properties. It is shown that the Liouvillian exceptional points are represented by the points in the parameter space where the matrix, , associated with is non-diagonalizable. We use our method to derive the low-temperature approximation for the superpropagator and to study the special case of a two mode system representing the photonic polarization modes. For this system, we describe the geometry of exceptional points in the space of frequency and relaxation vectors parameterizing the intermode couplings and, for a single-photon state, evaluate the time dependence of the speed of evolution as a function of the angles characterizing the couplings and the initial state.
arXiv comment21 pages, 3 figures, revised version
References in corpus (73)
- Quantum cryptography: Public key distribution and coin tossing
- Quantum sensing
- QuTiP: An open-source Python framework for the dynamics of open quantum systems
- Advances in Quantum Cryptography
- The Quantum Jump Approach to Dissipative Dynamics in Quantum Optics
- Quantum Non-Markovianity: Characterization, Quantification and Detection
- Advances in Quantum Teleportation
- Quantum trajectories and open many-body quantum systems
- Open Quantum Systems. An Introduction
- The maximum speed of dynamical evolution
- Advances in Photonic Quantum Sensing
- A short introduction to the Lindblad Master Equation
- Quantum speed limits: from Heisenberg's uncertainty principle to optimal quantum control
- Quantum speed limit for physical processes
- Quantum speed limit for non-Markovian dynamics
- Quantum speed limits in open system dynamics
- Third quantization: a general method to solve master equations for quadratic open Fermi systems
- Symmetries and conserved quantities in Lindblad master equations
- Quantum exceptional points of non-Hermitian Hamiltonians and Liouvillians: The effects of quantum jumps
- Quantum channels and memory effects
- Dynamics of the entanglement between two oscillators in the same environment
- The fundamental limit on the rate of quantum dynamics: the unified bound is tight
- Quantum Noise Theory of Exceptional Point Sensors
- Quantum Adiabatic Markovian Master Equations
- Generalized Geometric Quantum Speed Limits
- Quantization of quasinormal modes for open cavities and plasmonic cavity-QED
- General Theory of Spontaneous Emission Near Exceptional Points
- Hybrid-Liouvillian formalism connecting exceptional points of non-Hermitian Hamiltonians and Liouvillians via postselection of quantum trajectories
- Exact Master Equation and Quantum Decoherence of Two Coupled Harmonic Oscillators in a General Environment
- Entanglement and purity of two-mode Gaussian states in noisy channels
- Dynamical phases for the evolution of the entanglement between two oscillators coupled to the same environment
- Entangling oscillators through environment noise
- Accurate Lindblad-Form Master Equation for Weakly Damped Quantum Systems Across All Regimes
- Quantum Speed Limit Bounds in an Open Quantum Evolution
- Simple Derivation of the Lindblad Equation
- 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 and anti- symmetries
- Decoherence and Entanglement in Two-mode Squeezed Vacuum States
- Speeding up entanglement generation by proximity to higher-order exceptional points
- Continuous Gaussian Measurements of the Free Boson CFT: A model for Exactly Solvable and Detectable Measurement-Induced Dynamics
- Disentanglement in Bipartite Continuous-Variable Systems
- Exact solutions of interacting dissipative systems via weak symmetries
- Exceptional points for parameter estimation in open quantum systems: Analysis of the Bloch equations
- Exceptional entanglement phenomena: non-Hermiticity meeting non-classicality
- Role of non-Markovianity and backflow of information in the speed of quantum evolution
- Solution of the Lindblad Equation in the Kraus Representation
- Quantum metrology in a non-Markovian quantum evolution
- phase transition in open quantum systems with Lindblad dynamics
- Gaussian Quantum Trajectories for the Variational Simulation of Open Quantum-Optical Systems
- Evolution speed of open quantum dynamics
- Quantum statistics of overlapping modes in open resonators
- The quantum regression theorem for out-of-time-ordered correlation functions
- Solving the quantum master equation of coupled harmonic oscillators with Lie algebra methods
- Encircling the Liouvillian exceptional points: a brief review
- Quantum statistical signature of symmetry breaking
- Quantum and classical correlations in open quantum-spin lattices via truncated-cumulant trajectories
- Quantum speed limit in quantum sensing
- Spectral resolution of the Liouvillian of the Lindblad master equation for a harmonic oscillator
- Continuous-variable entanglement in a two-mode lossy cavity: an exact solution
- Quantum Regression theorem for multi-time correlators : A detailed analysis in the Heisenberg Picture
- On the Thermal Symmetry of the Markovian Master Equation
- Experimental Investigation of Geometric Quantum Speed Limits in an Open Quantum System
- Creating and controlling exceptional points of non-Hermitian Hamiltonians via homodyne Lindbladian invariance
- Stabilizing entanglement in two-mode Gaussian states
- Quantum speed limit of a noisy continuous-variable system
- The effect of thermal photons on exceptional points in coupled resonators
- Quantum Speed Limit in Terms of Coherence Variations
- Eigenvalues of the Liouvillians of Quantum Master Equation for a Harmonic Oscillator
- Quantum speed of evolution in a Markovian bosonic environment
- Unconventional steady states and topological phases in an open two-level non-Hermitian system
- Solutions of generic bilinear master equations for a quantum oscillator -- positive and factorized conditions on stationary states
- The effect of Homodyne-based feedback control on quantum speed limit time
- Simulation of exceptional-point systems on quantum computers for quantum sensing