$\mathcal{P}\mathcal{T}$-symmetry from Lindblad dynamics in an optomechanical system

Abstract

The optomechanical state transfer protocol provides effective, lossy, quantum beam-splitter-like dynamics where the strength of the coupling between the electromagnetic and mechanical modes is controlled by the optical steady-state amplitude. By restricting to a subspace with no losses, we argue that the transition from mode-hybridization in the strong coupling regime to the damped-dynamics in the weak coupling regime, is a signature of the passive parity-time ($\mathcal{P}\mathcal{T}$) symmetry breaking transition in the underlying non-Hermitian quantum dimer. We compare the dynamics generated by the quantum open system (Langevin or Lindblad) approach to that of the $\mathcal{P}\mathcal{T}$-symmetric Hamiltonian, to characterize the cases where the two are identical. Additionally, we numerically explore the evolution of separable and correlated number states at zero temperature as well as thermal initial state evolution at room temperature. Our results provide a pathway for realizing non-Hermitian Hamiltonians in optomechanical systems at a quantum level.

14 pages, 6 figures

References in corpus (21)

• Cavity Optomechanics
• Ground-state cooling of a micromechanical oscillator: generalized framework for cold damping and cavity-assisted cooling schemes
• Observation of parity-time symmetry breaking transitions in a dissipative Floquet system of ultracold atoms
• Physical realization of $\mathcal{P}\mathcal{T}$-symmetric potential scattering in a planar slab waveguide
• 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
• Parametric Normal-Mode Splitting in Cavity Optomechanics
• Phonon counting and intensity interferometry of a nanomechanical resonator
• Quantum noise and self-sustained radiation of PT-symmetric systems
• Spontaneous Generation of Photons in Transmission of Quantum Fields in PT Symmetric Optical Systems
• PT-symmetric photonic quantum systems with gain and loss do not exist
• Optical waveguide arrays: quantum effects and PT symmetry breaking
• Comparison and unification of non-Hermitian and Lindblad approaches with applications to open quantum optical systems
• Exceptional points of any order in a single, lossy, waveguide beamsplitter by photon-number-resolved detection
• Passive $\mathcal{P}\mathcal{T}$-symmetry breaking transitions without exceptional points in dissipative photonic systems
• Observation of slowly decaying eigenmodes without exceptional points in Floquet, dissipative, synthetic circuits
• Revisiting the optical $PT$-symmetric dimer
• Quantum interference and exceptional points
• Optical finite representation of the Lorentz group
• Robust optomechanical state transfer under composite phase driving
• Photon propagation through linearly active dimers

Cited by in corpus (21)

• Hybrid-Liouvillian formalism connecting exceptional points of non-Hermitian Hamiltonians and Liouvillians via postselection of quantum trajectories
• 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
• Dislocation Non-Hermitian Skin Effect
• Emergence of PT-symmetry breaking in open quantum systems
• Non-Dissipative Non-Hermitian Dynamics and Exceptional Points in Coupled Optical Parametric Oscillators
• Generating high-order quantum exceptional points in synthetic dimensions
• Experimental simulation of the Parity-Time-symmetric dynamics using photonics qubits
• Emergent $\mathcal{P}\mathcal{T}$ symmetry in a double-quantum-dot circuit QED set-up
• Quantum correlations in $\mathcal{P}\mathcal{T}$-symmetric systems
• Chiral current circulation and $\mathcal{P}\mathcal{T}$ symmetry in a trimer of oscillators
• Lyapunov equation in open quantum systems and non-Hermitian physics
• Universal subdiffusive behavior at band edges from transfer matrix exceptional points
• Parametrically driving a quantum oscillator into exceptionality
• Generating high-order exceptional points in coupled electronic oscillators using complex synthetic gauge fields
• Unbalanced gain and loss in a quantum photonic system
• Operator correlations in a quenched non-Hermitian Luttinger liquid
• Non-Hermitian physics and engineering in silicon photonics
• $\mathcal{P}\mathcal{T}$-Symmetry breaking in quantum spin chains with exceptional non-Hermiticities
• Density operator approach to turbulent flows in plasma and atmospheric fluids
• Improved coherence time of a non-Hermitian qubit in a $\mathcal{P}\mathcal{T}$-symmetric Environment
• Optomechanical simulation of a parametric oscillator