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

By Fabrizio Minganti, Adam Miranowicz, Ravindra W. Chhajlany, Franco Nori. Physical Review A, 2019

343 citations recorded by the source corpus.

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.

Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/0ae0d7f88ff1698ba61103916ed21d04e2ec7a52

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In Atomic and Molecular Physics, and Optics

In Statistical and Nonlinear Physics

Franco Nori

Citations in the corpus

Hybrid-Liouvillian formalism connecting exceptional points of non-Hermitian Hamiltonians and Liouvillians via postselection of quantum trajectories (2020, background): “From a Liouvillian point of view, postselecting the trajectories without quantum jumps corresponds to consider a Liouvillian without quantum jumps (L′) [13].”
Chiral control of quantum states in non-Hermitian spin–orbit-coupled fermions (2021, background): “This is an appropriate approximation for a large number of nearly non-interacting atoms, smearing out the effect of the quantum jumps [28, 42].”