Coupled Bose Einstein Condensates Research Articles

Quantum droplets with topological textures in a dipolar condensate

We investigate a spin–orbit coupled Bose–Einstein condensate containing both dipolar and non-dipolar components. Combined with Rashba spin–orbit coupling, the competition between contact and dipolar interaction reveals four distinctive exotic phases: droplet lattice phase, stripe phase, oblique stripe phase, and labyrinthine stripe phase. In particular, we adopt a condensate order parameter ansatz to characterize the superstripe phase in a harmonic trap through minimizing the analytical total energy. Furthermore, we find that the energy analysis of the dipolar condensate in the trap uncovers a higher order transition from lattice to stripe phases when contact interaction increases. Our results demonstrate the possibility for physicists to realize a wealth of controllable configurations in spin–orbit coupled dipolar condensates, including droplet lattice with topology and superstripe adjusted by changing the strength of contact and dipolar interactions. The topological phases we predict in this work can be realized by using state-of-the-art techniques in ultracold atomic experiments of chromium, erbium, or dysprosium condensates.

Excitation of chaotic atomic population oscillations in a spin-orbit coupled Bose-Einstein condensate with a square-wave driving

In this paper, we have investigated the excitation of chaotic atomic population oscillations in a spin-orbit (SO) coupled Bose-Einstein condensate (BEC). Unlike previous SOC system with monochrome and bichromatic driving, the present system reveals the chaotic excitation induced by the initial condition in the nondissipative regime and by the driving strength in the dissipative regime under the action of a square-wave driving. The damping-dependent chaotic parameter regions and the modulation of atomic population oscillations by the square-wave driving are studied. The existence of chaos is confirmed by computing the corresponding largest Lyapunov exponents. The results could be significant in the quantum transport of the SO coupled cold-atom system.

Tunneling dynamics of spin-orbit coupled BECs in a one-dimensional accelerating optical lattice

We theoretically investigate the energy band structure, nonlinear Landau–Zener tunneling dynamics and tunneling probability of spin-orbit coupled Bose–Einstein condensates in a one-dimensional accelerating optical lattice by using mean-field and two-mode approximation. The critical condition for the appearance of the loop structure is obtained numerically in parameter planes. When the intraspecies atomic interaction is less than the interspecies atomic interaction, the loop only appears in the lower band. In this case, Raman coupling inhibits the appearance of loop, while spin-orbit coupling (SOC) promotes the appearance of loop. If the intraspecies atomic interaction is larger than interspecies atomic interaction, the loop can appear in either the upper band or the lower band. In this case, Raman coupling promotes the loop appearing in the lower band, while SOC suppresses the loop appearing in upper band. Interestingly, when the interspecies atomic interaction is equal to the intraspecies atomic interaction, there is a critical atomic intercation value determined by the optical lattice depth, only when the intraspecies atomic interaction is greater than the critical value, the loop will occur only in lower band. Especially, the emergence of the loop structure destroys the Bloch oscillation of the system and results in the nonlinear Landau–Zener tunneling of the system. Furthermore, the Landau–Zener tunneling probability of the system is calculated, and it is found that the nonlinear Landau–Zener dynamics and the tunneling probability can be manipulated by SOC and Raman coupling.

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.

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.

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.

Interaction Control and Bright Solitons in Coherently Coupled Bose-Einstein Condensates.

We demonstrate fast control of the interatomic interactions in a Bose-Einstein condensate by coherently coupling two atomic states with intra- and interstate scattering lengths of opposite signs. We measure the elastic and inelastic scattering properties of the system and find good agreement with a theoretical model describing the interactions between dressed states. In the attractive regime, we observe the formation of bright solitons formed by dressed-state atoms. Finally, we study the response of the system to an interaction quench from repulsive to attractive values, and observe how the resulting modulational instability develops into a bright soliton train.

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.

Dynamic vortex evolution of harmonically trapped coupled Bose–Einstein condensate with quintic nonlinearity

In this study, we investigate the evolution of vortex in harmonically trapped two-component coupled Bose–Einstein condensate with quintic-order nonlinearity. We derive the vortex solution of this two-component system based on the coupled quintic-order Gross–Pitaevskii equation model and the variational method. It is found that the evolution of vortex is a metastable state. The radius of vortex soliton shrinks and expands with time, resulting in periodic breathing oscillation, and the angular frequency of the breathing oscillation is twice the value of the harmonic trapping frequency under infinitesimal nonlinear strength. At the same time, it is also found that the higher-order nonlinear term has a quantitative effect rather than a qualitative impact on the oscillation period. With practical experimental setting, we identify the quasi-stable oscillation of the derived vortex evolution mode and illustrated its features graphically. The theoretical results developed in this work can be used to guide the experimental observation of the vortex phenomenon in ultracold coupled atomic systems with quintic-order nonlinearity.

Spatial and Temporal Coherence in Strongly Coupled Plasmonic Bose-Einstein Condensates.

We report first-order spatial and temporal correlations in strongly coupled plasmonic Bose-Einstein condensates. The condensate is large, more than 20 times the spatial coherence length of the polaritons in the uncondensed system and 100 times the healing length, making plasmonic lattices an attractive platform for studying long-range spatial correlations in two dimensions. We find that both spatial and temporal coherence display nonexponential decay; the results suggest power-law or stretched exponential behavior with different exponents for spatial and temporal correlation decays.

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

Quantum oscillations between weakly coupled Bose–Einstein condensates: Evolution in a non-degenerate double well

In this paper, we discuss coherent atomic oscillations between two weakly coupled Bose–Einstein condensates that are energetically different. The weak link is notionally provided by a laser barrier in a (possibly asymmetric) multi-well trap or by Raman coupling between condensates in different hyperfine levels. The resultant boson Josephson junction dynamics is described by a double-well nonlinear Gross–Pitaevskii equation. On the basis of a new set of Jacobian elliptic function solutions, we describe the period of the oscillations as well as associated quantities and predict novel observable consequences of the interplay of the energy difference and initial phase difference between the two condensate populations.

Influence of Rashba spin–orbit and Rabi couplings on the spin-mixing and ground state phases of binary Bose–Einstein condensates

We study the miscibility properties and ground state phases of two-component spin–orbit (SO) coupled Bose–Einstein condensates (BECs) in a harmonic trap with strong axial confinement. By numerically solving the coupled Gross–Pitaevskii equations in the two-dimensional setting, we analyze the SO-coupled BECs for two possible permutations of the intra- and interspecies interactions, namely (i) weak intra- and weak interspecies interactions (W–W) and (ii) weak intra- and strong interspecies interactions (W–S). Considering the density overlap integral as a miscibility order parameter, we investigate the miscible–immiscible transition by varying the coupling parameters. We obtain various ground state phases, including plane wave, half quantum vortex, elongated plane wave, and different stripe wave patterns for W–W interactions. For finite Rabi coupling, an increase in SO coupling strength leads to the transition from the fully miscible to the partially miscible state. We also characterize different ground states in the coupling parameter space using the root mean square sizes of the condensate. The spin density vector for the ground state phases exhibits density, quadrupole and dipole like spin polarizations. For the W–S interaction, in addition to that observed in the W–W case, we witness semi vortex, mixed mode, and shell-like immiscible phases. We notice a wide variety of spin polarizations, such as density, dipole, quadrupole, symbiotic, necklace, and stripe-like patterns for the W–S case. A detailed investigation in the coupling parameter space indicates immiscible to miscible state phase transition upon varying the Rabi coupling for a fixed Rashba SO coupling. The critical Rabi coupling for the immiscible–miscible phase transition decreases upon increasing the SO coupling strength.

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

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.

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.