PT Symmetry of a Square-Wave Modulated Two-Level System

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 PT diagram are captured exactly.Two kinds of PT symmetry broken phases are found,whose effective Hamiltonians differ by a constant ω/2.For the time-periodic dissipation,a vanishingly small dissipation strength can lead to the PT symmetry breaking in the (2k-1)-photon resonance(△=(2k-1)ω),with k=1,2,3…It is worth noting that such a phenomenon can also happen in 2k-photon resonance(△=2kω),as long as the dissipation strengths or the driving times are imbalanced,namely γo≠-γ1orT0≠T1.For the time-periodic coupling,the weak dissipation induced$\mathcal{PT}$symmetry breaking occurs at △eff=kω,where △eff=(△0T0+△1 T1)/T.In the high frequency limit,the phase boundary is given by a simple relation γeff=±△eff.