Effect of quantum jumps on non-Hermitian system

Abstract

One among the possible realizations of non-Hermitian systems is based on open quantum systems by omitting quantum jumping terms in the master equation. This is a good approximation at short times where the effects of quantum jumps can be ignored. However, the jumps can affect the long time dynamics of the system, motivating us to take the jumps into account in these studies. In this paper, by treating the quantum jumps as perturbations, we examine the effect of the quantum jumps on the non-Hermitian system. For this purpose, we first derive an effective Hamiltonian to describe the dynamics of the open quantum system based on the master equation, then expand the eigenstates and eigenenergies up to the first and second order in the quantum jumps. Finally, we apply our theory to a dissipative two-level system and dissipative fermionic superfluids. The effect of quantum jump on the dynamics and the nonequilibrium phase transition is demonstrated and discussed.

9 pages,7 figures

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• Pseudo-Hermitian extensions of the harmonic and isotonic oscillators
• Topological extension including quantum jump
• Local Non-Hermitian Hamiltonian Formalism for Dissipative Fermionic Systems and Loss-Induced Population Increase in Fermi Superfluids
• A Hermitian bypass to the non-Hermitian quantum theory
• Adiabatic charge transport through non-Bloch bands