Mixture Of Bose-Einstein Condensates Research Articles

Properties of a trapped multiple-species bosonic mixture at the infinite-particle-number limit: A solvable model.

We investigate a trapped mixture of Bose-Einstein condensates consisting of a multiple number of P species. To be able to do so, an exactly solvable many-body model is called into play. This is the P-species harmonic-interaction model. After presenting the Hamiltonian, the ground-state energy and wavefunction are explicitly calculated. All properties of the mixture's ground state can, in principle, be obtained from the many-particle wavefunction. A scheme to integrate the all-particle density matrix is derived and implemented, leading to closed-form expressions for the reduced one-particle density matrices. Of particular interest is the infinite-particle-number limit, which is obtained when the numbers of bosons are taken to infinity while keeping the interaction parameters fixed. We first prove that at the infinite-particle-number limit all the species are 100% condensed. The mean-field solution of the P-species mixture is also obtained analytically and is used to show that the energy per particle and densities per particle computed at the many-body level of theory boil down to their mean-field counterparts. Despite these, correlations in the mixture exist at the infinite-particle-number limit. To this end, we obtain closed-form expressions for the correlation energy, namely, the difference between the mean-field and many-body energies, and the depletion of the species, i.e., the number of particles residing outside the condensed modes, at the infinite-particle-number limit. The depletion and the correlation energy per species are shown to critically depend on the number of species. Of separate interest is the entanglement between one species of bosons and the other P - 1 species. This quantity is governed by the coupling of the center-of-mass coordinates of the species and is obtained by the respective Schmidt decomposition of the P-species wavefunction. Interestingly, there is an optimal number of species, here P = 3, where the entanglement is maximal. Importantly, the manifestation of this interspecies entanglement in an observable is possible. It is the position-momentum uncertainty product of one species in the presence of the other P - 1 species, which is derived and demonstrated to correlate with the interspecies entanglement. All in all, we show and explain how correlations at the infinite-particle-number limit of a trapped multiple-species bosonic mixture depend on the interactions and how they evolve with the number of species. Generalizations and implications are briefly discussed.

Coupled-cluster theory for trapped bosonic mixtures.

We develop a coupled-cluster theory for bosonic mixtures of binary species in external traps, providing a promising theoretical approach to demonstrate highly accurately the many-body physics of mixtures of Bose-Einstein condensates. The coupled-cluster wavefunction for the binary species is obtained when an exponential cluster operator eT, where T = T(1) + T(2) + T(12) and T(1) accounts for excitations in species-1, T(2) for excitations in species-2, and T(12) for combined excitations in both species, acts on the ground state configuration prepared by accumulating all bosons in a single orbital for each species. We have explicitly derived the working equations for bosonic mixtures by truncating the cluster operator up to the single and double excitations and using arbitrary sets of orthonormal orbitals for each of the species. Furthermore, the comparatively simplified version of the working equations are formulated using the Fock-like operators. Finally, using an exactly solvable many-body model for bosonic mixtures that exists in the literature allows us to implement and test the performance and accuracy of the coupled-cluster theory for situations with balanced as well as imbalanced boson numbers and for weak to moderately strong intra- and interspecies interaction strengths. The comparison between our computed results using coupled-cluster theory with the respective analytical exact results displays remarkable agreement exhibiting excellent success of the coupled-cluster theory for bosonic mixtures. All in all, the correlation exhaustive coupled-cluster theory shows encouraging results and could be a promising approach in paving the way for high-accuracy modeling of various bosonic mixture systems.

Two-dimensional vector solitons in Bose-Einstein-condensate mixtures

We derive two decoupled KP-I equations from the system of two-dimensional (2D) Gross-Pitaevskii equations for a two-component Bose-Einstein condensate (BEC), using the multiple-scale expansion method. We produce asymptotic analytical vector-soliton solutions, viz., dark-dark (DD) and dark-antidark (DAD) one-soliton and two-soliton states, by tuning coupling constants and norms of species, and address their evolution numerically under the action of the harmonic-oscillator (HO) trap, in the local-density approximation. We find that shallow single-line DD and DAD solitons are stable, while single-lump DAD solutions (weakly localized truly-2D states) split and lead to nucleation of two half-vortices. We also find that the BEC mixture placed in the HO trap admits stable asymptotic multi-soliton solutions, e.g., two-line DD and DAD solitons and two-lump DD ones, which were not reported before. In particular, the two-lump solutions describe inelastic collisions between the lumps. The analysis developed in this work may also be applied to systems with spin-orbit coupling and gauge fields, which have been realized in atomic BEC.

Dynamical self-trapping of two-dimensional binary solitons in cross-combined linear and nonlinear optical lattices.

Dynamical and self-trapping properties of two-dimensional (2D) binary mixtures of Bose-Einstein condensates in cross-combined lattices, consisting of a one-dimensional (1D) linear optical lattice (LOL) in the x direction for the first component and a 1D nonlinear optical lattice (NOL) in the y direction for the second component, are analytically and numerically investigated. The existence and stability of 2D binary matter wave solitons in these settings are demonstrated both by variational analysis and by direct numerical integration of the coupled Gross-Pitaevskii equations. We find that in the absence of the NOL, binary solitons, stabilized by the action of the 1D LOL and by the attractive intercomponent interaction, can freely move in the y direction. In the presence of the NOL, we find, quite remarkably, the existence of threshold curves in the parameter space separating regions where solitons can move from regions where the solitons become dynamically self-trapped. The mechanism underlying the dynamical self-trapping phenomenon (DSTP) is qualitatively understood in terms of a dynamical barrier induced by the NOL, similar to the Peirls-Nabarro barrier of solitons in discrete lattices. DSTP is numerically demonstrated for binary solitons that are put in motion both by phase imprinting and by the action of external potentials applied in the y direction. In the latter case, we show that the trapping action of the NOL allows one to maintain a 2D binary soliton at rest in a nonequilibrium position of a parabolic trap or to prevent it from falling under the action of gravity. Possible applications of the results are also briefly discussed.

Dark quantum droplets and solitary waves in beyond-mean-field Bose-Einstein condensate mixtures

Quantum liquidlike states of matter have been realized in an ongoing series of experiments with ultracold Bose gases. Using a combination of analytical and numerical methods we identify the specific criteria for the existence of dark solitons in beyond-mean-field binary condensates, revealing how these excitations exist for both repulsive and attractive interactions, the latter leading to dark quantum droplets with properties intermediate between a dark soliton and a quantum droplet. The phenomenology of these excitations is explored within the full parameter space of the model, revealing a spatial profile of the excitation that differs significantly from the Zakharov-Shabat soliton, leading to a negative effective mass that is enhanced in the presence of the quantum fluctuations. Finally the dynamics of pairs of the excitations are explored, showing nonintegrable dynamics and dark soliton bound states in the attractive regime.

Compacton existence and spin-orbit density dependence in Bose-Einstein condensates.

We demonstrate the existence of compactons matter waves in binary mixtures of Bose-Einstein condensates (BEC) trapped in deep optical lattices (OL) subjected to equal contributions of intraspecies Rashba and Dresselhaus spin-orbit coupling (SOC) under periodic time modulations of the intraspecies scattering length. We show that these modulations lead to a rescaling of the SOC parameters that involves the density imbalance of the two components. This gives rise to density dependent SOC parameters that strongly influence the existence and the stability of compacton matter waves. The stability of SOC-compactons is investigated both by linear stability analysis and by time integrations of the coupled Gross-Pitaevskii equations. We find that SOC restricts the parameter ranges for stable stationary SOC-compacton existence but, on the other side, it gives a more stringent signature of their occurrence. In particular, SOC-compactons should appear when the intraspecies interactions and the number of atoms in the two components are perfectly balanced (or close to being balanced for the metastable case). The possibility to use SOC-compactons as a tool for indirect measurements of the number of atoms and/or the intraspecies interactions is also suggested.

Droplet to soliton crossover at negative temperature in presence of bi-periodic optical lattices

It is shown that the phenomenon of negative temperature essentially occurs in Bose-Einstein condensate due to the realization of the upper bound energy state utilizing a combination of expulsive harmonic oscillator and optical lattice potentials. We study the existence of quantum droplets at negative temperature and droplet-to-soliton crossover in the binary Bose-Einstein condensate mixture in the presence of bi-periodic optical lattices and expulsive-BOL confinements. Based on the beyond mean field approximation, we employ the extended Gross-Pitäevskii equation and calculate the exact analytical form of wavefunction solutions for BOL, expulsive-BOL confinements. An interesting transition of quantum droplets from positive to negative temperatures and the droplet-to-soliton crossover by modulating the disorder in BOL potential are illustrated. The affirmation of such crossover is performed by exploring the profile of atomic condensate density which smoothly transits from being a flat top density in optical lattice confinement to a bright soliton for BOL trap. Further, we confirm the crossover by exploring the energy per particle and the variation in the root mean square size of the condensate with respect to the potential depth of the BOL trap. Eventually, all of this aid us to construct a phase diagram in a space between the amplitude of BOL potential depth and particle number which reveals the formation of droplet and soliton phases. In expulsive-BOL confinement, it is seen that the impact of the expulsive trap is insignificant on atomic condensate density in the droplet phase and it becomes prominent in the soliton region. Further, the variation of total energy reveals that the amplitude of the expulsive oscillator strengthens the droplet phase and leads to an increase in the negative temperature of the considered system.

The Casimir Effect in Bose–Einstein Condensate Mixtures Confined by a Parallel Plate Geometry in the Improved Hartree–Fock Approximation

The Casimir Effect in Bose–Einstein Condensate Mixtures Confined by a Parallel Plate Geometry in the Improved Hartree–Fock Approximation

Location of Interface Bose-Einstein Condensate Mixtures in Semi-infinite Space under Neumann Boundary Condition

The location of interface plays a pivotal role in studying on wetting phase transition of Bose-Einstein condensates (BECs) mixture. Beside parameters of system, the position of the interface depends on the applied boundary condition. Using double-parabola approximation (DPA), we consider the dependence of position of interface on parameters in semi-infinite space under Neumann boundary condition.

Interface potential and line tension for Bose-Einstein condensate mixtures near a hard wall

Within Gross-Pitaevskii (GP) theory we derive the interface potential V (l) which describes the interaction between the interface separating two demixed Bose-condensed gases and an optical hard wall at a distance l. Previous work revealed that this interaction gives rise to extraordinary wetting and prewetting phenomena. Calculations that explore non-equilibrium properties by using l as a constraint provide a thorough explanation for this behavior. We find that at bulk two-phase coexistence, V (l) for both complete wetting and partial wetting is monotonic with exponential decay. Remarkably, at the first-order wetting phase transition, V(l) is independent of l. This anomaly explains the infinite continuous degeneracy of the grand potential reported earlier. As a physical application, using V(l) we study the three-phase contact line where the interface meets the wall under a contact angle theta. Employing an interface displacement model we calculate the structure of this inhomogeneity and its line tension tau. Contrary to what happens at a usual first-order wetting transition in systems with short-range forces, tau does not approach a nonzero positive constant for theta going to zero, but instead approaches zero (from below) as would be expected for a critical wetting transition. This hybrid character of tau is a consequence of the absence of a barrier in V(l) at wetting. For a typical V(l) we provide a conjecture for the exact line tension within GP theory.

Dynamical generation of dark-bright solitons through the domain wall of two immiscible Bose-Einstein condensates

We theoretically investigate the one-dimensional dynamics of a dark soliton in a two-component immiscible mixture of Bose-Einstein condensates with repulsive interactions. We analyze the reflection and transmission of a soliton when it propagates through the domain wall, and we show that a dark-bright soliton can be dynamically generated by the interaction of the dark soliton with the domain wall, outside the regime of parameters where stationary solutions are known to exist. The dynamics of this dark-bright soliton is harmonic like, with a numerical frequency that is in good agreement with the predictions of a semi-analytical model.

Observation of a Lee-Huang-Yang Fluid.

We observe monopole oscillations in a mixture of Bose-Einstein condensates, where the usually dominant mean-field interactions are canceled. In this case, the system is governed by the next-order Lee-Huang-Yang (LHY) correction to the ground state energy, which describes the effect of quantum fluctuations. Experimentally such a LHY fluid is realized by controlling the atom numbers and interaction strengths in a ^{39}K spin mixture confined in a spherical trap potential. We measure the monopole oscillation frequency as a function of the LHY interaction strength as proposed recently by Jrgensen etal. [Phys. Rev. Lett. 121, 173403 (2018)PRLTAO0031-900710.1103/PhysRevLett.121.173403] and find excellent agreement with simulations of the complete experiment including the excitation procedure and inelastic losses. This confirms that the system and its collective behavior are initially dominated by LHY interactions. Moreover, the monopole oscillation frequency is found to be stable against variations of the involved scattering lengths in a broad region around the ideal values, confirming the stabilizing effect of the LHY interaction. These results pave the way for using the nonlinearity provided by the LHY term in quantum simulation experiments and for investigations beyond the LHY regime.

Beyond-mean-field crossover from one dimension to three dimensions in quantum droplets of binary mixtures

The existence of quantum droplets in binary Bose-Einstein condensate mixtures relies on beyond-mean-field effects, competing with mean-field effects. Interestingly, the beyond-mean-field effects change from repulsive in three dimensions (3D) to attractive in 1D leading to drastically different behaviors. We quantitatively model quantum droplets in the beyond-mean-field crossover from 1D to 3D in the relevant case of an elongated harmonic trap and give realistic numbers for experimental realizations. We identify and quantify two main limiting factors: three-body losses and tiny energy scales. The crossover region is appealing as it offers a trade-off between these two main limitations opening the possibility of observing stable flat-top density profiles, a yet unobserved, characteristic feature of quantum droplets. It would permit testing of beyond-mean-field theories to an unprecedented precision.

Dynamics of massive point vortices in a binary mixture of Bose-Einstein condensates

We study the massive point-vortex model introduced in Ref. [Phys. Rev. A 101, 013630 (2020)], which describes two-dimensional point vortices of one species that have small cores of a different species. We derive the relevant Lagrangian itself, based on the time-dependent variational method with a two-component Gross-Pitaevskii (GP) trial function. The resulting Lagrangian resembles that of charged particles in a static electromagnetic field, where the canonical momentum includes an electromagnetic term. The simplest example is a single vortex with a rigid circular boundary, where a massless vortex can only precess uniformly. In contrast, the presence of a sufficiently large filled vortex core renders such precession unstable. A small core mass can also lead to small radial oscillations, which are, in turn, clear evidence of the associated inertial effect. Detailed numerical analysis of coupled two-component GP equations with a single vortex and small second-component core confirms the presence of such radial oscillations, implying that this more realistic GP vortex also acts as if it has a small massive core.

Thermodynamics of dilute Bose gases: Beyond mean-field theory for binary mixtures of Bose-Einstein condensates

We study the thermodynamic properties of binary Bose mixtures, by developing a beyond mean-field Popov theory which properly includes the effects of quantum and thermal fluctuations in both the density and spin channels. Results for key thermodynamic quantities, such as the isothermal compressibility and the magnetic susceptibility, are derived from a perturbative calculation of the grand-canonical potential. We find that thermal fluctuations can play a crucial role on the miscibility condition of a binary mixture, favoring phase separation at finite temperature even if the mixture is soluble at zero temperature, as already anticipated in a previous work [Ota et al., Phys. Rev. Lett. 123, 075301 (2019)]. We further investigate the miscibility condition for binary mixtures in the presence of asymmetry in the intra-species interactions, as well as in the masses of the two components. Furthermore, we discuss the superfluid behavior of the mixture and the temperature dependence of the Andreev-Bashkin effect.

Binary mixture of Bose-Einstein condensates in a double-well potential: Berry phase and two-mode entanglement

A binary mixtures of Bose-Einstein condensate structures exhibit an incredible richness in terms of holding different kinds of phases. Depending on the ratio of the inter- and intra-atomic interactions, the transition from mixed to separated phase, which is also known as the miscibility-immiscibility transition, has been reported in different setups and by different groups. Here, we describe such type of quantum phase transition in an effective Hamiltonian approach, by applying Holstein-Primakoff transformation in the limit of large number of particles. We demonstrate that non-trivial geometric phase near the critical coupling is present, which confirms the connection between Berry phase and quantum phase transition. We also show that, by using the spin form of Hillery & Zubairy criterion, a two mode entanglement accompanies this transition in the limit of large, but not infinite number of particles.

Vortices with massive cores in a binary mixture of Bose-Einstein condensates

We analyze a notable class of states relevant to an immiscible bosonic binary mixture loaded in a rotating box-like circular trap, i.e. states where vortices in one species host the atoms of the other species, which thus play the role of massive cores. Within a fully-analytical framework, we calculate the equilibrium distance distinguishing the motion of precession of two corotating massive vortices, the angular momentum of each component, the vortices healing length and the characteristic size of the cores. We then compare these previsions with the measures extracted from the numerical solutions of the associated coupled Gross-Pitaevskii equations. Interestingly, making use of a suitable change of reference frame, we show that vortices drag the massive cores which they host thus conveying them their same motion of precession, but that there is no evidence of tangential entrainment between the two fluids, since the cores keep their orientation constant while orbiting.

Finite-size effect on Bose–Einstein condensate mixtures in improved Hartree–Fock approximation

By means of Cornwal–Jackiw–Tomboulis effective action approach we considered the finite-size effect on Bose–Einstein condensate mixtures confined between two parallel palates. Keeping upto double-bubble approximation and taking into account the conservation of Goldstone boson, our results are quite different from those in previous works within one-loop approximation. The order parameters strongly depend on the distance between palates and can be expressed via the correction terms. The Casimir force is also considered.

Impact of higher-order nonlinearity on modulational instability in two-component Bose-Einstein condensates.

We investigate the effect of higher-order interactions induced by shape-dependent confinement in the modulational instability (MI) of a binary mixture of Bose-Einstein condensates. For this, we present and compute both analytically and numerically a system of coupled Gross-Pitaevskii equations with residual nonlinearity that rule the dynamics of the mixture. Using the linear stability approach, we obtain the instability criteria of the mixture and find that the MI can be excited in miscible condensates and altered in immiscible condensates due to the effect of residual nonlinearity. Direct numerical calculations are performed to support the analytical predictions, and a good agreement is found. The space-time evolution of the condensate density is displayed in both cases when the mixture is miscible and immiscible, showing the generation of bright solitons for modes predicted to be unstable.

Vortex patterns in rotating dipolar Bose–Einstein condensate mixtures with squared optical lattices

Vortex-lattice patterns with transitions from regular to other variety vortex shapes are predicted in rotating binary mixtures of dipolar Bose–Einstein condensates loaded in squared optical lattices (OLs). We focus our investigation on the experimentally accessible dipolar isotopes of dysprosium (162,164Dy), erbium (168Er), chromium (52Cr), and rubidium (87Rb), by considering the binary mixtures (164Dy-162Dy, 168Er-164Dy, 164Dy-52Cr and 164Dy-87Rb), which are confined in strong pancake-shaped traps and loaded in squared two-dimensional (2D) OLs, where we vary the polarization angle of the dipoles, the inter-species contact interactions and the rotation frequency. The ratio between inter- to intra-species contact interaction is used for altering the miscibility properties, with the polarization of the dipolar species used for tuning the dipole–dipole interactions to repulsive or attractive. For enough higher rotation, where the inter- to intra-species scattering length ratio is larger than one, in which a richer variety of vortex-lattice patterns are predicted, including vortex sheets and 2D rotating droplet formations. The patterns can be controlled by changing the OL parameters, as shown for the symmetric 164Dy-162Dy dipolar mixture. For mixtures with stronger differences in the dipole moments, such as 164Dy-52Cr and 164Dy-87Rb, only half the quantum vortices and circular ones have been observed, which will depend on the dipole orientations.