One-dimensional Spin-orbit Coupling Research Articles

Multi-Type Solitons in Spin-Orbit Coupled Spin-1 Bose–Einstein Condensates

Recently, research of solitons in Bose–Einstein condensates has become a popular topic. Here, we mainly study exact analytical solutions of Gross–Pitaevskii equations describing spin-orbit coupled spin-1 Bose–Einstein condensates. To begin with, we show the analytical relation between different types of one-dimensional spin-orbit coupling and Zeeman effect. In addition, we find a transformation that can simplify the three-component Gross–Pitaevskii equations with spin-orbit coupling into the nonlinear Schrödinger equation. The abundant stripe phase and dynamic characteristics of the system are investigated.

Polaron and molecular states of a spin-orbit coupled impurity in a spinless Fermi sea* *Project supported by the National Natural Science Foundation of China (Grant No. 11875195) and the Foundation of Beijing Education Committees (Grant Nos. CIT&TCD201804074 and KZ201810028043).

We investigate the polaron and molecular states of a fermionic atom with one-dimensional spin–orbit coupling (SOC) coupled to a three-dimensional spinless Fermi sea. Because of the interplay among the SOC, Raman coupling and spin-selected interatomic interactions, the polaron state induced by the spin–orbit coupled impurity exhibits quite unique features. We find that the energy dispersion of the polaron generally has a double-minimum structure, which results in a finite center-of-mass (c.m.) momentum in the ground state, different from the zero-momentum polarons where SOC are introduced into the majority atoms. By further tuning the parameters such as the atomic interaction strength, a discontinuous transition between the polarons with different c.m. momenta may occur, signaled by the singular behavior of the quasiparticle residue and effective mass of the polaron. Meanwhile, the molecular state as well as the polaron-to-molecule transition is also strongly affected by the Raman coupling and the effective Zeeman field, which are introduced by the lasers generating SOC on the impurity atom. We also discuss the effects of a more general spin-dependent interaction and mass ratio. These results would be beneficial for the study of impurity physics brought by SOC.

Enhanced transport of spin-orbit-coupled Bose gases in disordered potentials.

Anderson localization is a single-particle localization phenomena in disordered media that is accompanied by an absence of diffusion. Spin-orbit coupling (SOC) describes an interaction between a particle's spin and its momentum that directly affects its energy dispersion, for example, creating dispersion relations with gaps and multiple local minima. We show theoretically that combining one-dimensional spin-orbit coupling with a transverse Zeeman field suppresses the effects of disorder, thereby increasing the localization length and conductivity. This increase results from a suppression of backscattering between states in the gap of the SOC dispersion relation. Here, we focus specifically on the interplay of disorder from an optical speckle potential and SOC generated by two-photon Raman processes in quasi-one-dimensional Bose-Einstein condensates. We first describe backscattering by using a Fermi golden rule approach, and then numerically confirm this picture by solving the time-dependent one-dimensional Gross-Pitaevskii equation for a weakly interacting Bose-Einstein condensate with SOC and disorder. We find that on the tens of millisecond timescale of typical cold atom experiments moving in harmonic traps, initial states with momentum in the zero-momentum SOC gap evolve with negligible backscattering, while without SOC these same states rapidly localize.

Realization and Detection of Nonergodic Critical Phases in an Optical Raman Lattice.

The critical phases, being delocalized but nonergodic, are fundamental phases different from both the many-body localization and ergodic extended quantum phases, and have so far not been realized in experiment. Here we propose an incommensurate topological insulating model of AIII symmetry class to realize such critical phases through an optical Raman lattice scheme, which possesses a one-dimensional (1D) spin-orbit coupling and an incommensurate Zeeman potential. We show the existence of both noninteracting and many-body critical phases, which can coexist with the topological phase, and show that the critical-localization transition coincides with the topological phase boundary in noninteracting regime. The dynamical detection of the critical phases is proposed and studied in detail based on the available experimental techniques. Finally, we demonstrate how the proposed critical phases can be achieved within the current ultracold atom experiments. This work paves the way to observe the novel critical phases.

Topological phases in pseudospin-1 Fermi gases with two-dimensional spin-orbit coupling

The recent experimental realization of spin-orbit (SO) coupling for ultracold bosons and fermions opens an exciting avenue for engineering quantum matter that may be challenging to realize in solid state materials such as SO coupled spin-1 fermions. While one-dimensional SO coupling for spin-1 bosons has been experimentally realized, the generation of two-dimensional (2D) SO coupling and its topological properties are largely unexplored. Here we propose an experimental scheme for realizing a 2D Dresselhaus-type SO coupling in a square lattice for spin-1 Fermi gases. Because of the extended spin degree of freedom, many interesting topological phases could exist without relying on lattice point group symmetries that are crucial in solid state materials. These exotic phases include triply-degenerate points, quadratic band touching, a large Chern number ($C=5$) superfluid with 5 Majorana modes, triple-Weyl fermions, etc. Our scheme can be generalized to larger spins and provides a new route for engineering topological quantum matter by utilizing large spin degrees of freedom, instead of specific lattice symmetries.

Bound-state band reconstruction and resonance in a spin-1/2 Bose gas with one-dimensional spin-orbit coupling

In this work, we study two-body bound states in two-component Bose gas with a one-dimensional (1D) spin-orbit coupling (SOC) induced by Raman lasers. The finite Raman coupling strength generates coupling among three spin channels, resulting in the reconstruction of three bound-state bands. In addition, multiple resonances can be induced at finite scattering lengths. By tuning the interaction in one intra-species channel, one bound-state band can be lifted and three resonances can be achieved at different center-of-mass momenta, which can be observable under current experimental conditions in ${}^{87}$Rb atoms.

Energetics and structural properties of two- and three-boson systems in the presence of one-dimensional spin-orbit coupling

It was shown recently that the discrete scaling symmetry, which underlies the Efimov effect in the three identical boson system with two-body short-range interactions, survives when single-particle 1D spin-orbit coupling terms are added to the Hamiltonian. Each three-body energy level in the ordinary Efimov scenario turns into an energy manifold that contains four energy levels in the presence of 1D spin-orbit coupling (equal mixture of Rashba-Dresselhaus coupling). This work provides a detailed characterization of the energy levels in these manifolds. The two-boson energies, which enter into the three-boson scattering threshold, are analyzed in detail. Moreover, the structural properties, e.g., momentum distributions of the two- and three-boson systems, are analyzed for various parameter combinations.

Core filling of dark solitons in a topological superfluid with one-dimensional spin-orbit coupling

Core filling of dark solitons in a topological superfluid with one-dimensional spin-orbit coupling

One-dimensional spin-orbit coupling Bose gases with harmonic trapping

Rabi model is a popular model in quantum optics and describes a two-level system coupling to a quantum resonator. The fruitful physics appears when the coupling strength is comparable to the frequency of the resonator. We investigate the Bose gases of Raman induced spin-orbit coupling with an external harmonic trapping. Using the displacement Fock state in quantum optics we seek for an approximate ground state. We find the superposition state of left and right displaced oscillator state with odd parity has lower energy than the displaced state itself. Besides, we study the time evolution of both the momentum and the position of the system at single particle level to demonstrate the Zitterbewegung oscillating characteristics, which present an intuitive physical picture and are in qualitative agreement with the relevant experimental results. The results are useful to study the Rabi model in deep-strong coupling regime, the model that is difficult to realize in today’s experiment based on the high controllability property of laser, and these results are also instructive for the cold atom physics field.

Infrared stability of ground states of spin-orbit coupled Bose–Einstein condensates

We proved that the spin-1 Bose–Einstein condensate with one-dimensional spin-orbit coupling at the tricritical point is stable against excitations of Goldstone modes. The dispersion relations of these modes are anisotropic and cubic in some directions in the momentum space, which are much softer than the ordinary ones with linear form. A particular scaling form of the quantum depletions fraction on spin-orbit coupling strength is found, which is due to the special form of the dispersion relations of the Goldstone modes.

K -matrix formulation of two-particle scattering in a waveguide in the presence of one-dimensional spin-orbit coupling

The creation of artificial gauge fields in neutral ultracold atom systems has opened the possibility to study the effects of spin-orbit coupling terms in clean environments. This work considers the multi-channel scattering properties of two atoms confined by a wave guide in the presence of spin-orbit coupling terms within a K-matrix scattering framework. The tunability of resonances, induced by the interplay of the external wave guide geometry, the interactions, and the spin-orbit coupling terms, is demonstrated. Our results for the K-matrix elements as well as partial and total reflection coefficients for two identical fermions interacting through a finite-range interaction potential in the singlet channel only are compared with those obtained for a strictly one-dimensional effective low- energy Hamiltonian, which uses the effective coupling constant derived in Zhang et al. [Scientific Reports 4, 1 (2014)] and Zhang et al. [Phys. Rev. A 88, 053605 (2013)] as input. In the regime where the effective Hamiltonian is applicable, good agreement is obtained, provided the energy- dependence of the coupling constant is accounted for. Our approach naturally describes the energy regime in which the bands associated with excited transverse modes lie below a subset of the bands associated with the lowest transverse modes. The threshold behavior is discussed and scattering observables are linked to bound state properties.

Nodal Topological Phases in s-wave Superfluid of Ultracold Fermionic Gases**Supported by National Natural Science Foundation of China under Grant Nos. 11547047 and 11504143

The gapless Weyl superfluid has been widely studied in the three-dimensional ultracold fermionic superfluid. In contrast to Weyl superfluid, there exists another kind of gapless superfluid with topologically protected nodal lines, which can be regarded as the superfluid counterpart of nodal line semimetal in the condensed matter physics, just as Weyl superfluid with Weyl semimetal. In this paper we study the ground states of the cold fermionic gases in cubic optical lattices with one-dimensional spin-orbit coupling and transverse Zeeman field and map out the topological phase diagram of the system. We demonstrate that in addition to a fully gapped topologically trivial phase, some different nodal line superfluid phases appear when the Zeeman field is adjusted. The presence of topologically stable nodal lines implies the dispersionless zero-energy flat band in a finite region of the surface Brillouin zone. Experimentally these nodal line superfluid states can be detected via the momentum-resolved radio-frequency spectroscopy. The nodal line topological superfluid provide fertile grounds for exploring exotic quantum matters in the context of ultracold atoms.

Dynamics of bright–bright solitons in Bose–Einstein condensate with Raman-induced one-dimensional spin–orbit coupling

We investigate the dynamics of bright–bright solitons in one-dimensional two-component Bose–Einstein condensates with Raman-induced spin–orbit coupling, via the variational approximation and the numerical simulation of Gross–Pitaevskii equations. For the uniform system without trapping potential, we obtain two population balanced stationary solitons. By performing the linear stability analysis, we find a Goldstone eigenmode and an oscillation eigenmode around these stationary solitons. Moreover, we derive a general dynamical solution to describe the center-of-mass motion and spin evolution of the solitons under the action of spin–orbit coupling. The effects of a harmonic trap have also been discussed.

Exotic topological states with Raman-induced spin-orbit coupling

We propose a simple experimental scheme to realize simultaneously the one-dimensional spin-orbit coupling and the staggered spin-flip in ultracold pseudospin-$1/2$ atomic Fermi gases trapped in square optical lattices. In the absence of interspecies interactions, the system supports gapped Chern insulators and gapless topological semimetal states. By turning on the $s$-wave interactions, a rich variety of gapped and gapless inhomogeneous topological superfluids can emerge. In particular, a gapped topological Fulde-Ferrell superfluid, in which the chiral edge states at opposite boundaries possess the same chirality, is predicted.

Hidden nonsymmorphic symmetry in optical lattices with one-dimensional spin-orbit coupling

We uncover the nonsymmorphic symmetry and investigate its effects on the noncollinear band structures of a quasi-two-dimensional optical lattice with synthetic one-dimensional spin-orbit coupling and a tunable Zeeman field. The perpendicular Zeeman field breaks time-reversal symmetry and lifts the Kramers degeneracy which is protected by time-reversal and generalized inversion symmetries. Interestingly, we find that the degeneracy of Bloch bands on the border of the Brillouin zone is immune to the Zeeman field. This degeneracy, reminiscent of that in nonsymmorphic crystals, is protected by the hidden glide-plane symmetry that comprises a physical reflection involving both spatial and spin degrees of freedom followed by a nonprimitive lattice translation. Furthermore, we show that the band degeneracy can be lifted by the glide-plane-symmetry-breaking lattice potential. Finally, we propose to detect these effects by measuring a dynamical structure factor with optical Bragg spectroscopy.