Spin-orbit Coupled Bose-Einstein Condensate Research Articles

Harnessing center-of-mass excitations in quantum metrology

In quantum metrology, one typically creates correlations among atoms or photons to enhance measurement precision. Here, we show how one can use other excitations to perform quantum-enhanced measurements on the example of center-of-mass excitations of a spin-orbit coupled Bose-Einstein condensate and a Coulomb crystal. We also present a method to simulate a homodyne detection of cent er-of-mass excitations in these systems, which is required for optimal estimation.

Vortex gap solitons in spin–orbit-coupled Bose–Einstein condensates with competing nonlinearities

The formation and dynamics of full vortex gap solitons (FVGSs) are investigated in two-component Bose–Einstein condensates with spin–orbit coupling (SOC), Zeeman splitting (ZS), and competing cubic and quintic nonlinear terms, while the usual kinetic energy is neglected, assuming that it is much smaller than the SOC and ZS terms. Unlike previous SOC system with the cubic-only attractive nonlinearity, in which solely semi-vortices may be stable, with the vorticity carried by a single component, the present system supports stable FVGS states, with the vorticity present in both components (such states are called here “full vortex solitons”, to stress the difference from the half-vortices). They populate the bandgap in the system’s linear spectrum. In the case of the cubic self-attraction and quintic repulsion, stable FVGSs with a positive effective mass exist near the top of the bandgap. On the contrary, the system with cubic self-repulsion and quintic attraction produces stable FVGSs with a negative mass near the bottom of the bandgap. Mobility and collisions of FVGSs with different topological charges are investigated too.

Topological nonlinear optics with spin-orbit coupled Bose-Einstein condensate in cavity

We investigate topological nonlinear optics with spin-orbit coupled Bose-Einstein condensate in a cavity. The cavity is driven by a pump laser and a weak probe laser. Both lasers excite Bose-Einstein condensate, in the presence of standard Raman process for spin-orbit coupling, to an intermediate storage level. We theoretically show that the quantum interference at the transitional pathways of dressed atomic states results in different types of optical transparencies, which get completely inverted in atomic damping induced gain regime. The synthetic pseudo-spin states also implant different phases in the probe field forcing modes in probe transparencies to form gapless Dirac cones, which become gapped in presence of Raman detuning. These features get interestingly enhanced in gain regime where the amplified part of probe transparencies appear as gapless topological edge-like states between the probe bulk modes and cause non-trivial phase transition. We illustrate that the nonlinear interactions of the pseudo-spin states also enhance the slow light features in probe transmission. The manipulation of dressed states for topological optical transparencies in our findings could be a crucial step towards topological photonics and their application in quantum computation.

One- and two-dimensional solitons in spin–orbit-coupled Bose–Einstein condensates with fractional kinetic energy

We address effects of spin–orbit coupling (SOC), phenomenologically added to a two-component Bose–Einstein condensate composed of particles moving by Lévy flights, in one- and two-dimensional (1D) and (2D) settings. The corresponding system of coupled Gross–Pitaevskii equations includes fractional kinetic-energy operators, characterized by the Lévy index, α < 2 (the normal kinetic energy corresponds to α = 2). The SOC terms, with strength λ, produce strong effects in the 2D case: they create families of stable solitons of the semi-vortex and mixed-mode types in the interval of 1 < α < 2, where the supercritical collapse does not admit the existence of stable solitons in the absence of the SOC. At λ → 0, amplitudes of these solitons vanish ∼λ 1/(α−1).

Bloch oscillations in supersolids

We show that the motion of an accelerated atomic impurity immersed in a spin–orbit coupled Bose–Einstein condensate in the supersolid stripe phase undergoes oscillations, similar to the well-known phenomenon of Bloch oscillations in solids. While the back-action of the oscillatory movement onto the condensate excites phonon modes inside the supersolid, it does not affect the position of the roton minimum and therefore not the periodicity of the matter wave lattice. The ultimate decay of the oscillations is mostly due to the dispersion of the wavepacket and we show that this can be counteracted to a large extent by assuming that the impurity is a bright soliton.

Anderson localization of a spin–orbit coupled Bose–Einstein condensate in disorder potential

We present numerical results of a one-dimensional spin–orbit coupled Bose–Einstein condensate expanding in a speckle disorder potential by employing the Gross–Pitaevskii equation. Localization properties of a spin–orbit coupled Bose–Einstein condensate in zero-momentum phase, magnetic phase and stripe phase are studied. It is found that the localizing behavior in the zero-momentum phase is similar to the normal Bose–Einstein condensate. Moreover, in both magnetic phase and stripe phase, the localization length changes non-monotonically as the fitting interval increases. In magnetic phases, the Bose–Einstein condensate will experience spin relaxation in disorder potential.

Gap solitons of spin–orbit-coupled Bose–Einstein condensates in periodic potential

We numerically investigate the gap solitons in Bose–Einstein condensates (BECs) with spin–orbit coupling (SOC) in the parity–time ()-symmetric periodic potential. We find that the depths and periods of the imaginary lattice have an important influence on the shape and stability of these single-peak gap solitons and double-peak gap solitons in the first band gap. The dynamics of these gap solitons are checked by the split-time-step Crank–Nicolson method. It is proved that the depths of the imaginary part of the -symmetric periodic potential gradually increase, and the gap solitons become unstable. But the different periods of imaginary part hardly affect the stability of the gap solitons in the corresponding parameter interval.

Collapse of quasi-two-dimensional symmetrized Dresselhaus spin-orbit coupled Bose–Einstein condensate

Here, we study the collapse process of quasi-two-dimensional Bose–Einstein condensate with symmetrized Dresselhaus spin–orbit coupling. We show that at a sufficiently strong spin–orbit coupling the arising spin-dependent velocity compensates the attraction between particles and can prevent the collapse of the condensate. As a result, spin–orbit coupling can lead to a stable condensate rather than the collapse process.

Dynamics and formation of vortices collapsed from ring dark solitons in a two-dimensional spin-orbit coupled Bose-Einstein condensate

Dynamics and formation of vortices collapsed from ring dark solitons in a two-dimensional spin-orbit coupled Bose-Einstein condensate

The population transfer and superflow associated with the spatiotemporal Bloch states for a high-frequency driven spin–orbit coupled Bose–Einstein condensate

In this paper, we give the normal and abnormal Bloch states at the Brillouin zone edge to a spin–orbit (SO) coupled Bose–Einstein condensate (BEC) with a high-frequency driving and confined in a periodic lattice. The generation of the spatiotemporal Bloch states and the associated the population transfer and the superflow are studied. We find that Rabi coupling strength can enhance or reduce the population transfer between two BEC components for the obtained Bloch states. In addition, we can realize the transition between superfluid state and critical balance state by adjusting system parameters, which could be helpful to the quantum transport of the SO coupled cold-atom system.

Vortex formation in a spin–orbit-coupled Bose–Einstein condensates with static quadrupole magnetic field

The ground-state phases of Rashba spin–orbit (SO)-coupled Bose–Einstein condensates (BECs) in a quadrupole magnetic field are studied. The coupling of quadrupole magnetic field and spin induces local nonzero gauge particle current, accompanied by the generation of equal and opposite canonical particle current, and leads to the spontaneous nucleation of quantized vortices. The condensates exhibit a variety of rich density patterns and vortex arrangements resulting from the competition among quadrupole magnetic field, SO coupling, and interatomic interactions. Novel vortex structures, such as static vortex dipole, three-vortex molecule and the structure of a cross-arranged vortices and anti-vortices surrounded by a density annulus are found in the condensates. These structures greatly enrich the ground-state phases of SO-coupled BECs, and help to understand the superfluid behavior of a BEC and the nonlinear behavior of coherent matter waves.

Effects of optical lattices on bright solitons in spin-orbit coupled Bose-Einstein condensates

The stationary bright solitons that appear in the ground state of the spin-orbit coupled Bose-Einstein condensate (SOC-BEC) exhibit nodes. We consider SOC-BEC in combined linear and nonlinear optical lattices and study their effects on the matter-wave bright soliton and find that the parameters of the nonlinear lattice or atomic scattering length can be judiciously manipulated to have useful control over the nodes of the soliton. It is seen that the soliton with large number of nodes is less stable compared to one having fewer number of nodes. We infer that the synthetic spin-orbit coupling induces instability in the ordinary matter-wave soliton.

Exact Bloch States of a Spin-orbit Coupled Bose-Einstein Condensate in an Optical Lattice

Exact Bloch States of a Spin-orbit Coupled Bose-Einstein Condensate in an Optical Lattice

Landau–Zener–Stückelberg–Majorana interference of a spin-orbit-coupled Bose–Einstein condensate

The spin-orbit-coupled (SOC) ultracold atomic gases provide unique opportunities for exploring exotic quantum phases and introduce new capabilities into the quantum simulation. In this paper, we study the coherent control of spin states in SOC Bose–Einstein condensate (BEC) by exploiting and implementing the general concept of Landau–Zener–Stueckelberg–Majorana (LZSM) interference. For a SOC BEC, the Landau–Zener (LZ) transition between the dressed eigenlevels occurs as the BEC is accelerated through the SOC-avoided crossing, which corresponds to a breakdown of the spin momentum locking. In our scheme, two LZ pulses are separated by an intermediate holding period of variable duration. The nice LZSM interference patterns can be generated and controlled by controlling several parameters, corresponding to coherent control of the spin state of the SOC BEC. In particular, the destructive and constructive patterns of LZSM interference are observed and well explained through analytical analysis. Our results suggest a potential application of the LZSM interferometry in calibrating the spin states of a SOC BEC.

Interaction-induced topological Bogoliubov excitations in a spin-orbit-coupled Bose-Einstein condensate

We study topologically non-trivial excitations of a weakly interacting, spin-orbit coupled Bose-Einstein condensate in a two-dimensional square optical lattice, a system recently realized in experiment [W. Sun et al., Phys. Rev. Lett. 121, 150401 (2018)]. We focus on situations where the system is not subjected to a Zeeman field and thus does not exhibit nontrivial single-particle band topology. Of special interest then is the role of particle interaction as well as its interplay with the symmetry properties of the system in producing topologically non-trivial excitations. We find that the non-interacting system possesses a rich set of symmetries, including the $\mathcal{PT}$ symmetry, the modified dihedral point group symmetry $\tilde D_4$ and the nonsymmorphic symmetry. These combined symmetries ensure the existence of pairs of degenerate Dirac points at the edge of Brillouin zone for the single-particle energy bands. In the presence of particle interaction and with sufficient spin-orbit coupling, the atoms condense in a ground state with net magnetization which spontaneously breaks the $\mathcal{PT}$ and $\tilde D_4$ symmetry. We demonstrate that this symmetry breaking leads to a gap opening at the Dirac point for the Bogoliubov spectrum and consequentially topologically non-trivial excitations. We confirm the non-trivial topology by calculating the Chern numbers of the lowest excitation bands and show that gapless edge states form at the interface of systems characterized by different values of the Chern number.

Time-splitting Galerkin method for spin–orbit-coupled Bose–Einstein condensates

In this paper, we develop a time-splitting method to investigate the evolution of the spin–orbit-coupled Bose–Einstein condensates. The fully discrete scheme is constructed by combining the second-order time-splitting method for temporal discretization and the framework of Galerkin finite element method for spatial discretization. Ample numerical simulations are performed to validate the features of the designed numerical method, including the optimal order of error norms, the conservation law and the center-of-mass. Moreover, the interaction of waves with typical trapping potentials in two and three dimensions is numerically simulated.

Exploring Inhomogeneous Kibble-Zurek Mechanism in a Spin-Orbit Coupled Bose-Einstein Condensate.

The famous Kibble-Zurek mechanism offers us a significant clue to study quantum phase transitions out of equilibrium. Here, we investigate an intriguing phenomenon of a spin-orbit coupled Bose-Einstein condensate by quenching the Raman coupling strength from a high-symmetry phase (nonmagnetic phase) to a low-symmetry phase (magnetic phase). When crossing the critical point, the fluctuation of momentum distribution leads to delayed bifurcation structures. Simultaneously, the domain information emerges in momentum space. Moreover, the universal scalings of spatiotemporal dynamics are extracted from the fluctuations and domains, which manifests homogeneous and inhomogeneous Kibble-Zurek power laws at different timescales. Our work demonstrates a paradigmatic study on the inhomogeneous Kibble-Zurek mechanism.

Dynamics of rotating spin–orbit-coupled Bose–Einstein condensates in a quasicrystalline optical lattice

We investigate the dynamics of rotating pseudo-spin-1/2 Bose–Einstein condensates (BECs) with Rashba spin–orbit coupling (SOC) in a quasicrystalline optical lattice (QOL). For given parameters, the system evolves from an initial heliciform-stripe phase into a final visible vortex necklace with a giant vortex and a hidden vortex necklace. Simultaneously, the corresponding spin texture undergoes a transition from a meron–antimeron pair to a half-antiskyrmion necklace. During the dynamic evolution process, the angular momentum increases gradually, and then approaches to a convergent value. Furthermore, typical quantum phases of rotating two-component BECs with SOC in different external potentials are summarized.

Visible stripe phases in spin–orbital-angular-momentum coupled Bose–Einstein condensates

Recently, stripe phases in spin–orbit coupled Bose–Einstein condensates (BECs) have attracted much attention since they are identified as supersolid phases. In this paper, we exploit experimentally reachable parameters and show that annular stripe phases with large stripe spacing and high stripe contrast can be achieved in spin–orbital-angular-momentum coupled (SOAMC) BECs. In addition to using Gross–Pitaevskii numerical simulations, we develop a variational ansatz that captures the essential interaction effects to first order, which are not present in the ansatz employed in previous literature. Our work should open the possibility towards directly observing stripe phases in SOAMC BECs in experiments.

Quenching dynamics of the bright solitons and other localized states in spin–orbit coupled Bose–Einstein condensates

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 39K condensates.