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arXiv:2210.13724

Exact solutions for a spin-orbit coupled bosonic double-well system

Yunrong Luo, Xuemei Wang, Jia Yi, Wenjuan Li, Xin Xie, Wenhua Hai

Published Oct 25, 2022• 1 citation
arXivHTMLPDF

Abstract

Exact solutions for spin-orbit (SO) coupled cold atomic systems are very important and rare in physics. In this paper, we propose a simple method of combined modulations to generate the analytic exact solutions for an SO-coupled boson held in a driven double well. For the cases of synchronous combined modulations and the spin-conserving tunneling, we obtain the general analytical accurate solutions of the system respectively. For the case of spin-flipping tunneling under asynchronous combined modulations, we get the special exact solutions in simple form when the driving parameters satisfy certain conditions. Based on these obtained exact solutions, we reveal some intriguing quantum spin dynamical phenomena, for instance, the arbitrary population transfer (APT) with and/or without spin-flipping, the controlled coherent population conservation (CCPC), and the controlled coherent population inversion (CCPI). The results may have potential applications in the preparation of accurate quantum entangled states and quantum information processing.

DOI
10.48550/arxiv.2210.13724

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Exact solutions for spin-orbit (SO) coupled cold atomic systems are very important and rare in physics. In this paper, we propose a simple method of combined modulations to generate the analytic exact solutions for an SO-coupled boson held in a driven double well. For the cases of synchronous combined modulations and the spin-conserving tunneling, we obtain the general analytical accurate solutions of the system respectively. For the case of spin-flipping tunneling under asynchronous combined modulations, we get the special exact solutions in simple form when the driving parameters satisfy certain conditions. Based on these obtained exact solutions, we reveal some intriguing quantum spin dynamical phenomena, for instance, the arbitrary population transfer (APT) with and/or without spin-flipping, the controlled coherent population conservation (CCPC), and the controlled coherent population inversion (CCPI). The results may have potential applications in the preparation of accurate quantum entangled states and quantum information processing.
Abstract Exact solutions for spin-orbit (SO)-coupled cold atomic systems are very important and rare in physics. In this paper, we propose a simple method of combined modulations to generate the exactly analytic solutions for a single SO-coupled ultracold atom held in a driven double well. For the cases of synchronous combined modulations and the spin-conserving tunneling, we obtain the generally accurate solutions of this system respectively. For the case of spin-flipping tunneling under asynchronous combined modulations, we get the specially exact solutions in simple form when the driving parameters are appropriately chosen. Based on these obtained exact solutions, we reveal some intriguing quantum spin dynamical phenomena, for instance, the arbitrary coherent population transfer with and/or without spin-flipping, the controlled coherent population conservation, and the controlled coherent population inversion. The results may provide a possibility for generating the accurate quantum entangled states and the exact control of spin dynamics for a SO-coupled ultracold atomic system.
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 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 We investigate the coherent control of spin tunneling for a spin–orbit (SO) coupled boson trapped in a driven triple well. In the high-frequency limit, the quasienergies of the system are obtained analytically and the fine energy band structures are shown. By regulating the driving parameters, we reveal that the directed spin-flipping or spin-conserving tunneling of an SO-coupled boson occurs along different pathways and in different directions. The analytical results are demonstrated by numerical simulations and good agreements are found. Further, an interesting scheme of quantum spin tunneling switch with or without spin-flipping is presented. The results may have potential applications in the design of spintronic devices.
We study the coherent manipulation of quantum spin dynamics via simple analytic solutions for a spin–orbit (SO) coupled ultracold atom held in a driven double well. In the high-frequency regime, we analytically obtain the quasienergies, the Floquet states, and the non-Floquet state of this system. When the system parameters are properly selected, the non-Floquet state reduces to special quantum states of simple forms which can provide a more intuitive understanding of some interesting quantum spin dynamical phenomena, such as the intrawell spin–flipping, the interwell spin-conserving tunneling, and the interwell spin–flipping tunneling. Specially, for the interwell spin–flipping tunneling, we surprisingly find that the selective coherent destruction of tunneling (SCDT) can occur at the anti-crossing (non-collapse) points of quasienergy spectrum, which breaks the conventional understanding that the SCDT is associated with the crossing of quasienergy levels. Further, we reveal the interwell spin–flipping tunneling strongly depends on the initial spin direction and the initial position of the SO-coupled atom. These novel results can be readily tested by the current experimental setups and may be useful for the design of spintronic devices.
Analytically exact solutions of a driven two-level system are extremely important in many areas of physics [E. Barnes and S. Das Sarma, Phys. Rev. Lett. 109, 060401 (2012)]. Here we present a simple method of synchronous and asynchronous combined modulations to generate such exact solutions, and apply several of the simplest solutions to perform the coherent control of quantum states. The interesting physical phenomena, such as the arbitrary population transfers between the different and/or asymptotic stationary states and the controlled coherent population oscillation, are achieved analytically and numerically. Simplification of the exact solutions and the modulated fields renders the control strategies more transparent and the qubit manipulation more convenient in experiments.