Two-species Bose-Einstein Condensates Research Articles

Dipole dynamics of an interacting bosonic mixture

We unravel the coupled dipole dynamics of a two-species Bose-Einstein condensate with tunable interspecies interaction. We produce a degenerate mixture of $^{41}\mathrm{K}\text{\ensuremath{-}}^{87}\mathrm{Rb}$ in an optical trap and we study the dipole oscillations of both atomic species in the linear response regime. Varying the interspecies interaction from the weakly to the strongly attractive side, we measure the frequencies and the composition of the two dipole eigenmodes. For sufficiently strong interactions, even beyond the mean-field collapse, we find that the frequency of the low-energy eigenmode is determined only by the bare trap frequencies and the species population imbalance. The experimental results are well reproduced by numerical simulations based on two coupled Gross-Pitaevskii equations. Our findings provide a detailed picture of the dipole excitations in asymmetric bosonic mixtures.

Quantum fluctuations on top of a PT -symmetric Bose-Einstein condensate

We investigate the effects of quantum fluctuations in a parity-time($\mathcal{PT}$) symmetric two-species Bose-Einstein Condensate(BEC). It is found that the $\mathcal{PT}$-symmetry, though preserved by the macroscopic condensate, can be spontaneously broken by its Bogoliubov quasi-particles under quantum fluctuations. The associated $\mathcal{PT}$-breaking transitions in the Bogoliubov spectrum can be conveniently tuned by the interaction anisotropy in spin channels and the strength of $\mathcal{PT}$ potential. In the $\mathcal{PT}$-unbroken regime, the real Bogoliubov modes are generally gapped, in contrast to the gapless phonon mode in Hermitian case. Moreover, the presence of $\mathcal{PT}$ potential is found to enhance the mean-field collapse and thereby intrigue the droplet formation after incorporating the repulsive force from quantum fluctuations. These remarkable interplay effects of $\mathcal{PT}$-symmetry and interaction can be directly probed in cold atoms experiments, which shed light on related quantum phenomena in general $\mathcal{PT}$-symmetric systems.

Scattering of Matter Wave Solitons on Localized Potentials

We study the reflection and transmission properties of matter wave solitons impinging on localized scattering potentials in one spatial dimension. By mean field analysis we identify regimes where the solitons behave more like waves or more like particles as a result of the interplay between the dispersive wave propagation and the attractive interactions between the atoms. For a bright soliton propagating together with a dark soliton void in a two-species Bose-Einstein condensate, we find different reflection and transmission properties of the dark and the bright components.

Effect of the interspecies interaction on the density profiles of miscible two-species Bose–Einstein condensates

We study harmonically trapped two-species Bose–Einstein condensates within the Gross–Pitaevskii formalism. By invoking the Thomas–Fermi approximation, we derive an analytical solution for the miscible ground state in a particular region of the system’s parameter space. This solution furnishes a simple formula that relates the interspecies interaction strength to the second spatial moments of the density distribution of the minority condensate species. Accompanying numerical simulations confirm the accuracy of the solution and the interaction strength formula for sufficiently large numbers of condensed particles. The introduced formula may provide an additional scheme for determining interspecies scattering lengths that complements existing methods, such as those based on collective-excitation spectroscopy of the two-species condensates or on collisional measurements on thermal samples.

Dynamics of phase separation in two-species Bose-Einstein condensates with vortices

We examine the dynamics associated with the miscibility-immiscibility transition of trapped two-component Bose-Einstein condensates (TBECs) of dilute atomic gases in presence of vortices. In particular, we consider TBECs of Rb hyperfine states, and Rb-Cs mixture. There is an enhancement of the phase-separation when the vortex is present in both condensates. In the case of a singly charged vortex in only one of the condensates, there is enhancement when the vortex is present in the species which occupy the edges at phase-separation. But, suppression occurs when the vortex is in the species which occupies the core region. To examine the role of the vortex, we quench the inter-species interactions to propel the TBEC from miscible to immiscible phase, and use the time dependent Gross-Pitaevskii equation to probe the phenomenon of phase-separation. We also examine the effect of higher charged vortex.

Two types of phase diagrams for two-species Bose–Einstein condensates and the combined effect of the parameters

Under the Thomas–Fermi approximation, an approach is proposed to solve the coupled Gross–Pitaevskii equations (CGP) for the two-species Bose–Einstein condensate analytically. The essence of this approach is to find out the building blocks to build the solution. By introducing the weighted strengths, relatively simpler analytical solutions have been obtained. A number of formulae have been deduced to relate the parameters when the system is experimentally tuned at various status. These formulae demonstrate the combined effect of the parameters, and are useful for the evaluation of their magnitudes. The whole parameter space is divided into zones, where each supports a specific phase. All the boundaries separating these zones have analytical expressions. Based on the division, the phase diagrams against any set of parameters can be plotted. In addition, by introducing a model for the asymmetric states, the total energies of the lowest symmetric and asymmetric states have been compared. Thereby, in which case the former will be replaced by the latter has been evaluated. The CGP can be written in a matrix form. For repulsive inter-species interaction VAB, when the parameters vary and cross over the singular point of the matrix, a specific state transition will happen and the total energy of the lowest symmetric state will increase remarkably. This provides an excellent opportunity for the lowest asymmetric state to emerge as the ground state. For attractive VAB, when the parameters tend to a singular point, the system will tend to collapse. The effects caused by the singular points have been particularly studied.

Characteristic temperature for the immiscible-miscible transition of binary condensates in optical lattices

We study a two-species Bose-Einstein condensates confined in quasi-two-dimensional (quasi-2D) optical lattices at finite temperatures, employing the Hartree-Fock-Bogoliubov theory with the Popov approximation. We examine the role of thermal fluctuations on the ground-state density distributions, and the quasiparticle mode evolution. At zero temperature, the geometry of the ground-state in the immiscible domain is side-by-side. Our results show that the thermal fluctuations enhance the miscibility of the condensates, and at a characteristic temperature the system becomes miscible with rotationally symmetric overlapping density profiles. This immiscible-miscible transition is accompanied by a discontinuity in the excitation spectrum, and the low-lying quasiparticle modes such as slosh mode becomes degenerate at the characteristic temperature.

Chaos-assisted formation of immiscible matter-wave solitons and self-stabilization in the binary discrete nonlinear Schrödinger equation

Binary discrete nonlinear Schrödinger equation is used to describe dynamics of two-species Bose–Einstein condensate loaded into an optical lattice. Linear inter-species coupling leads to Rabi transitions between the species. In the regime of strong nonlinearity, a wavepacket corresponding to condensate separates into localized and ballistic fractions. Localized fraction is predominantly formed by immiscible solitons consisted of only one species. Immiscible solitons are formed from initially non-separated states after transient chaotic regime. We calculate the finite-time Lyapunov exponent as a rate of wavepacket divergence in the Hilbert space. Appearance of immiscible solitons to spontaneous self-stabilization of the wavepacket. It is found that onset of chaos is accompanied by fast variations of interaction energy and energy of inter-site tunneling. Crossover to self-stabilization is accompanied by reduction of condensate density due to emittance of ballistically propagating waves.

Optical-lattice-influenced geometry of quasi-two-dimensional binary condensates and quasiparticle spectra

We explore the collective excitations of optical lattices filled with two-species Bose-Einstein condensates (TBECs). We use a set of coupled discrete nonlinear Schr\"odinger equations to describe the system, and employ Hartree-Fock-Bogoliubov (HFB) theory with the Popov approximation to analyze the quasiparticle spectra at zero temperature. The ground state geometry, evolution of quasiparticle energies, structure of quasiparticle amplitudes, and dispersion relations are examined in detail. The trends observed are in stark contrast to the case of TBECs only with a harmonic confining potential. One key observation is the quasiparticle energies are softened as the system is tuned towards phase separation, but harden after phase separation and mode degeneracies are lifted.

Two-species Bose–Einstein condensate in an optical lattice: analytical approximate formulae

Employing a general variational method and perturbation theory, we derived explicit solutions for the description of one-dimensional two species Bose–Einstein condensates confined by a harmonic trap potential in an optical lattice. We consider the system of two coupled Gross–Pitaevskii equations (GPE) and derive explicit expressions for the chemical potentials and wavefunctions in terms of the atom–atom interaction parameters and laser intensity. We have compared our results with the numerical solutions of the GPE and performed a quantitative analysis for the both considered methods. We underline the importance of the obtained explicit solutions to characterize the density profile or degree of miscibility of the two components.

Optical Bistability and Normal-Mode Splitting of Two-Species Bose-Einstein Condensates in An Optical Cavity

We investigate the optical bistable behavior for a weakly interacting two-species Bose-Einstein condensates inside a pumped optical cavity by considering the two possible regimes- the phase mixed regime and the phase segregated regime. We find that the cavity-pump detuning plays a significant role in controlling the threshold of the optical bistability and the constrast between the bistability values depending upon the state we are working in. We also demonstrate the occurence of normal mode splitting in the optical spectrum for both the regimes which further showing the position and amplitude discrepancies in the spectral peaks.

Selective distillation phenomenon in two-species Bose-Einstein condensates in open boundary optical lattices.

We investigate the formation of discrete breathers (DBs) and the dynamics of the mixture of two-species Bose-Einstein condensates (BECs) in open boundary optical lattices using the discrete nonlinear Schrödinger equations. The results show that the coupling of intra- and interspecies interaction can lead to the existence of pure single-species DBs and symbiotic DBs (i.e., two-species DBs). Furthermore, we find that there is a selective distillation phenomenon in the dynamics of the mixture of two-species BECs. One can selectively distil one species from the mixture of two-species BECs and can even control dominant species fraction by adjusting the intra- and interspecies interaction in optical lattices. Our selective distillation mechanism may find potential application in quantum information storage and quantum information processing based on multi-species atoms.

Nonautonomous vector matter waves in two-component Bose-Einstein condensates with combined time-dependent harmonic-lattice potential

We construct exact self-similar soliton solutions of three-dimensional coupled Gross–Pitaevskii equations for two-species Bose–Einstein condensates (BECs) in a combined time-dependent harmonic-lattice potential. Based on these solutions, we investigate the control and manipulation of solitary waves for three kinds of BECs with changing diffraction and nonlinearity coefficients; the solutions include Ma breathers and Peregrine and Akhmediev soliton solutions. Our results indicate that matter waves readily propagate in this system. It is shown that diffraction and lattice potential factors play important roles in the beam evolution characteristics, such as the peak, the phase offset, the linear phase, and the chirp.

Interactions and collisions of discrete breathers in two-species Bose-Einstein condensates in optical lattices.

The dynamics of static and traveling breathers in two-species Bose-Einstein condensates in a one-dimensional optical lattice is modelled within the tight-binding approximation. Two coupled discrete nonlinear Schrödinger equations describe the interaction of the condensates in two cases of relevance: a mixture of two ytterbium isotopes and a mixture of (87)Rb and (41)K. Depending on their initial separation, interaction between static breathers of different species can lead to the formation of symbiotic structures and transform one of the breathers from a static into a traveling one. Collisions between traveling and static discrete breathers composed of different species are separated into four distinct regimes ranging from totally elastic when the interspecies interaction is highly attractive to mutual destruction when the interaction is sufficiently large and repulsive. We provide an explanation of the collision features in terms of the interspecies coupling and the negative effective mass of the discrete breathers.

Transformation of vector solitons in twospecies Bose-Einstein condensates

Considering the interspecies and intraspecies interactions as being repulsive, we study the dynamic behaviors of the gray-gray and black-black solitons in two-species Bose-Einstein condensates trapped in the harmonic external potentials. The results show that in the absence of the axial trapping frequencies, both the gray-gray and black-black solitons can keep localization stable. In the presence of the axial trapping frequencies, the gray-gray can be converted into bright-bright solitons.

Oscillation and fission behavior of bright-bright solitons in two-species Bose-Einstein condensates trapped in an optical potential

We have studied the dynamic behavior of bright-bright solitons in two-species Bose-Einstein condensates trapped in an optical lattice. It is shown that the directions of motion and oscillations of the bright-bright solitons can be effectively controlled by adjusting the lattice spacing and height, respectively. Especially, two separated solitons can be localized in the optical lattice, and the fission of each localized soliton is newly observed due to the increase of the lattice height.

Exact Temporal Evolution of Two-Species Bose—Einstein Condensates

We construct exact stationary solutions to the one-dimensional coupled Gross—Pitaevskii equations for the two-species Bose—Einstein condensates with equal intraspecies and interspecies interaction constants. Three types of complex solutions as well as their soliton limits are derived. By making use of the SU(2) unitary symmetry, we further obtain analytical time-evolving solutions. These solutions exhibit spatiotemporal periodicity.

Dark-soliton dynamics in a two-species Bose–Einstein condensate with the external potential and thermal cloud effects

Considering the time-dependent external potential and thermal cloud effects, this paper investigates via symbolic computation the dark-soliton dynamics in a two-species Bose–Einstein condensate (BEC), which can be described by the quasi-one-dimensional coupled Gross–Pitaevskii equations. Under the balance between the harmonic potential and thermal cloud effects, dark multi-soliton solutions are derived for the two-species BEC through the Hirota bilinear method. Regions of the s-wave scattering lengths are ascertained for the existence of the dark solitons in two species. Influence of the scattering lengths and external potential on the background density, soliton width and velocity is examined. Graphical analysis demonstrates that the harmonic and linear potentials can change the propagation paths, collision positions and collision time of the dark solitons, and that the thermal cloud effects can affect the number of atoms in the two-species BEC.

Single-Particle Coherence and RMQFI in Two-Species BECs

We investigate the relation between the single-particle coherence and the reciprocal of the mean quantum Fisher information per particle (RMQFI) in Bose-Einstein condensates (BECs) in the presence of interatomic interaction and interspecies interaction. The single-particle coherence and RMQFI depend on the interatomic interaction. It is shown that the larger interatomic interaction more rapidly induces entanglement.

Equilibrium solutions for immiscible two-species Bose-Einstein condensates in perturbed harmonic traps

We investigate the mean-field equilibrium solutions for a two-species immiscible Bose-Einstein condensate confined by a harmonic confinement with additional linear perturbations. We observe a range of equilibrium density structures, including ball and shell formations and axially or radially separated states, with a marked sensitivity to the potential perturbations and the relative atom number in each species. Incorporation of linear trap perturbations, albeit weak, are found to be essential to match the range of equilibrium density profiles observed in a recent ${}^{87}$Rb-${}^{133}$Cs Bose-Einstein condensate experiment [McCarron et al., Phys. Rev. A 84, 011603(R) (2011)]. Our analysis of this experiment demonstrates that sensitivity to linear trap perturbations is likely to be an important factor in interpreting the results of similar experiments in the future.