Coupled Bose Einstein Condensates Research Articles

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.

(2+1) -dimensional sonic black hole from a spin-orbit-coupled Bose-Einstein condensate and its analog Hawking radiation

We study the properties of a $2+1$ dimensional Sonic black hole (SBH) that can be realised, in a quasi-two-dimensional two-component spin-orbit coupled Bose-Einstein condensate (BEC). The corresponding equation for phase fluctuations in the total density mode that describes phonon field in the hydrodynamic approximation is described by a scalar field equation in $2+1$ dimension whose space-time metric is significantly different from that of the SBH realised from a single component BEC that was studied experimentally, and, theoretically meticulously in literature. Given the breakdown of the irrotationality constraint of the velocity field in such spin-orbit coupled BEC, we study in detail how the time evolution of such condensate impacts the various properties of the resulting SBH. By time evolving the condensate in a suitably created laser-induced potential, we show that such a sonic black hole is formed, in an annular region bounded by inner and outer event horizon as well as elliptical ergo-surfaces. We observe amplifying density modulation due to the formation of such sonic horizons and show how they change the nature of analogue Hawking radiation emitted from such sonic black hole by evaluating the density-density correlation at different times, using the truncated Wigner approximation (TWA) for different values of spin-orbit coupling parameters. We finally investigate the thermal nature of such analogue Hawking radiation.

Phase separation in spin-orbit-angular-momentum coupling Bose–Einstein condensate systems

We study the phase separation in three-component spin-orbit-angular-momentum coupled Bose–Einstein condensate with spin-1 in three dimensions. Different types of phase-separation are acquired upon an increase of the coupling strength, magnetic gradient strength, spin-dependent interaction strength and particle number above a critical value. Increasing the value of coupling strength and other related parameters shows distinct behaviors which are produced by repulsion for large strengths of spin-orbit angular-momentum (SOAM) coupling. The present investigation is carried out through a numerical Crank–Nicolson method of the underlying mean-field Gross–Pitaevskii equation.

Four-wave mixing in spin–orbit coupled Bose–Einstein condensates

We describe possibilities of spontaneous, degenerate four-wave mixing (FWM) processes in spin–orbit coupled Bose–Einstein condensates. Phase matching conditions (i.e., energy and momentum conservation laws) in such systems allow one to identify four different configurations characterized by involvement of distinct spinor states in which such a process can take place. We derived these conditions from first principles and then illustrated dynamics with direct numerical simulations. We found, among others, the unique configuration, where both probe waves have smaller group velocity than pump wave and proved numerically that it can be observed experimentally under proper choice of the parameters. We also reported the case when two different FWM processes can occur simultaneously. The described resonant interactions of matter waves is expected to play an important role in the experiments of BEC with artificial gauge fields. Beams created by FWM processes are an important source of correlated particles and can be used in the experiments testing quantum properties of atomic ensembles.

六极子磁场中自旋轨道耦合玻色-爱因斯坦凝聚体的基态结构

六极子磁场中自旋轨道耦合玻色-爱因斯坦凝聚体的基态结构

Spontaneous Symmetry Breaking in Coupled Bose–Einstein Condensates

We study a system of two hardcore bosonic Hubbard models weakly coupled with each other by tunneling. Assuming that the single uncoupled model exhibits off-diagonal long-range order, we prove that the coupled system exhibits spontaneous symmetry breaking (SSB) in the infinite volume limit, in the sense that the two subsystems maintain a definite relative U(1) phase when the tunneling is turned off. Although SSB of the U(1) phase is never observable in a single system, SSB of the relative U(1) phase is physically meaningful and observable by interference experiments. The present theorem is made possible by the rigorous theory of low-lying states and SSB in quantum antiferromagnets developed over the years.

Experimental realization of a non-magnetic one-way spin switch

Controlling magnetism through non-magnetic means is highly desirable for future electronic devices, as such means typically have ultra-low power requirements and can provide coherent control. In recent years, great experimental progress has been made in the field of electrical manipulation of magnetism in numerous material systems. These studies generally do not consider the directionality of the applied non-magnetic potentials and/or magnetism switching. Here, we theoretically conceive and experimentally demonstrate a non-magnetic one-way spin switch device using a spin-orbit coupled Bose–Einstein condensate subjected to a moving spin-independent repulsive dipole potential. The physical foundation of this unidirectional device is based on the breakdown of Galilean invariance in the presence of spin-orbit coupling. Such a one-way spin switch opens an avenue for designing quantum devices with unique functionalities and may facilitate further experimental investigations of other one-way spintronic and atomtronic devices.

SU(3) spin–orbit-coupled Bose–Einstein condensate confined in a harmonic plus quartic trap

We consider a SU(3) spin–orbit coupled Bose–Einstein condensate confined in a harmonic plus quartic trap. The ground-state wave functions of such a system are obtained by minimizing the Gross–Pitaevskii energy functional, and the effects of the spin-dependent interaction and spin–orbit coupling are investigated in detail. For the case of ferromagnetic spin interaction, the SU(3) spin–orbit coupling induces a threefold-degenerate plane wave ground state with nontrivial spin texture. For the case of antiferromagnetic spin interaction, the system shows phase separation for weak SU(3) spin–orbit coupling, where three discrete minima with unequal weights in momentum space are selected, while hexagonal honeycomb lattice structure for strong SU(3) SOC, where three discrete minima with equal weights are selected.

Experimental realization of a long-lived striped Bose-Einstein condensate induced by momentum-space hopping

In the past few decades, the search for supersolid-like phases has attracted great attention in condensed matter and ultracold atom communities. Here we experimentally demonstrate a route for realizing a superfluid stripe-phase in a spin-orbit coupled Bose-Einstein condensate by employing a weak optical lattice to induce momentum-space hopping between two spin-orbit band minima. We characterize the striped ground state as a function of lattice coupling strength and spin-orbit detuning and find good agreement with mean-field simulations. We observe coherent Rabi oscillations in momentum space between two band minima and demonstrate a long lifetime of the ground state. Our work offers an exciting new and stable experimental platform for exploring superfluid stripe-phases and their exotic excitations, which may shed light on the properties of supersolid-like states.

Two-fluid theory for a superfluid system with anisotropic effective masses

In this work, we generalize the two-fluid theory to a superfluid system with anisotropic effective masses along different principal axis directions. As a specific example, such a theory can be applied to spin-orbit coupled Bose-Einstein condensate (BEC) at low temperature. The normal density from phonon excitations and the second sound velocity are obtained analytically. Near the phase transition from the plane wave to zero-momentum phases, due to the effective mass divergence, the normal density from phonon excitation increases greatly, while the second sound velocity is suppressed significantly. With quantum hydrodynamic formalism, we give unified derivations for suppressed superfluid density and Josephson relation. At last, the momentum distribution function and fluctuation of phase for the long wave length are also discussed.

Spatiotemporal Bloch states of a spin–orbit coupled Bose–Einstein condensate in an optical lattice**Project supported by the National Natural Science Foundation of China (Grant No. 11475060).

We study the spatiotemporal Bloch states of a high-frequency driven two-component Bose–Einstein condensate (BEC) with spin–orbit coupling (SOC) in an optical lattice. By adopting the rotating-wave approximation (RWA) and applying an exact trial-solution to the corresponding quasistationary system, we establish a different method for tuning SOC via external field such that the existence conditions of the exact particular solutions are fitted. Several novel features related to the exact states are demonstrated; for example, SOC leads to spin–motion entanglement for the spatiotemporal Bloch states, SOC increases the population imbalance of the two-component BEC, and SOC can be applied to manipulate the stable atomic flow which is conducive to control quantum transport of the BEC for different application purposes.

Spin Mixing Dynamics in a Spin–Orbit Coupled Bose–Einstein Condensate

We investigate the spin mixing dynamics of a spin–orbit coupled Bose–Einstein condensate by using a variational approach. It is shown that the spin mixing dynamics can be well described by an internal Josephson equation. In the nonzero momentum phase, the spin mixing dynamics leads to a spin polarization, i.e., most atoms are suppressed in the one of the two spin states. In the zero momentum phase, the internal Josephson oscillation between the two spin states takes place. Thus, the coupling effects of spin–orbit coupling, Raman coupling and atomic interaction can result in the transition between the spin polarization and the internal Josephson oscillation of the two spin states, which provide a theoretical evidence for elaborating the spin mixing dynamics. Moreover, at the phase transition point, the oscillation period of the spin mixing dynamics tends to infinity. This can be used to explore the phase transition experimentally. The accurate manipulation of the spin mixing dynamics can provide a theoretical evidence for designing the atomic device.

Strong quadrature squeezing and quantum amplification in a coupled Bose–Einstein condensate—optomechanical cavity based on parametric modulation

We consider an optomechanical cavity with a movable end-mirror as a quantum mechanical oscillator (MO) containing an interacting cigar-shaped Bose–Eisenstein condensate (BEC). It is assumed that both the MO and the BEC interact with the radiation pressure of the cavity field in the red-detuned and weak coupling regimes while the two-body atomic collisions frequency of the BEC and the mechanical spring coefficient of the MO are coherently modulated. By analyzing the scattering matrix, we show that in the largely different cooperativities regime together with strong modulations, the mechanical mode of the MO and the Bogoliubov mode of the BEC exhibit quadrature squeezing which can surpass the so-called 3dB limit (up to 75 dB) with high robustness to the thermal noises. Surprisingly, in this regime by controlling the system and modulation parameters, a very high degree of squeezing (up to 16 dB) together with high purity of quantum state for the output cavity field is achievable. Furthermore, one can attain simultaneous strong quantum amplification, added-noise suppression, and controllable gain-bandwidth for the complementary quadratures of squeezed ones in the subsystems.

Ground-State Phase Diagram of a Spin-Orbital-Angular-Momentum Coupled Bose-Einstein Condensate.

By inducing a Raman transition using a pair of Gaussian and Laguerre-Gaussian laser beams, we realize a ^{87}Rb condensate whose orbital angular momentum (OAM) and its internal spin states are coupled. By varying the detuning and the coupling strength of the Raman transition, we experimentally map out the ground-state phase diagram of the system for the first time. The transitions between different phases feature a discontinuous jump of the OAM and the spin polarization, and hence are of first order. We demonstrate the hysteresis loop associated with such first-order phase transitions. The role of interatomic interaction is also elucidated. Our work paves the way to explore exotic quantum phases in the spin-orbital-angular-momentum coupled quantum gases.

Effect of spin–orbit coupling on tunnelling escape of Bose–Einstein condensate

We theoretically investigate quantum tunnelling escape of a spin–orbit (SO)-coupled Bose–Einstein condensate (BEC) from a trapping well. The condensate is initially prepared in a quasi-one-dimensional harmonic trap. Depending on the system parameters, the ground state can fall in different phases—single minimum, separated or stripe. Then, suddenly the trapping well is opened at one side. The subsequent dynamics of the condensate is studied by solving nonlinear Schrödinger equations. We found that the diverse phases will greatly change the tunneling escape behavior of SO-coupled BECs. In the single minimum and separated phases, the condensate escapes the trapping well continuously, while in the stripe phase it escapes the well as an array of pulses. We also found that SO coupling has a suppressing effect on the tunnelling escape of atoms. Especially, for BECs without inter-atom interaction, the tunnelling escape can be almost completely eliminated when the system is tuned near the transition point between the single minimum and stripe phases. Our work thus suggests that SO coupling may be a useful tool to control the tunnelling dynamics of BECs, and potentially be applied in the realization of atom lasers and matter wave switches.

Interaction induced localization of a spin–orbit-coupled Bose-Einstein condensate in a double-well potential

We investigate atomic interaction induced localization of a spin–orbit coupled Bose-Einstein condensate loaded in a double-well potential. We confirm the existence of the localization in the presence of the spin–orbit coupling for differences between the spin-dependent nonlinear atomic interaction strength between intraspin and interspin. We find a quantum phase transition from spin balance to spin localization for the different strengths of nonlinear atomic interaction strength. We also obtain the parametric dependence of the transitions to spin localization. The results play a constructive role to control spin localization of spin–orbit coupled Bose-Einstein condensate in a double-well potential.

Ring phases of spin-orbit coupled Bose-Einstein condensate in the radial optical lattices

We study the ground-state phases of two-dimensional spin-orbit coupled Bose-Einstein condensate loaded in the spin-dependent radial optical lattices. For strong depth of the spin-dependent radial optical lattice, three new types of the ring phases are found with isotropic spin-orbit coupling, i.e., the ring-stripe phase with the periodic density modulation along the radial direction, the ring-supersolid phase with the periodic density modulation both the radial and azimuthal directions and the windmill-supersolid phase with four vanes along the azimuthal direction. By increasing spin-orbit coupling, the system undergoes a sequence phase transitions from the ring-stripe phase to the ring-sueprsolid phase, and to the windmill-supersolid phase for the weak depth of radial optical lattice, however, the ring-stripe phase transforms to the windmill-supersolid phase directly for the strong depth of radial optical lattice. We also discuss the ground-state phases with anisotropic spin-orbit coupling, two-component Bose-Einstein condensates are easier condensed along the direction with larger spin-orbit coupling.

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.

Estimating ergodization time of a chaotic many-particle system from a time reversal of equilibrium noise

We propose a method of estimating ergodization time of a chaotic many-particle system by monitoring equilibrium noise before and after time reversal of dynamics (Loschmidt echo). The ergodization time is defined as the characteristic time required to extract the largest Lyapunov exponent from a system’s dynamics. We validate the method by numerical simulation of an array of coupled Bose–Einstein condensates in the regime describable by the discrete Gross–Pitaevskii equation. The quantity of interest for the method is a counterpart of out-of-time-order correlators in the quantum regime.