$\mathcal{P}\mathcal{T}$ symmetry of a square-wave modulated two-level system

Abstract

We study a non-Hermitian two-level system with square-wave modulated dissipation and coupling. Based on the Floquet theory, we achieve an effective Hamiltonian from which the boundaries of the $\mathcal{P}\mathcal{T}$ phase diagram are captured exactly. Two kinds of $\mathcal{P}\mathcal{T}$ symmetry broken phases are found whose effective Hamiltonians differ by a constant $\omega /2$. For the time-periodic dissipation, a vanishingly small dissipation strength can lead to the $\mathcal{P}\mathcal{T}$ symmetry breaking in the $(2k-1)$-photon resonance ($\Delta =(2k-1)\omega$), with $k=1,2,3\dots$ It is worth noting that such a phenomenon can also happen in $2k$-photon resonance ($\Delta =2k\omega$), as long as the dissipation strengths or the driving times are imbalanced, namely ${\gamma }_0\ne -{\gamma }_1$ or $T_0\ne T_1$. For the time-periodic coupling, the weak dissipation induced $\mathcal{P}\mathcal{T}$ symmetry breaking occurs at ${\Delta }_{\mathrm{eff}}=k\omega$, where ${\Delta }_{\mathrm{eff}}=\left({\Delta }_0{T}_0+{\Delta }_1{T}_1\right)/T$. In the high frequency limit, the phase boundary is given by a simple relation ${\gamma }_{\mathrm{eff}}=\pm {\Delta }_{\mathrm{eff}}$.

arXiv comment9 pages, 5 figures

References in corpus (35)

• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• Making Sense of Non-Hermitian Hamiltonians
• Edge states and topological invariants of non-Hermitian systems
• Complex Extension of Quantum Mechanics
• Topological phases of non-Hermitian systems
• Symmetry and Topology in Non-Hermitian Physics
• Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems
• Topological Band Theory for Non-Hermitian Hamiltonians
• Nonlinear waves in $\mathcal{P}\mathcal{T}$-symmetric systems
• Anomalous edge state in a non-Hermitian lattice
• Non-Bloch Band Theory of Non-Hermitian Systems
• Non-Hermitian Chern bands
• Edge Modes, Degeneracies, and Topological Numbers in Non-Hermitian Systems
• Non-Hermitian skin effect and chiral damping in open quantum systems
• Observation of parity-time symmetry breaking transitions in a dissipative Floquet system of ultracold atoms
• Introduction to PT-Symmetric Quantum Theory
• Second-Order Topological Phases in Non-Hermitian Systems
• Physical realization of $\mathcal{P}\mathcal{T}$-symmetric potential scattering in a planar slab waveguide
• Observation of the exceptional point in cavity magnon-polaritons
• Topological unification of time-reversal and particle-hole symmetries in non-Hermitian physics
• Observation of critical phenomena in parity-time-symmetric quantum dynamics
• Generating Many Majorana Modes via Periodic Driving: A Superconductor Model
• Entanglement and spin squeezing in non-Hermitian phase transitions
• Higher-order exceptional point in a cavity magnonics system
• Pseudo Parity-Time Symmetry in Optical Systems
• Experimental realization of Floquet PT-symmetric systems
• Towards large-Chern-number topological phases by periodic quenching
• PT spectroscopy of the Rabi problem
• Stabilizing Non-Hermitian Systems by Periodic Driving
• PT-symmetric Rabi model: Perturbation theory
• Floquet control of quantum dissipation in spin chains
• Non-Hermitian Hamiltonian for a Modulated Jaynes-Cummings Model with PT Symmetry
• Analytical results for a parity-time symmetric two-level system under synchronous combined modulations
• Dark soliton of polariton condensates under nonresonant PT-symmetric pumping
• Piecewise Adiabatic Following: General Analysis and Exactly Solvable Models

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