Dynamical Stability in a Non-Hermitian Kicked Rotor Model

Abstract

We investigate the quantum irreversibility and quantum diffusion in a non-Hermitian kicked rotor model for which the kicking strength is complex. Our results show that the exponential decay of Loschmidt echo gradually disappears with increasing the strength of the imaginary part of non-Hermitian driven potential, demonstrating the suppress of the exponential instability by non-Hermiticity. The quantum diffusion exhibits the dynamical localization in momentum space, namely, the mean square of momentum increases to saturation with time evolution, which decreases with the increase of the strength of the imaginary part of the kicking. This clearly reveals the enhancement of dynamical localization by non-Hermiticity. We find, both analytically and numerically, that the quantum state are mainly populated on a very few quasieigenstates with significantly large value of the imaginary part of quasienergies. Interestingly, the average value of the inverse participation ratio of quasieigenstates decreases with the increase of the strength of the imaginary part of the kicking potential, which implies that the feature of quasieigenstates determines the stability of wavepacket’s dynamics and the dynamical localization of energy diffusion.

Dynamical localization in a non-Hermitian Floquet synthetic system

“…[47][48][49] Recently, the extension of Floquet synthetic systems to non-Hermitian regime enables the investigations on novel physics that might not be easily achievable in Hermitian settings. It is found that the combination of non-Hermiticity and nonlinear interaction leads to superexponentially fast energy diffusion, [50] the non-Hermitian driven potential enhances the degree of DL [51][52][53][54] and induces the quantum criticality of information scrambling. [55] The versatile nature of Floquet synthetic systems opens the opportunity for exploring diverse regimes of quantum behavior by tailoring system parameters and controlling interactions.…”

Scaling laws of the out-of-time-order correlators at the transition to the spontaneous $\cal{PT}$-symmetry breaking in a Floquet system

“…Theoretical advances have enabled exponential realizations of PT symmetric systems in various fields, such as optical settings [26][27][28][29][30][31][32][33][34][35][36][37], electronic circuits [38], and optomechanical systems [39]. Moreover, the extension of Floquet-driven systems to the PT symmetric regime has opened up unique opportunities for understanding fundamental concepts such as quantum chaos [40] and quantum-classical transition [41,42]. Interestingly, chaos is found to facilitate the scaling law of the spontaneous PT symmetry breaking in a PT symmetric kicked rotor (PTKR) model [43].…”