Three-component Bose-Einstein Condensate Research Articles

Six types of spin solitons in three-component Bose–Einstein condensates

Exact analytical solutions are good candidates for studying and explaining the dynamics of solitons in nonlinear systems. We further extend the region of existence of spin solitons in the nonlinearity coefficient space for the spin-1 Bose–Einstein condensate. Six types of spin soliton solutions can be obtained, and they exist in different regions. Stability analysis and numerical simulation results indicate that three types of spin solitons are stable against weak noise. The non-integrable properties of the model can induce shape oscillation and increase in speed after the collision between two spin solitons. These results further enrich the soliton family for non-integrable models and can provide theoretical references for experimental studies.

Rayleigh-Taylor instability in a phase-separated three-component Bose-Einstein condensate

Rayleigh-Taylor instability in a phase-separated three-component Bose-Einstein condensate

Effects of residual nonlinearities on the modulational instability of three-component Bose–Einstein condensates

We study the modulation instability in a three-component Bose–Einstein condensate and the impact of higher-order interactions brought on by shape-dependent confinement. Using the modified Gross–Pitaevskii equation that accounts for the higher-order residual nonlinearity and the linear stability method, we analyze the dispersion relations and the gain spectrum for instability. In particular, we investigate the role of higher-order interactions over the MI in miscible and immiscible condensates. The observed MI spectrum shows a new regime for soliton generation in a ternary mixture of Bose–Einstein condensates. Our results show that the residual nonlinearity can effectively control the MI gain profile in both miscible and immiscible condensates. This allows one manipulate the MI in a ternary mixture of Bose–Einstein condensates to control the dynamics.

Bio-inspired computing with magnetic skyrmions using deep learning

Spintronic systems demonstrate significant value due to variety of features that can be used in bio-inspired computing applications. Skyrmion is a magnetic nanostructure which can be used as an information carrier. In this paper, we simulate vortex-free Gaussian wave packet by incorporating spin–orbit coupling (SoC) into three-component Bose–Einstein condensates (BECs). We next observe that skyrmions can be naturally generated from vortex-free Gaussian wave packet, further these structurally asymmetric devices are constructed and initial device classifications are carried out. A spin device consisting of vertically-stacked multiple skyrmions is proposed termed as skyrmion spintronic synapse (SkSS) and skyrmion spintronic Neuron (SkSN). This paper depicts training the neural network with surrogate gradients with deep learning strategies using topologically nontrivial spin textures. The current popular Graphics Processing Unit (GPU)-based neural network computations are compared with the proposed method. This research paves a way for a neuromorphic computing systems on exotic topological solitons.

Dynamics of matter-wave solitons in three-component Bose-Einstein condensates with time-modulated interactions and gain or loss effect

The gain or loss effect on the dynamics of the matter-wave solitons in three-component Bose–Einstein condensates with time-modulated interactions trapped in parabolic external potentials are investigated analytically. Some exact matter-wave soliton solutions to the three-coupled Gross–Pitaevskii equation describing the three-component Bose–Einstein condensates are constructed by similarity transformation. The dynamical properties of the matter-wave solitons are analyzed graphically, and the effects of the gain or loss parameter and the frequency of the external potentials on the matter-wave solitons are explored. It is shown that the gain coefficient makes the atom condensate to absorb energy from the background, while the loss coefficient brings about the collapse of the condensate.

Surfactant behavior in three-component Bose-Einstein condensates

Interface properties of a three-component Bose-Einstein condensate, in which component 3 is sandwiched by components 1 and 2 at the interface, are investigated. It is shown that component 3 can serve as a surfactant: the net interfacial tension is reduced by the presence of component 3. We calculate the interfacial tension as a function of the interaction coefficients. The stability of the interface is studied by Bogoliubov analysis. When the interfacial tension has a spatial gradient, interfacial flow is induced, which resembles the Marangoni flow.

Vector kink-dark complex solitons in a three-component Bose–Einstein condensate

We investigate kink-dark complex solitons (KDCSs) in a three-component Bose–Einstein condensate (BEC) with repulsive interactions and pair-transition (PT) effects. Soliton profiles critically depend on the phase differences between dark solitons excitation elements. We report a type of kink-dark soliton profile which shows a droplet-bubble-droplet with a density dip, in sharp contrast to previously studied bubble-droplets. The interaction between two KDCSs is further investigated. It demonstrates some striking particle transition behaviours during their collision processes, while soliton profiles survive after the collision. Additionally, we exhibit the state transition dynamics between a kink soliton and a dark soliton. These results suggest that PT effects can induce more abundant complex solitons dynamics in multi-component BEC.

The research progress of topological properties in spinor Bose-Einstein condensates

Most of the atoms that realize Bose-Einstein condensation have internal spin degree of freedom. In the optical potential trap, the internal spin of the atom is thawed, and the atom can be condensed into each hyperfine quantum state to form the spinor Bose-Einstein condensate. Flexible spin degrees of freedom become dynamic variables related to the system, which can make the system appear novel topological quantum states, such as spin domain wall, vortex, magnetic monopole, skymion, and so on. In this paper, the experimental and theoretical study of spinor Bose-Einstein condensation, the types of topological defects in spinor Bose-Einstein condensate, and the research progress of topological defects in spinor two-component and three-component Bose-Einstein condensate are reviewed.

Skyrmions and composite vortex states in three-component Bose–Einstein condensates with spin–orbit coupling

Stable and metastable vortex states in two-dimensional three-component Bose–Einstein condensates are studied in the presence of spin–orbit coupling. The ground states exhibit two skyrmion structures which respectively correspond to the d-skyrmion in antiferromagnetic or the F-skyrmion in ferromagnetic condensates. The half skyrmion and full skyrmion can be controlled by changing the strength of the spin–orbit coupling. We also find a stable composite vortex state which is associated to mixing of the ferromagnetic and antiferromagnetic manifolds.

Cavity-induced emergent topological spin textures in a Bose–Einstein condensate

The coupled nonlinear dynamics of ultracold quantum matter and electromagnetic field modes in an optical resonator exhibits a wealth of intriguing collective phenomena. Here we study a Λ-type, three-component Bose–Einstein condensate coupled to four dynamical running-wave modes of a ring cavity, where only two of the modes are externally pumped. However, the unpumped modes play a crucial role in the dynamics of the system due to coherent backscattering of photons. On a mean- field level we identify three fundamentally different steady-state phases with distinct characteristics in the density and spatial spin textures: a combined density and spin-wave, a continuous spin spiral with a homogeneous density, and a spin spiral with a modulated density. The spin-spiral states, which are topological, are intimately related to cavity-induced spin–orbit coupling emerging beyond a critical pump power. The topologically trivial density-wave–spin-wave state has the characteristics of a supersolid with two broken continuous symmetries. The transitions between different phases are either simultaneously topological and first-order, or second-order. The proposed setup allows the simulation of intriguing many-body quantum phenomena by solely tuning the pump amplitudes and frequencies, with the cavity output fields serving as a built-in nondestructive observation tool.

Absence of Landau damping in driven three-component Bose\u2013Einstein condensate in optical lattices

We explore the quantum many-body physics of a three-component Bose-Einstein condensate in an optical lattice driven by laser fields in V and Λ configurations. We obtain exact analytical expressions for the energy spectrum and amplitudes of elementary excitations, and discover symmetries among them. We demonstrate that the applied laser fields induce a gap in the otherwise gapless Bogoliubov spectrum. We find that Landau damping of the collective modes above the energy of the gap is carried by laser-induced roton modes and is considerably suppressed compared to the phonon-mediated damping endemic to undriven scalar condensates

Superfluid drag in multicomponent Bose-Einstein condensates on a square optical lattice

The superfluid drag-coefficient of a weakly interacting three-component Bose-Einstein condensate is computed deep into the superfluid phase, starting from a Bose-Hubbard model with component-conserving, on-site interactions and nearest-neighbor hopping. Rayleigh-Schr\"odinger perturbation theory is employed to provide an analytic expression for the drag density. In addition, the Hamiltonian is diagonalized numerically to compute the drag within mean-field theory at both zero and finite temperatures to all orders in inter-component interactions. Moreover, path integral Monte Carlo simulations have been performed to support the mean-field results. In the two-component case the drag increases monotonically with the magnitude of the inter-component interaction $\gamma_{AB}$ between the two components A and B. This no longer holds when an additional third component C is included. Instead of increasing monotonically, the drag can either be strengthened or weakened depending on the details of the interaction strengths, for weak and moderately strong interactions. The general picture is that the drag-coefficient between component A and B is a non-monotonic function of the inter-component interaction strength $\gamma_{AC}$ between A and a third component C. For weak $\gamma_{AC}$ compared to the direct interaction $\gamma_{AB}$ between A and B, the drag-coefficient between A and B can {\it decrease}, contrary to what one naively would expect. When $\gamma_{AC}$ is strong compared to $\gamma_{AB}$, the drag between A and B increases with increasing $\gamma_{AC}$, as one would naively expect. We attribute the subtle reduction of $\rho_{d,AB}$ with increasing $\gamma_{AC}$, which has no counterpart in the two-component case, to a renormalization of the inter-component scattering vertex $\gamma_{AB}$ via intermediate excited states of the third condensate $C$.

Stable 2D skyrmion and half-skyrmion in three-component Bose–Einstein condensates

Skyrmion spin textures were experimentally created in an antiferromagnetic spin-1 Bose–Einstein condensate by Choi et al. However, the stability of 2D skyrmion excitations is still controversial. Theoretical calculations show that 2D skyrmion excitations are energetically unstable. However, we find that the 2D skyrmion as well as the half-skyrmion can be naturally generated from a vortex-free Gaussian wave packet by incorporating spin–orbit coupling into three-component Bose–Einstein condensates.

Vortex-bright solitons in a spin-orbit-coupled spin-1 condensate

We study the vortex-bright solitons in a quasi-two-dimensional spin-orbit-coupled (SO-coupled) hyperfine spin-1 three-component Bose-Einstein condensate (BEC) using variational method and numerical solution of a mean-field model. The ground state of these vortex-bright solitons is radially symmetric for weak ferromagnetic and polar interactions. For a sufficiently strong ferromagnetic interaction, we observe the emergence of an asymmetric vortex-bright soliton as the ground state. We also numerically investigate stable moving solitons and binary collision between them. The present mean-field model is not Galilean invariant, and we use a Galilean-transformed model for generating the moving solitons. At low velocities, the head-on collision between two {\em in-phase} solitons results either in collapse or fusion of the soliton pair. On the other hand, in head-on collision, the two {\em out-of-phase} solitons strongly repel each other and trace back their trajectories before the actual collision. At low velocities, in a collision with an impact parameter, the {\em out-of-phase} solitons get deflected from their original trajectory like two rigid classical disks. These {\em out-of-phase solitons} behave like classical disks, and their collision dynamics is governed by classical laws of motion. However, at large velocities two SO-coupled spinor solitons, irrespective of phase difference, can pass through each other in a head-on collision like two quantum solitons.

Skyrmionic vortex lattices in coherently coupled three-component Bose-Einstein condensates

We show numerically that a harmonically trapped and coherently Rabi-coupled three-component Bose-Einstein condensate can host unconventional vortex lattices in its rotating ground state. The discovered lattices incorporate square and zig-zag patterns, vortex dimers and chains, and doubly quantized vortices, and they can be quantitatively classified in terms of a skyrmionic topological index, which takes into account the multicomponent nature of the system. The exotic ground-state lattices arise due to the intricate interplay of the repulsive density-density interactions and the Rabi couplings as well as the ubiquitous phase frustration between the components. In the frustrated state, domain walls in the relative phases can persist between some components even at strong Rabi coupling, while vanishing between others. Consequently, in this limit the three-component condensate effectively approaches a two-component condensate with only density-density interactions. At intermediate Rabi coupling strengths, however, we face unique vortex physics that occurs neither in the two-component counterpart nor in the purely density-density-coupled three-component system.

Bound vortex states and exotic lattices in multicomponent Bose-Einstein condensates: The role of vortex-vortex interaction

We numerically study the vortex-vortex interaction in multi-component homogeneous Bose-Einstein condensates within the realm of the Gross-Pitaevskii theory. We provide strong evidences that pairwise vortex interaction captures the underlying mechanisms which determine the geometric configuration of the vortices, such as different lattices in many-vortex states, as well as the bound vortex states with two (dimer) or three (trimer) vortices. Specifically, we discuss and apply our theoretical approach to investigate intra- and inter-component vortex-vortex interactions in two- and three-component Bose-Einstein condensates, thereby shedding light on the formation of the exotic vortex configurations. These results correlate with current experimental efforts in multi-component Bose-Einstein condensates, and the understanding of the role of vortex interactions in multiband superconductors.

Quantum exact non-abelian vortices in non-relativistic theories

Non-Abelian vortices arise when a non-Abelian global symmetry is exact in the ground state but spontaneously broken in the vicinity of their cores. In this case, there appear (non-Abelian) Nambu-Goldstone (NG) modes confined and propagating along the vortex. In relativistic theories, the Coleman-Mermin-Wagner theorem forbids the existence of a spontaneous symmetry breaking, or a long-range order, in 1+1 dimensions: quantum corrections restore the symmetry along the vortex and the NG modes acquire a mass gap. We show that in non-relativistic theories NG modes with quadratic dispersion relation confined on a vortex can remain gapless at quantum level. We provide a concrete and experimentally realizable example of a three-component Bose-Einstein condensate with U(1) x U(2) symmetry. We first show, at the classical level, the existence of S^3 = S^1 |x S^2 (S^1 fibered over S^2) NG modes associated to the breaking U(2) -> U(1) on vortices, where S^1 and S^2 correspond to type I and II NG modes, respectively. We then show, by using a Bethe ansatz technique, that the U(1) symmetry is restored, while the SU(2) symmery remains broken non-pertubatively at quantum level. Accordingly, the U(1) NG mode turns into a c=1 conformal field theory, the Tomonaga-Luttinger liquid, while the S^2 NG mode remains gapless, describing a ferromagnetic liquid. This allows the vortex to be genuinely non-Abelian at quantum level.

Non-autonomous bright–dark solitons and Rabi oscillations in multi-component Bose–Einstein condensates

We study the dynamics of non-autonomous bright–dark matter-wave solitons in two- and three-component Bose–Einstein condensates. Our setting includes a time-dependent parabolic potential and scattering length, as well as Rabi coupling of the separate hyperfine states. By means of a similarity transformation, we transform the non-autonomous coupled Gross–Pitaevskii equations into the completely integrable Manakov model with defocusing nonlinearity, and construct the explicit form of the non-autonomous soliton solutions. The propagation characteristics for the one-soliton state, and collision scenarios for multiple soliton states are discussed in detail for two types of time-dependent nonlinearities: a kink-like one and a periodically modulated one, with appropriate time-dependence of the trapping potential. We find that in the two-component condensates the nature of soliton propagation is determined predominantly by the nature of the nonlinearity, as well as the temporal modulation of the harmonic potential; switching in this setting is essentially due to Rabi coupling. We also perform direct numerical simulation of the non-autonomous two-component coupled Gross–Pitaevskii equations to corroborate our analytical predictions. More interestingly, in the case of the three-component condensates, we find that the solitons can lead to collision-induced energy switching (energy sharing collision), that can be profitably used to control Rabi switching or vice versa. An interesting possibility of reversal of the nature of the constituent soliton, i.e., bright (dark) into dark (bright) due to Rabi coupling is demonstrated in the three-component setting.

Vortex Molecules in Bose-Einstein Condensates

Stable vortex dimers are known to exist in coherently coupled two component Bose-Einstein condensates (BECs). We construct stable vortex trimers in three component BECs and find that the shape can be controlled by changing the internal coherent (Rabi) couplings. Stable vortex N-omers are also constructed in coherently coupled N-component BECs. We classify all possible N-omers in terms of the mathematical graph theory. Next, we study effects of the Rabi coupling in vortex lattices in two-component BECs. We find how the vortex lattices without the Rabi coupling known before are connected to the Abrikosov lattice of integer vortices with increasing the Rabi coupling. In this process, vortex dimers change their partners in various ways at large couplings. We then find that the Abrikosov lattices are robust in three-component BECs.

Vortex trimer in three-component Bose-Einstein condensates

Vortex trimer is predicted in three-component Bose-Einstein condensates (BEC's) with internal coherent couplings. The molecule is made by three constituent vortices which are bounded by domain walls of the relative phases. We show that the shape and the size of the molecule can be controlled by changing the internal coherent couplings.