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arXiv:2005.04627 · New Journal of Physics

Controlling stable tunneling in a non-Hermitian spin–orbit coupled bosonic junction

Yunrong Luo, Xuemei Wang, Yuxin Luo, Zheng Zhou, Zhao‐Yun Zeng, Xiaobing Luo

Published Aug 20, 2020• 17 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1088/1367-2630/abb03f

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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.
We present an analytical framework for stabilizing second-order correlated tunneling of two spin-orbit-coupled bosons in a periodically driven non-Hermitian double-well potential. By combining Floquet theory with multiple-scale asymptotic analysis, we derive effective second-order dynamics and exact quasienergy spectra in the strongly interacting regime. Our analysis reveals distinct stability mechanisms for three fundamental tunneling channels: interwell spin-conserving, interwell spin-flipping, and intrawell spin-flipping. For balanced gain and loss, we identify discrete, well-defined parameter regions where stable pair tunneling emerges, with the spin-flipping channel exhibiting a characteristic symmetry absent in its spin-conserving counterpart. Under unbalanced gain-loss conditions, stability is achieved only when the gain and loss coefficients satisfy specific parametric relations, enabling dissipation-controlled tunneling. Most notably, stable intrawell spin-flipping, while inherently unstable for an initial Fock state, becomes accessible when the system is prepared in a coherent superposition state, thereby revealing that initial-state coherence can serve as a control parameter for dynamical stability in non-Hermitian systems. These results expand the possibilities for controlling correlated tunneling in many-body systems with engineered dissipation.
We study the stability of spin dynamics for a spin-orbit (SO) coupled boson held in a driven non-Hermitian double-well potential. Under high-frequency approximation, we analytically derive the Floquet states and complex Floquet quasienergies of the system and reveal a striking parity-dependent stability criterion: when the ratio of the Zeeman field strength to the driving frequency Ω/ωΩ/ωΩ/ω is even, stable spin dynamics can be achieved for \emph{arbitrary} SO coupling strength. However, when Ω/ωΩ/ωΩ/ω is odd, stability requires the SO coupling strength to be integer or half-integer values. Particularly, we find four types of stability boundary lines for non-zero bias field strength, in sharp contrast to the commonly observed stability regions. These results establish a tunable parity-governed mechanism for stabilizing spin dynamics in non-Hermitian cold atomic systems.
Abstract We propose a simple method of synchronous combined modulations to generate the exact analytic solutions for a spin–orbit (SO) coupled ultracold atom held in a non-Hermitian double-well potential. Based on the obtained analytical solutions, we mainly study the parity-time ( P T ) symmetry of this system and the system stability for both balanced and unbalanced gain–loss between two wells. Under balanced gain and loss, the effect of the proportional constants between synchronous combined modulations and the SO-coupling strength on the P T -symmetry breaking is revealed analytically. Surprisingly, we find when the Zeeman field is present, the stable spin-flipping tunneling between two wells cannot occur in the non-Hermitian SO-coupled ultracold atomic system, but the stable spin-conserving tunneling can be performed. Under unbalanced gain and loss, the unique set of parameter conditions that can cause the system to stabilize is found. The results may provide a possibility for the exact control of P T -symmetry breaking and quantum spin dynamics in a non-Hermitian SO-coupled system.
Abstract In this paper, we investigate the spin and tunneling dynamics of a spin–orbit-coupled noninteracting Bose–Einstein condensate in a periodically driven non-Hermitian double-well potential. Under high-frequency driving, we obtain the effective time-averaged Hamiltonian by using the standard time-averaging method, and analytically calculate the Floquet quasienergies, revealing that the parity-time ( )-breaking phase transition appears even for arbitrarily small non-Hermitian parameters when the spin–orbit coupling strength takes half-integer value, irrespective of the values of other parameters used. When the system is -symmetric with balanced gain and loss, we find numerically and analytically that in the broken -symmetric regions, there will exist the net spin current together with a vanishing atomic current, if we drop the contribution of the exponential growth of the norm to the current behaviors. When the system is non- -symmetric, though the quasienergies are partial complex, a stable net spin current can be generated by controlling the periodic driving field, which is accompanied by a spatial localization of the condensate in the well with gain. The results deepen the understanding of non-Hermitian physics and could be useful for engineering a variety of devices for spintronics.
We propose a simple method of synchronous combined modulations to generate the exact analytic solutions for a spin-orbit (SO) coupled ultracold atom held in a non-Hermitian double-well potential. Based on the obtained analytical solutions, we mainly study the parity-time (PT\mathcal{PT}PT) symmetry of this system and the system stability for both balanced and unbalanced gain-loss between two wells. Under balanced gain and loss, the effect of the proportional constants between synchronous combined modulations and the SO-coupling strength on the PT\mathcal{PT}PT-symmetry breaking is revealed analytically. Surprisingly, we find when the Zeeman field is present, the stable spin-flipping tunneling between two wells can not occur in the non-Hermitian SO-coupled ultracold atomic system, but the stable spin-conserving tunneling can be performed. Under unbalanced gain and loss, the unique set of parameter conditions that can cause the system to stabilize is found. The results may provide a possibility for the exact control of PT\mathcal{PT}PT-symmetry breaking and quantum spin dynamics in a non-Hermitian SO-coupled system.
Abstract We theoretically study the tunneling dynamics of two interacting spin–orbit-coupled (SOC) atoms trapped in a periodically perturbed double-well potential. We find that the phenomenon of coherent destruction of tunneling (CDT) can exist only for certain values of SOC, and two different mechanisms for the appearance of CDT are identified in this system. One is the conventional CDT resulting from quasi-energy degeneracy, while the other CDT originates from the dark Floquet state with zero quasi-energy for all values of the driving parameters. We discover that under double modulation combining the double-well potential shaking and a time-periodic Zeeman field, it is possible to realize spin-flipping single-atom Rabi tunneling and the CDT induced by the dark Floquet state at any value of SOC strength, which is not accessible with a single-drive field. Furthermore, we show that the detuning of Zeeman field with respect to the multiphoton energy is particularly significant in the case of the correlated two-particle tunneling mediated by SOC. We expect that these results will stimulate further exploration of the many-body dynamics in the interacting systems and expand the possibilities for manipulating the spin dynamics.