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

• URL: http://arxiv.org/abs/2008.07068v1
• Date: Mon, 17 Aug 2020 03:18:36 GMT
• Title: $\mathcal{PT}$ symmetry of a square-wave modulated two-level system
• Authors: Liwei Duan, Yan-Zhi Wang, Qing-Hu Chen
• Abstract summary: 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 $mathcalPT$ phase diagram are captured.
• Score: 23.303857456199328
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 $\mathcal{PT}$ phase diagram are captured exactly. Two kinds of $\mathcal{PT}$ 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 $\mathcal{PT}$ 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 $\mathcal{PT}$ 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 $\gamma_{\mathrm{eff}}=\pm\Delta_{\mathrm{eff}}$.

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