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arXiv:1605.02108 · Physical Review A

Optical-lattice-assisted magnetic phase transition in a spin-orbit-coupled Bose-Einstein condensate

Giovanni Italo Martone, Tomoki Ozawa, Chunlei Qu, S. Stringari

Published Oct 14, 2016• 17 citations
arXivHTMLPDF

Abstract

We investigate the effect of a periodic potential generated by a one-dimensional optical lattice on the magnetic properties of an $S=1/2$ spin-orbit-coupled Bose gas. By increasing the lattice strength one can achieve a magnetic phase transition between a polarized and an unpolarized Bloch wave phase, characterized by a significant enhancement of the contrast of the density fringes. If the wave vector of the periodic potential is chosen close to the roton momentum, the transition could take place at very small lattice intensities, revealing the strong enhancement of the response of the system to a weak density perturbation. By solving the Gross-Pitaevskii equation in the presence of a three-dimensional trapping potential, we shed light on the possibility of observing the magnetic phase transition in currently available experimental conditions.

DOI
10.1103/physreva.94.043629

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We investigate the effect of a periodic potential generated by a one-dimensional optical lattice on the magnetic properties of an S=1/2S=1/2S=1/2 spin-orbit-coupled Bose gas. By increasing the lattice strength one can achieve a magnetic phase transition between a polarized and an unpolarized Bloch wave phase, characterized by a significant enhancement of the contrast of the density fringes. If the wave vector of the periodic potential is chosen close to the roton momentum, the transition could take place at very small lattice intensities, revealing the strong enhancement of the response of the system to a weak density perturbation. By solving the Gross-Pitaevskii equation in the presence of a three-dimensional trapping potential, we shed light on the possibility of observing the magnetic phase transition in currently available experimental conditions.
Spin-orbit-coupled bosons can exhibit rich equilibrium phases at low temperature and in the presence of particle-particle interactions. In the case with a 1D synthetic spin-orbit interaction, it has been observed that the ground state of a Bose gas can be a normal phase, stripe phase, or magnetized phase in different parameter regimes. The magnetized states are doubly degenerate and consist of a many-particle two-state system. In this work, we investigate the nonequilibrium quantum dynamics by switching on a simple one-dimensional optical lattice potential as external perturbation to induce resonant couplings between the magnetized phases, and predict a quantum spin dynamics which cannot be obtained in the single-particle systems. In particular, due to particle-particle interactions, the transition of the Bose condensate from one magnetized phase to the other is forbidden when the external perturbation strength is less than a critical value, and a full transition can occur only when the perturbation exceeds such critical strength. This phenomenon manifests itself a dynamical phase transition, with the order parameter defined by the time-averaged magnetization over an oscillation period, and the critical point behavior being exactly solvable. The thermal fluctuations are also considered in detail. From numerical simulations and exact analytic studies we show that the predicted many-body effects can be well observed with the current experiments.
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.
Abstract We consider matter–wave solitons in spin–orbit coupled Bose–Einstein condensates embedded in an optical lattice and study the dynamics of the soliton within the framework of Gross–Pitaevskii equations. We express spin components of the soliton pair in terms of nonlinear Bloch equations and investigate the effective spin dynamics. It is seen that the effective magnetic field that appears in the Bloch equation is affected by optical lattices, and thus the optical lattice influences the precessional frequency of the spin components. We make use of numerical approaches to investigate the dynamical behavior of density profiles and center-of-mass of the soliton pair in the presence of the optical lattice. It is shown that the spin density is periodically varying due to flipping of spinors between the two states. The amplitude of spin-flipping oscillation increases with lattice strength. We find that the system can also exhibit interesting nonlinear behavior for chosen values of parameters. We present a fixed point analysis to study the effects of optical lattices on the nonlinear dynamics of the spin components. It is seen that the optical lattice can act as a control parameter to change the dynamical behavior of the spin components from periodic to chaotic.
We report on the Bose-Einstein condensate in the Bloch bands with off-diagonal periodic potential (ODPP), which simultaneously plays the role of spin-orbit coupling and Zeeman field. This model can be realized using two independent Raman couplings in the same three-level system, in which the time-reversal symmetry ensures the energy degeneracy between the two states with opposite momenta. We find that these two Raman couplings can be used to tune the spin polarization in momentum space, thus greatly modifying the effective scatterings over the Bloch bands. We observe a transition from the Bloch plane wave phase with condensate at one wave vector to the Bloch stripe phase with condensate at the two Bloch states with opposite wave vectors. These two phases will exhibit different spin textures and density modulations in real space, which are totally different from that in free space. In momentum space, multiple peaks differing by some reciprocal lattice vectors can be observed in both phases, reflecting the periodic structure of the ODPP. A three-band effective model is proposed to understand these observations. This ODPP will never approach the tight-binding limit, thus can provide an alternative platform in the investigations of various physics, such as collective excitations, polaron, and topological superlfuids, over the Bloch bands.
In a recent experiment (Z. Wu, L. Zhang, W. Sun, X.-T. Xu, B.-Z. Wang, S.-C. Ji, Y. Deng, S. Chen, X.-J. Liu, and J.-W. Pan, arXiv:1511.08170 [cond-mat.quant-gas]), a Raman-assisted two-dimensional spin-orbit coupling has been realized for a Bose-Einstein condensate in an optical lattice potential. In light of this exciting progress, we study in detail key properties of the system. As the Raman lasers inevitably couple atoms to high-lying bands, the behaviors of the system in both the single- and many-particle sectors are significantly affected. In particular, the high-band effects enhance the plane-wave phase and lead to the emergence of ``roton'' gaps at low Zeeman fields. Furthermore, we identify high-band-induced topological phase boundaries in both the single-particle and the quasiparticle spectra. We then derive an effective two-band model, which captures the high-band physics in the experimentally relevant regime. Our results not only offer valuable insights into the two-dimensional lattice spin-orbit coupling, but also provide a systematic formalism to model high-band effects in lattice systems with Raman-assisted spin-orbit couplings.
Abstract We study the ground state and the Bloch oscillations of the spin-orbit coupled Bose-Einstein condensates in one-dimensional deep optical lattices. The phase transition between the zero-momentum phase and the plane-wave phase in untilted deep optical lattices is studied analytically. The Bloch oscillations in tilted lattices started in different ground state phases are analyzed. It is found that the Bloch dynamics is harmonic (anharmonic) in the zero-momentum phase (plane-wave phase). Furthermore, the modification of the Bloch oscillations induced by spin-orbit coupling, tunnelling coefficient and the external force (the inclination of the tilt) is revealed. In addition, the analytical condition for emerging the long-lived Bloch oscillations is obtained and the corresponding diagram in parameter space is provided. Particularly, we find that the spin-orbit coupling can extend the duration of the Bloch oscillations in the plane-wave phase. We provide an effective method to manipulate the Bloch dynamics in the deep optical lattices.