Abstract
In this paper, we study how to apply a periodic driving field to control stable spin tunneling in a non-Hermitian spin–orbit (SO) coupled bosonic double-well system. By means of a high-frequency approximation, we obtain the analytical Floquet solutions and their associated quasienergies and thus construct the general non-Floquet solutions of the dissipative SO coupled bosonic system. Based on detailed analysis of the Floquet quasienergy spectrum, the profound effect of system parameters and the periodic driving field on the stability of spin-dependent tunneling is investigated analytically and numerically for both balanced and unbalanced gain–loss between two wells. Under balanced gain and loss, we find that the stable spin-flipping tunneling is preferentially suppressed with the increase of gain–loss strength. When the ratio of Zeeman field strength to periodic driving frequency Ω/ω is even, there is a possibility that continuous stable parameter regions will exist. When Ω/ω is odd, nevertheless, only discrete stable parameter regions are found. Under unbalanced gain and loss, whether Ω/ω is even or odd, we can get parametric equilibrium conditions for the existence of stable spin tunneling. The results could be useful for the experiments of controlling stable spin transportation in a non-Hermitian SO coupled system.
Highlights
Based on the stability analysis, we find the stability of spin-dependent dynamics depends on the competition and balance between the effective coupling parameters and the gain-loss coefficients
We have systematically explored how the interplay between periodic driving, dissipation, and other system parameters influences the stability of the spindependent tunneling in the SO-coupled bosonic junction, by taking into account balanced/unbalanced gain-loss between two wells
We find that the continuous stable parameter regions disappear and the discrete stable parameter regions instead emerge, as shown in Fig. 1 (b)
Summary
Over the last two decades, non-Hermitian systems have attracted increasing interest from both fundamental and application viewpoints[1,2,3,4,5,6,7,8,9,10,11], which has spawned a great deal of research work in many branches of physics, ranging from atomic and molecular physics[1, 12] to spin and magnetic systems[13, 14], quantum computing[15, 16], and mesoscopic solid-state structures[17, 18]. There have been some works focusing on the intriguing dynamics of the SO-coupled cold atomic gases, including Josephson dynamics of a SO-coupled Bose-Einstein condensate in a double-well potential[57,58,59], collective dynamics[54, 60, 61], selective coherent spin transportation in a SO-coupled bosonic junction[62], Klein tunneling[63], nonequilibrium dynamics of SO-coupled lattice bosons[64], tunable LandauZener transitions in SO-coupled atomic gases[65], controlling spin-dependent localization and directed transport in a bipartite lattice[66], Bloch oscillations of SOcoupled cold atoms in an optical lattice[67], dynamics of SO-coupled cold atomic gases in a Floquet lattice with an impurity[68], and so on All these achievements are hitherto limited in studying the properties of quantum dynamics of SO-coupled cold atoms with Hermitian potential. The results could be useful for the experiments of manipulating stable spin transportation via a periodic driving field in a non-Hermitian SO-coupled system
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