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arXiv:1511.04588 · Physical Review Letters

Dynamics of Spin-Orbit Coupled Bose-Einstein Condensates in a Random Potential

Sh. Mardonov, Michele Modugno, Eugene Ya. Sherman

Published Oct 26, 2015• 49 citations
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Abstract

Disorder plays a crucial role in spin dynamics in solids and condensed matter systems. We demonstrate that for a spin-orbit coupled Bose-Einstein condensate in a random potential two mechanisms of spin evolution that can be characterized as "precessional" and "anomalous" are at work simultaneously. The precessional mechanism, typical for solids, is due to the condensate displacement. The unconventional anomalous mechanism is due to the spin-dependent velocity producing the distribution of the condensate spin polarization. The condensate expansion is accompanied by a random displacement and fragmentation, where it becomes sparse, as clearly revealed in the spin dynamics. Thus, different stages of the evolution can be characterized by looking at the condensate spin.

DOI
10.1103/physrevlett.115.180402

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We investigate theoretically the dynamics of a spin-orbit-coupled soliton formed by a self-interacting Bose-Einstein condensate immersed in a random potential, in the presence of an artificial magnetic field. We find that, due to the anomalous spin-dependent velocity, the synthetic Zeeman coupling can play a critical role in the soliton dynamics by causing its localization or delocalization, depending on the coupling strength and on the parameters of the random potential. The observed effects of the Zeeman coupling qualitatively depend on the type of self-interaction in the condensate, since the spin state and the self-interaction energy of the condensate are mutually related if the invariance of the latter with respect to the spin rotation is lifted.
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A finite-size quasi-two-dimensional Bose-Einstein condensate collapses if the attraction between atoms is sufficiently strong. Here we present a theory of collapse for condensates with the interatomic attraction and spin-orbit coupling. We consider two realizations of spin-orbit coupling: the axial Rashba coupling and the balanced, effectively one-dimensional Rashba-Dresselhaus one. In both cases spin-dependent ``anomalous'' velocity, proportional to the spin-orbit-coupling strength, plays a crucial role. For the Rashba coupling, this velocity forms a centrifugal component in the density flux opposite to that arising due to the attraction between particles and prevents the collapse at a sufficiently strong coupling. For the balanced Rashba-Dresselhaus coupling, the spin-dependent velocity can spatially split the initial state in one dimension and form spin-projected wave packets, reducing the total condensate density. Depending on the spin-orbit-coupling strength, interatomic attraction, and initial state, this splitting either prevents the collapse or modifies the collapse process. These results show that the collapse can be controlled by a spin-orbit coupling, thus extending the domain of existence of condensates of attracting atoms.
We study the quench dynamics of a Bose-Einstein condensate under a Raman-assisted synthetic spin-orbit coupling. To model the dynamical process, we adopt a self-consistent Bogoliubov approach, which is equivalent to applying the time-dependent Bogoliubov--de Gennes equations. We investigate the dynamics of the condensate fraction as well as the momentum distribution of the Bose gas following a sudden change of system parameters. Typically, the system evolves into a steady state in the long-time limit, which features an oscillating momentum distribution and a stationary condensate fraction. We investigate how different quench parameters such as the inter- and intraspecies interactions and the spin-orbit-coupling parameters affect the condensate fraction in the steady state. Furthermore, we find that the time average of the oscillatory momentum distribution in the long-time limit can be described by a generalized Gibbs ensemble with two branches of momentum-dependent Gibbs temperatures. Our study is relevant to the experimental investigation of dynamical processes in a spin-orbit-coupled Bose-Einstein condensate.
In a trapped spin-1/21/21/2 Bose-Einstein condensate with miscible interactions, a two-dimensional spin-orbit coupling can introduce an unconventional spatial separation between the two components. We reveal the physical mechanism of such a spin-orbit-coupling-induced phase separation. Detailed features of the phase separation are identified in a trapped Bose-Einstein condensate. We further analyze differences of phase separation in Rashba and anisotropic spin-orbit-coupled Bose gases. An adiabatic splitting dynamics is proposed as an application of the phase separation.
Ring-trapped Bose-Einstein condensates subject to spin-orbit coupling support localized dark-soliton excitations that show periodic density dynamics in real space. In addition to the density feature, the solitons also carry a localized pseudospin magnetization that exhibits a rich and tunable dynamics. Analytical results for Rashba-type spin-orbit coupling and spin-invariant interactions predict a conserved magnitude and precessional motion for the soliton magnetization that allows for the simulation of spin-related geometric phases recently seen in electronic transport measurements.