Quantum exceptional points of non-Hermitian Hamiltonians and Liouvillians: The effects of quantum jumps

被引:208
|
作者
Minganti, Fabrizio [1 ]
Miranowicz, Adam [1 ,2 ]
Chhajlany, Ravindra W. [1 ,2 ]
Nori, Franco [1 ,3 ]
机构
[1] RIKEN, Cluster Pioneering Res, Theoret Quantum Phys Lab, Wako, Saitama 3510198, Japan
[2] Adam Mickiewicz Univ, Fac Phys, PL-61614 Poznan, Poland
[3] Univ Michigan, Dept Phys, Ann Arbor, MI 48109 USA
基金
日本学术振兴会; 日本科学技术振兴机构;
关键词
PARITY-TIME SYMMETRY; PHOTON; STATES;
D O I
10.1103/PhysRevA.100.062131
中图分类号
O43 [光学];
学科分类号
070207 ; 0803 ;
摘要
Exceptional points (EPs) correspond to degeneracies of open systems. These are attracting much interest in optics, optoelectronics, plasmonics, and condensed matter physics. In the classical and semiclassical approaches, Hamiltonian EPs (HEPs) are usually defined as degeneracies of non-Hermitian Hamiltonians such that at least two eigenfrequencies are identical and the corresponding eigenstates coalesce. HEPs result from continuous, mostly slow, nonunitary evolution without quantum jumps. Clearly, quantum jumps should be included in a fully quantum approach to make it equivalent to, e.g., the Lindblad master equation approach. Thus, we suggest to define EPs via degeneracies of a Liouvillian superoperator (including the full Lindbladian term, LEPs), and we clarify the relations between HEPs and LEPs. We prove two main theorems: Theorem 1 proves that, in the quantum limit, LEPs and HEPs must have essentially different properties. Theorem 2 dictates a condition under which, in the "semiclassical" limit, LEPs and HEPs recover the same properties. In particular, we show the validity of Theorem 1 studying systems which have (1) an LEP but no HEPs and (2) both LEPs and HEPs but for shifted parameters. As for Theorem 2, (3) we show that these two types of EPs become essentially equivalent in the semiclassical limit. We introduce a series of mathematical techniques to unveil analogies and differences between the HEPs and LEPs. We analytically compare LEPs and HEPs for some quantum and semiclassical prototype models with loss and gain.
引用
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页数:17
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