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Acta Physica Sinica

Quench dynamics of a spin-orbital coupled Bose-Einstein condensate with nonlinear interactions

Huan Wang, Xia-Yao He, Shuai Li, Bo Liu

Published Jan 1, 2023• 1 citation
Publisher

Abstract

In this work, we study the non-equilibrium quench dynamics from the superfluid stripe phase to the supersolid phase of a two dimensional spin-orbital coupled interacting Bose-Einstein condensate in the presence of a one dimensional optical lattice. The quench protocol here is constructed through varying the lattice depth linearly with the evolution time. By using the time-dependent Gutzwiller method, various physical quantities, such as the vortex number and the overlap of wave-function, have been investigated with respect to the quench time. Through analyzing the dynamical behavior of the above physical quantities, we find out the transition time of the quench procedure, which captures the freeze out time indicating the moment that the system catches the quench speed beginning to evolve quickly. Before the transition time, the dynamics is frozen and the state of the system cannot follow the changes in the Hamiltonian. While passing the transition time, we find that there are significant alterations to both the vortex number and the wave-function. At the transition time, on one hand the vortex number abruptly increases from zero; on the other hand the overlap of wave-function departures from 1 shortly. These signatures indicate that the system evolves rapidly when passing the transition time. Furthermore, we also find that due to the presence of spin-orbital coupling, the spin texture represents a periodic magnetic structure accompanying with the emergence of the supersolid dynamically. It is shown that during the quench procedure, the density distribution of the system are always accompanied with the spatial structure of spin texture, i.e., the central position of topological spin skyrmion (antiskyrmion) corresponding to the minimum position of the density distribution. The topological charge of the above spin structures also shows interesting dynamical properties. We find that the quantized topological charge appears with the emergence of the supersolid dynamically.

DOI
10.7498/aps.72.20222401

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In this work, we study the non-equilibrium quench dynamics from the superfluid stripe phase to the supersolid phase of a two dimensional spin-orbital coupled interacting Bose-Einstein condensate in the presence of a one dimensional optical lattice. The quench protocol here is constructed through varying the lattice depth linearly with the evolution time. By using the time-dependent Gutzwiller method, various physical quantities, such as the vortex number and the overlap of wave-function, have been investigated with respect to the quench time. Through analyzing the dynamical behavior of the above physical quantities, we find out the transition time of the quench procedure, which captures the freeze out time indicating the moment that the system catches the quench speed beginning to evolve quickly. Before the transition time, the dynamics is frozen and the state of the system cannot follow the changes in the Hamiltonian. While passing the transition time, we find that there are significant alterations to both the vortex number and the wave-function. At the transition time, on one hand the vortex number abruptly increases from zero; on the other hand the overlap of wave-function departures from 1 shortly. These signatures indicate that the system evolves rapidly when passing the transition time. Furthermore, we also find that due to the presence of spin-orbital coupling, the spin texture represents a periodic magnetic structure accompanying with the emergence of the supersolid dynamically. It is shown that during the quench procedure, the density distribution of the system are always accompanied with the spatial structure of spin texture, i.e., the central position of topological spin skyrmion (antiskyrmion) corresponding to the minimum position of the density distribution. The topological charge of the above spin structures also shows interesting dynamical properties. We find that the quantized topological charge appears with the emergence of the supersolid dynamically.
We study the ground-state phases of a two-dimensional rotating spin-orbit–coupled Bose-Einstein condensate loaded in a one-dimensional spin-dependent optical lattice. In the absence of rotation, the system undergoes a phase transition from the stripe phase to the supersolid phase gradually for weak spin-orbit coupling strength and directly for strong spin-orbit coupling strength as the depth of the optical lattice increases. With increasing the rotation strength, the stripe phase transforms to the ringlike state, and the domain number of the ringlike state increases when the Bose-Einstein condensate is in the weak depth of the optical lattice. The supersolid phase transforms to the phase with a single domain of a vortex line for small rotation strength, and alternating vortex lines along the x -direction appear for large rotation strength when the Bose-Einstein condensate is in the strong depth of the optical lattice. The spin textures of the ground-state phases are also discussed.
We investigate the quench dynamics of a two-dimensional Rashba spin-orbit-coupled Bose-Einstein condensate. Our study focuses on quenching the system from a zero-momentum phase to a stripe phase. During this quench, topological defects emerge in the form of vortices. These vortices and antivortices exhibit a random spatial distribution with equal numbers. In a uniform system, we observe an exponential scaling of both the vortex production time and the vortex number with the quench rate, consistent with the conventional Kibble-Zurek mechanism, the decay of which adheres to a logarithmic law, aligning with experimental observations.
We investigate the quench dynamics of the dipolar bosons in two dimensional optical lattice of square geometry using the time dependent Gutzwiller method. The system exhibits different density orders like the checkerboard and the striped pattern, depending upon the polarization angle of the dipoles. We quench the hopping parameter across the striped density wave (SDW) to striped supersolid (SSS) phase transition, and obtain the scaling laws for the correlation length and topological vortex density, as function of the quench rate. The results are reminiscent of the Kibble-Zurek mechanism (KZM). We also investigate the dynamics from the striped supersolid phase to the checkerboard supersolid phase, obtained by quenching the dipole tilt angle θθθ. This is a first order structural quantum phase transition, and we study the non-equilibrium dynamics from the perspective of the KZM. In particular, we find the number of the domains with checkerboard order follows a power law scaling with the quench rate. This indicates the applicability of the KZM to this first order quantum phase transition.
We study the ground-state phases of two-dimensional spin-orbit coupled spin-2 Bose-Einstein condensates in a one-dimensional spin-dependent optical lattice. Due to the competition among optical lattice, spin-orbit coupling and spin-exchange interaction, the exotic ground-state phases are found, i.e. three types of the stripe phases and three types of the supersolid phases. The spin-exchange interaction can adjust the direction of the stripe in the stripe phase and generate various vortex lattice structures in the supersolid phase, which shows that the spin-exchange interaction plays an important role in the formation of the stripe and supersolid phases of spin-orbit coupled spin-2 Bose-Einstein condensates in an optical lattice.
Despite ground-breaking observations of supersolidity in spin-orbit-coupled Bose-Einstein condensates, until now the dynamics of the emerging spatially periodic density modulations has been vastly unexplored. Here, we demonstrate the nonrigidity of the density stripes in such a supersolid condensate and explore their dynamic behavior subject to spin perturbations. We show both analytically in infinite systems and numerically in the presence of a harmonic trap how spin waves affect the supersolid's density profile in the form of crystal waves, inducing oscillations of the periodicity as well as the orientation of the fringes. Both these features are well within reach of present-day experiments. Our results show that this system is a paradigmatic supersolid, featuring superfluidity in conjunction with a fully dynamic crystalline structure.
Recent experimental advances to create tunable synthetic spin-orbit coupling (SOC) in ultracold gases provide new possibilities to access fruitful spin-orbit coupled quantum many-body physics. In this paper, we demonstrate that the combined effect of two-dimensional (2D) SOC and one-dimensional (1D) optical lattice in interacting bosons can provide an alternative scheme in ultracold gases to achieve the crossover of the commensurate-incommensurate supersolid ground state ``with respect to the background optical lattice.'' Interestingly, it is shown that the anharmonicity arising from the lattice potential leads to the ``pin'' effect and make the ground-state break the continuous translational symmetry along the direction perpendicular to the 1D lattice, whereas the competition between the lattice period and the SOC length results in the crossover of commensurate-incommensurate ground state along the direction of 1D lattice with discrete translational symmetry breaking. Such a combined effect of SOC and optical lattice, thus, induces a new 2D periodic pattern in the ground state, accompanying with nonzero 2D superfluid density characterizing the supersolid nature in 2D of the ground state. Furthermore, a skyrmion-anti-skyrmion lattice is found associated with the appearance of such supersolid ground state, indicating its topological nontrivial properties. Experimental signature of our proposed supersolid ground state is also predicted by means of the time-of-flight measurement.