Long-time fidelity and chaos for a kicked nonlinear oscillator system

Abstract

We deal with a system comprising a nonlinear (Kerr-like) oscillator excited by a series of ultra-short external pulses. We introduce the fidelity-based entropic parameter that can be used as an indicator of quantum chaos. Moreover, we propose to use the fidelity-like parameter comprising the information about the mean number of photons in the system. We shall concentrate on the long-time behaviour of the parameters discussed, showing that for deep chaos cases the quantum fidelities behave chaotically in the classical sense despite their strictly quantum character.

Relaxation Dynamics in the Spin-1 Heisenberg Antiferromagnetic Chain after a Quantum Quench of the Uniaxial Anisotropy

“…Nonetheless, the time evolution of the initial state |ψ(t) = e − i Ht |ψ 0 (11) takes place in the anisotropic Hamiltonian subspace again corresponding to total spin zero. In order to measure the overlap of the time-evolved state and the initial state we can use, so-called, the Loschmidt echo (also called "quantum fidelity" commonly applied in the fields of quantum information and quantum chaos [36]) defined as [37]:…”

High fidelity state mapping performed in a V-type level structure via stimulated Raman transition

“…Moreover, it seems likely that there is no prefect state mapping consisting of more than one laser pulse. However, it is hard to prove it because there are infinitely many possible sequences of laser pulses -from two different pulses to series of very many ultra-short pulses as in [67].…”

Nonclassical light at exceptional points of a quantum PT -symmetric two-mode system

“…without considering mode amplification and even its balance with damping, they already allow for the observation of squeezing and antibunching as well as the generation of quantum entanglement [77]. Such quantum Kerr oscillators, as nonlinear systems, also exhibit quantum chaotic behavior under suitable conditions [78][79][80][81][82]. When analyzed at the single-photon level, the so-called photon (phonon) blockade effects may occur in the Kerr coupled systems.…”