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arXiv:2405.10727 · Physical Review A

Fast transport and splitting of spin-orbit-coupled spin-1 Bose-Einstein condensates

Yaning Xu, Yuanyuan Chen, Xi Chen

Published Jun 5, 2024• 4 citations
arXivHTMLPDF

Abstract

In this study we investigate the dynamics of tunable spin-orbit-coupled spin-1 Bose-Einstein condensates confined within a harmonic trap, focusing on rapid transport, spin manipulation, and splitting dynamics. Using shortcuts to adiabaticity, we design time-dependent trap trajectories and spin-orbit-coupling strength to facilitate fast transport with simultaneous spin flip. Additionally, we showcase the creation of spin-dependent coherent states via engineering the spin-orbit-coupling strength. To deepen our understanding, we elucidate nonadiabatic transport and associated spin dynamics, contrasting them with simple scenarios characterized by constant spin-orbit coupling and trap velocity. Furthermore, we discuss the transverse Zeeman potential and nonlinear effect induced by interatomic interactions using the Gross-Pitaevskii equation, highlighting the stability and feasibility of the proposed protocols for the state-of-the-art experiments with cold atoms.

DOI
10.1103/physreva.109.063310

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In this study we investigate the dynamics of tunable spin-orbit-coupled spin-1 Bose-Einstein condensates confined within a harmonic trap, focusing on rapid transport, spin manipulation, and splitting dynamics. Using shortcuts to adiabaticity, we design time-dependent trap trajectories and spin-orbit-coupling strength to facilitate fast transport with simultaneous spin flip. Additionally, we showcase the creation of spin-dependent coherent states via engineering the spin-orbit-coupling strength. To deepen our understanding, we elucidate nonadiabatic transport and associated spin dynamics, contrasting them with simple scenarios characterized by constant spin-orbit coupling and trap velocity. Furthermore, we discuss the transverse Zeeman potential and nonlinear effect induced by interatomic interactions using the Gross-Pitaevskii equation, highlighting the stability and feasibility of the proposed protocols for the state-of-the-art experiments with cold atoms.
We investigate fast transport and spin manipulation of tunable spin-orbit-coupled Bose-Einstein condensates in a moving harmonic trap. Motivated by the concept of shortcuts to adiabaticity, we design inversely the time-dependent trap position and spin-orbit-coupling strength. By choosing appropriate boundary conditions we obtain fast transport and spin flip simultaneously. The nonadiabatic transport and relevant spin dynamics are illustrated with numerical examples and compared with the adiabatic transport with constant spin-orbit-coupling strength and velocity. Moreover, the influence of nonlinearity induced by interatomic interaction is discussed in terms of the Gross-Pitaevskii approach, showing the robustness of the proposed protocols. With the state-of-the-art experiments, such an inverse engineering technique paves the way for coherent control of spin-orbit-coupled Bose-Einstein condensates in harmonic traps.
Spin-orbit coupling (SOC), the intrinsic interaction between a particle spin and its motion, is responsible for various important phenomena, ranging from atomic fine structure to topological condensed matter physics. The recent experimental breakthrough on the realization of SOC for ultra-cold atoms provides a completely new platform for exploring spin-orbit coupled superfluid physics. However, the SOC strength in the experiment is not tunable. In this report, we propose a scheme for tuning the SOC strength through a fast and coherent modulation of the laser intensities. We show that the many-body interaction between atoms, together with the tunable SOC, can drive a quantum phase transition (QPT) from spin-balanced to spin-polarized ground states in a harmonic trapped Bose-Einstein condensate (BEC), which resembles the long-sought Dicke QPT. We characterize the QPT using the periods of collective oscillations of the BEC, which show pronounced peaks and damping around the quantum critical point.
Dynamical characteristics of internal and external states of a Bose-Einstein condensate are generally different and independent, thus requiring different experimental manipulation techniques. The spin-orbit coupling recently achieved in Bose-Einstein condensates essentially connects spin and motion degree of freedom, endowing spin states with the ability to respond to orbital manipulation, and vice versa. In this work, a dynamical response effect, induced by simultaneously manipulating the internal and external states of a spin-orbit-coupled Bose-Einstein condensate, is predicted. Here, the “simultaneously manipulating the internal and external states” means that the driving field combines the Zeeman field applied to the internal state of the atom and the orbital potential affecting the external states of the atom. Specifically, the Bose-Einstein condensate is assumed to be activated by an abruptly applied Zeeman field and a sudden shake of the trapping potential. After some reasonable simplification and approximation of the model (i.e. neglecting the inter-atomic interactions and modelling the shake of the trapping potential by a short time-dependent pulse), an analytical relationship connecting spin frequency spectrum and the parameters of the driving fields is derived. The numerical calculations based on directly integrating the Gross-Pitaevskii equation are in good agreement with the results from the analytical relationship. The physical origin of the predicted spin dynamical response can be traced back to the quantum interference among different spin-orbit states. Due to the fact that a series of characteristic parameters of the condensate can be manifested in the spin frequency spectrum, the dynamical response effect predicted here provides a candidate method for determining and calibrating various system parameters by measuring the spin frequency spectrum.
In this paper, we investigate the dynamic properties of spin–orbit coupling spin-1 ferromagnetic Bose–Einstein condensates with different trap geometry. Our results are obtained in terms of the three-component Gross–Pitaevskii equation of mean-field theory. Two kinds of trap potential are discussed: isotropic and anisotropic. It is shown that the spin-exchange dynamics are greatly influenced by trap geometry. For the latter with weak spin–orbit coupling strength, we find that the three-component oscillation accelerates and some small difference emerges between component m=1 and m=-1. With the increase in spin–orbit coupling strength, the three components reach almost the same population. In addition, the kinetic energy of the system changes within a small scope for strong spin–orbit coupling, as opposed to a constant value in an isotropic trap. The density distributions display that the stripe phase appears with the increase in spin–orbit coupling strength. The method of generating stripe structure is different from the ground state of ferromagnetic condensate. For isotropic trap, the spatial separation of top and bottom spin–orbit condensates in component m=1 and m=-1 occurs at weak spin–orbit coupling, and square lattice appears at strong spin–orbit coupling.
Abstract We study the dynamics of binary Bose–Einstein condensates made of ultracold and dilute alkali-metal atoms in a quasi-one-dimensional setting. Numerically solving the two coupled Gross–Pitaevskii equations which accurately describe the system dynamics, we demonstrate that the spin transport can be controlled by suitably quenching spin–orbit and Rabi coupling strengths. Moreover, we predict a variety of dynamical features induced by quenching: broken oscillations, breathers-like oscillating patterns, spin-mixing–demixing, miscible–immiscible transition, emerging dark–bright states, dark solitons, and spin-trapping dynamics. We also outline the experimental relevance of the present study in manipulating the spin states in 39 K condensates.
We study the fast transport of a particle or a Bose-Einstein condensate in a harmonic potential. An exact expression for the final excitation energy in terms of the Fourier transform of the trap acceleration is used to engineer optimal transport protocols (with no final excitation) that are robust with respect to spring-constant errors. The same technique provides a way to design the simultaneous and robust transport of a few noninteracting species that experience different harmonic trap frequencies in the same trap.