Symmetry of a Square-Wave Modulated Two-Level System**Supported by the National Natural Science Foundation of China (Grant Nos. 11674285 and 11834005) and the National Key Research and Development Program of China (Grant No. 2017YFA0303002).

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 phase diagram are captured exactly. Two kinds of 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 symmetry breaking in the (2k – 1)-photon resonance (Δ = (2k – 1) ω), with k = 1,2,3… It is worth noting that such a phenomenon can also happen in 2k-photon resonance (Δ = 2kΔ), as long as the dissipation strengths or the driving times are imbalanced, namely γ0 ≠ – γ1 or T0 ≠ T1. For the time-periodic coupling, the weak dissipation induced symmetry breaking occurs at Δeff = kω, where Δeff = (Δ0T0 + Δ1T1)/T. In the high frequency limit, the phase boundary is given by a simple relation γeff = ±Δeff.