{\mathscr{P}}{\mathscr{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 ${\mathscr{P}}{\mathscr{T}}$ phase diagram are captured exactly. Two kinds of ${\mathscr{P}}{\mathscr{T}}$ 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 ${\mathscr{P}}{\mathscr{T}}$ 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 ${\mathscr{P}}{\mathscr{T}}$ 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. *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).
- Publication:
-
Chinese Physics Letters
- Pub Date:
- August 2020
- DOI:
- 10.1088/0256-307X/37/8/081101
- arXiv:
- arXiv:2008.07068
- Bibcode:
- 2020ChPhL..37h1101D
- Keywords:
-
- 11.30.Er;
- 42.82.Et;
- 03.65.Yz;
- 42.50.-p;
- Quantum Physics;
- Physics - Atomic Physics
- E-Print:
- 9 pages, 5 figures