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本文研究了一个周期驱动的非宇称-时间对称二能级量子系统的非厄米动力学。通过经典相空间分析方法,解出了该非厄米系统的Floquet态和准能谱，并解析构造了由该非厄米哈密顿量支配下的量子态的非幺正时间演化算符，给出了不同参数区域的量子态演化。本文数值和分析证明，该非宇称-时间对称二能级Floquet系统，类似于宇称-时间对称系统，存在一个准能谱从实数谱到复数谱的相变。本文还揭示了在量子态的动态演化中存在一种准宇称-时间对称动力学，即，该系统的粒子布居概率演化完全满足时间空间对称（宇称-时间对称），但是由于相位演化违反了宇称-时间对称性的要求，因此包含相位信息的量子态演化不满足时间空间对称（宇称-时间对称）。这些结果加深了对非厄米物理的理解，拓展和推广了传统的宇称-时间对称概念。In recent years, there have been intensive studies on non-Hermitian physics and parity-time (PT) symmetry, due to their fundamental importance in theory and outstanding applications. A distinctive character in PT-symmetric systems is phase transition (spontaneous PT-symmetry breaking), where the energy spectrum changes from all real to complex when the non-Hermitian parameter exceeds a certain threshold. However, the conditions for PT-symmetric system with real energy spectrum to occur are rather restrictive. Generalization of PT-symmetric potentials to wider classes of non-PT-symmetric complex potentials with all-real spectra is a currently important endeavor. The simple PT-symmetric two-level Floquet quantum system is now being actively explored, because it holds potential for realization of non-unitary single-qubit quantum gate. However, studies on the evolution dynamics of non-PT-symmetric two-level non-Hermitian Floquet quantum system still remain relatively rare.
In this paper, we investigate the non-Hermitian physics of a periodically driven non-PT-symmetric two-level quantum system. By phase-space analysis, we find that there exist so-called pseudo fixed points in phase space representing the Floquet solutions with fixed population difference and a time-dependent relative phase between the two levels. Based on these pseudo fixed points, we analytically construct the non-unitary evolution operator and then explore the dynamics of the non-PT-symmetric two-level quantum system in different parameter regions. We confirm both analytically and numerically that the two-level non-Hermitian Floquet quantum system, although being non-parity-time-symmetric, still features a phase transition with the quasienergy spectrum changing from all real to complex, just as for PT symmetric systems. Furthermore, we reveal that a novel phenomenon called quasi-PT symmetric dynamics occurs in the time evolution process. The quasi-PT symmetric dynamics is so named in our paper, in the sense that the time-evolution of population probabilities in the non-PT-symmetric two-level system respects fully the time-space symmetry (PT symmetry), while time-evolution of the quantum state (containing the phase) does not, due to the fact that time-evolution of the phases of the probability amplitudes on the two levels violates the PT symmetry requirement.-
Keywords:
- Parity-Time symmetry /
- periodically driven two-level systems /
- non-Hermitian physics /
- dynamical evolution
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