$\mathcal{P}\mathcal{T}$ 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 ${\gamma }_{\mathrm{eff}}=\pm {\Delta }_{\mathrm{eff}}$.

9 pages, 5 figures

References in corpus (9)

• Making Sense of Non-Hermitian Hamiltonians
• Edge Modes, Degeneracies, and Topological Numbers 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
• Entanglement and spin squeezing in non-Hermitian phase transitions
• PT spectroscopy of the Rabi problem
• Stabilizing Non-Hermitian Systems by Periodic Driving
• Floquet control of quantum dissipation in spin chains
• Non-Hermitian Hamiltonian for a Modulated Jaynes-Cummings Model with PT Symmetry