论文标题
$ \ MATHCAL {PT} $ Square-Wave调制的两级系统的对称性
$\mathcal{PT}$ symmetry of a square-wave modulated two-level system
论文作者
论文摘要
我们研究了具有方波调制耗散和耦合的非热式两级系统。基于Floquet理论，我们实现了一个有效的哈密顿量，从该理论中，准确地捕获了$ \ Mathcal {pt} $相位图的边界。发现了两种$ \ MATHCAL {PT} $对称损坏的相位，其有效的汉密尔顿人的有效hamiltonians差异为常数$ω/ 2 $。对于时间周期的耗散，消失的小耗散强度可能会导致$ \ mathcal {pt} $对称性在$（2k-1）$ - 光子共振（$Δ=（2k-1）ω$）中，$ k = 1,2,3 \ dots $也可以指出，这也可以指出 - $ k = 1,2,3 \ dots $ $ 2 （$δ=2kΩ$），只要耗散强度或驱动时间不平衡，即$γ_0\ ne -γ_1$或$ t_0 \ ne t_1 $。对于时间周期耦合，$ \ Mathcal {pt} $对称破裂的弱耗散发生在$δ_{\ Mathrm {eff}} =kΩ$，其中$Δ_{\δ_{\ m atrm {eff}}} = \ lest（在高频限制中，相边界由简单的关系$γ_ {\ mathrm {eff}}} = \pmδ_ {\ mathrm {eff}} $给出。
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 $ω/ 2$. For the time-periodic dissipation, a vanishingly small dissipation strength can lead to the $\mathcal{PT}$ symmetry breaking in the $(2k-1)$-photon resonance ($Δ= (2k-1) ω$), with $k=1,2,3\dots$ It is worth noting that such a phenomenon can also happen in $2k$-photon resonance ($Δ= 2k ω$), as long as the dissipation strengths or the driving times are imbalanced, namely $γ_0 \ne - γ_1$ or $T_0 \ne T_1$. For the time-periodic coupling, the weak dissipation induced $\mathcal{PT}$ symmetry breaking occurs at $Δ_{\mathrm{eff}}=kω$, where $Δ_{\mathrm{eff}}=\left(Δ_0 T_0 + Δ_1 T_1\right)/T$. In the high frequency limit, the phase boundary is given by a simple relation $γ_{\mathrm{eff}}=\pmΔ_{\mathrm{eff}}$.
