Institute of Spintronics and Quantum Information, Faculty of Physics, Adam Mickiewicz University, 61-614, Poznań, Poland.
RCPTM, Joint Laboratory of Optics of Palacký University and Institute of Physics of Czech Academy of Sciences, 17. listopadu 12, 771 46, Olomouc, Czech Republic.
Sci Rep. 2023 Apr 11;13(1):5859. doi: 10.1038/s41598-023-32864-2.
We analyse two quantum systems with hidden parity-time ([Formula: see text]) symmetry: one is an optical device, whereas another is a superconducting microwave-frequency device. To investigate their symmetry, we introduce a damping frame (DF), in which loss and gain terms for a given Hamiltonian are balanced. We show that the non-Hermitian Hamiltonians of both systems can be tuned to reach an exceptional point (EP), i.e., the point in parameter space at which a transition from broken to unbroken hidden [Formula: see text] symmetry takes place. We calculate a degeneracy of a Liouvillian superoperator, which is called the Liouvillian exceptional point (LEP), and show that, in the optical domain, LEP is equivalent to EP obtained from the non-Hermitian Hamiltonian (HEP). We also report breaking the equivalence between LEP and HEP by a non-zero number of thermal photons for the microwave-frequency system.
我们分析了两个具有隐藏宇称-时间（PT）对称性的量子系统：一个是光学器件，另一个是超导微波频率器件。为了研究它们的对称性，我们引入了一个耗散框架（DF），在这个框架中，给定哈密顿量的损耗和增益项是平衡的。我们表明，这两个系统的非厄米哈密顿量都可以被调谐到一个异常点（EP），即在参数空间中，从被破坏的隐藏 PT 对称性到未被破坏的对称性的转变发生的点。我们计算了李雅普诺夫超算符的简并度，称为李雅普诺夫异常点（LEP），并表明，在光学领域，LEP 等价于由非厄米哈密顿量（HEP）得到的 EP。我们还报告了通过微波频率系统中的非零数目的热光子打破了 LEP 和 HEP 之间的等价性。
