Repulsive Bose-Einstein Condensate Research Articles

Stationary solutions for the1+1nonlinear Schrödinger equation modeling repulsive Bose-Einstein condensates in small potentials

Stationary solutions for the 1+1 cubic nonlinear Schrödinger equation modeling repulsive Bose-Einstein condensates (BEC) in a small potential are obtained through a form of nonlinear perturbation. In particular, for sufficiently small potentials, we determine the perturbation theory of stationary solutions, by use of an expansion in Jacobi elliptic functions. This idea was explored before in order to obtain exact solutions [Bronski, Carr, Deconinck, and Kutz, Phys. Rev. Lett. 86, 1402 (2001)], where the potential itself was fixed to be a Jacobi elliptic function, thereby reducing the nonlinear ODE into an algebraic equation, (which could be easily solved). However, in the present paper, we outline the perturbation method for completely general potentials, assuming only that such potentials are locally small. We do not need to assume that the nonlinearity is small, as we perform a sort of nonlinear perturbation by allowing the zeroth-order perturbation term to be governed by a nonlinear equation. This allows us to consider even poorly behaved potentials, so long as they are bounded locally. We demonstrate the effectiveness of this approach by considering a number of specific potentials: for the simplest potentials, and we recover results from the literature, while for more complicated potentials, our results are new. Dark soliton solutions are constructed explicitly for some cases, and we obtain the known one-soliton tanh-type solution in the simplest setting for the repulsive BEC. Note that we limit our results to the repulsive case; similar results can be obtained for the attractive BEC case.

Matter-wave dark solitons and their excitation spectra in spin-orbit coupled Bose-Einstein condensates

We present three types of dark solitons in quasi–one-dimensional spin-orbit coupled repulsive Bose-Einstein condensates. Among these families, two are always stable, while the third one is only stable sufficiently close to the linear regime. The solitons' excitation spectra reveal the potential existence of a second anomalous mode. While the first such mode describes the soliton oscillatory motion in a parabolic trap, the second, when present, reflects the double-well structure of the underlying single-particle spectrum. This novel mode results in moving density stripes in the vicinity of the soliton core, or in an out-of-phase oscillation of the constituent components, with little effect on the nearly stationary striped total density of the composite soliton.

Matter-Wave Bright Solitons in Spin-Orbit Coupled Bose-Einstein Condensates

We study matter-wave bright solitons in spin-orbit coupled Bose-Einstein condensates with attractive interactions. We use a multiscale expansion method to identify solution families for chemical potentials in the semi-infinite gap of the linear energy spectrum. Depending on the linear and spin-orbit coupling strengths, the solitons may present either a sech2-shaped or a modulated density profile reminiscent of the stripe phase of spin-orbit coupled repulsive Bose-Einstein condensates. Our numerical results are in excellent agreement with our analytical findings and demonstrate the potential robustness of solitons for experimentally relevant conditions.

Strong-coupling dynamics of Bose–Einstein condensate in a double-well trap

Dynamics of the repulsive Bose–Einstein condensate (BEC) in a double-well trap is explored within the 3D time-dependent Gross–Pitaevskii equation. The model avoids numerous common approximations (two-mode treatment, time-space factorization, fixed values of the chemical potential and barrier penetrability, etc) and thus may provide a realistic description of BEC dynamics, including both weak-coupling (sub-barrier) and strong-coupling (above-barrier) regimes and their crossover. The strong coupling regime is achieved by increasing the number N of BEC atoms and thus the chemical potential. The evolution with N of Josephson oscillations (JO) and macroscopic quantum self-trapping (MQST) is examined and the crucial impact of the BEC interaction is demonstrated. At weak coupling, the calculations well reproduce the JO/MQST experimental data. At strong coupling with a significant overlap of the left and right BECs, we observe a remarkable persistence of the Josephson-like dynamics: the JO and MQST converge to a high-frequency JO-like mode where both population imbalance and phase difference oscillate around the zero averages.

Three-dimensional ring vortex solitons and their stabilities in Bose-Einstein condensates under magnetic confinement

A three-dimensional study of the ring vortex solitons is conducted for both attractive and repulsive Bose-Einstein condensates subject to harmonic potential confinement. A family of stationary ring vortex solitons, which is defined by the radial excitation number and the winding number of the intrinsic vorticity, are obtained numerically for a given atomic interaction strength. We find that stabilities of the ground and radially excited states of the ring vortex soliton are dependent on the winding number differently. The ground state of the ring vortex soliton with the large winding number is unstable dynamically against random perturbation. The radially excited state of the ring vortex soliton with large winding number corresponds to the increased collapse threshold and therefore can be made stable for sufficiently small atomic interaction strengths. The ground and radially excited states also demonstrate different dynamic evolutions under large atomic interaction strengths. The former exhibits simultaneous symmetric splitting in the transverse plane, while the latter displays periodic expand-merge cycles in the longitudinal direction.

Landau Damping of Collective Mode in a Quasi-One-Dimensional Repulsive Bose—Einstein Condensate

We investigate the Landau damping of the collective mode in a quasi-one-dimensional repulsive Bose—Einstein condensate by using the self-consistent time-dependent Hartree—Fock—Bogoliubov approximation. We put forward a new method to calculate the Landau damping rate of the collective mode in the condensate and discuss the dependence of the Landau damping on temperature, on transverse trapping frequency, on atom number in the condensate, and on length of the system. Different from the usual calculation method for the three dimension system, our new calculation method is an interactive one by considering the practical relaxation of the elementary excitation. With little approximation, our theoretical calculation results agree with the experimental ones. Comparing with the usual calculation method, our theory is helpful to deduce the inter-particle interactions in damping phenomenon.

Hartree-Fock-Bogoliubov model and simulation of attractive and repulsive Bose-Einstein condensates

We describe a model of dynamic Bose-Einstein condensates near a Feshbach resonance that is computationally feasible under assumptions of spherical or cylindrical symmetry. Simulations in spherical symmetry approximate the experimentally measured time to collapse of an unstably attractive condensate only when the molecular binding energy in the model is correct, demonstrating that the quantum fluctuations and atom-molecule pairing included in the model are the dominant mechanisms during collapse. Simulations of condensates with repulsive interactions find some quantitative disagreement, suggesting that pairing and quantum fluctuations are not the only significant factors for condensate loss or burst formation. Inclusion of three-body recombination was found to be inconsequential in all of our simulations, though we do not consider recent experiments [1] conducted at higher densities.

Azimuthal vortex clusters in Bose-Einstein condensates

We describe, analytically and numerically, topologically nontrivial stationary states with azimuthal modulation of density in a repulsive Bose-Einstein condensate (BEC) confined in a harmonic trap. We show that, depending on the number of density peaks and total topological charge, these states can have a sophisticated phase texture associated with a vortex cluster. For a given topological charge, the form of density distribution and the structure of phase singularities are uniquely linked, thus simultaneous phase and density modulation enforces the formation of a vortex cluster both in rotating and in nonrotating BEC clouds.

Stationary states of a nonlinear Schrödinger lattice with a harmonic trap

We study a discrete nonlinear Schrödinger lattice with a parabolic trapping potential. The model, describing, e.g., an array of repulsive Bose-Einstein condensate droplets confined in the wells of an optical lattice, is analytically and numerically investigated. Starting from the linear limit of the problem, we use global bifurcation theory to rigorously prove that – in the discrete regime – all linear states lead to nonlinear generalizations thereof, which assume the form of a chain of discrete dark solitons (as the density increases). The stability of the ensuing nonlinear states is studied and it is found that the ground state is stable, while the excited states feature a chain of stability/instability bands. We illustrate the mechanisms under which discreteness destabilizes the dark-soliton configurations, which become stable only in the continuum regime. Continuation from the anti-continuum limit is also considered, and a rich bifurcation structure is revealed.

Landau damping of collective mode in a quasi-two-dimensional repulsive Bose—Einstein condensate

We investigate the Landau damping of the collective mode in a quasi-two-dimension repulsive Bose—Einstein condensate by using the self-consistent time-dependent Hatree—Fock—Bogoliubov approximation and a complete and orthogonal eigenfunction set for the elementary excitation of the system. We calculate the three-mode coupling matrix element between the collective mode and the thermal excited quasi-particles and the Landau damping rate of the collective mode. We discuss the dependence of the Landau damping on temperature, on atom number in the condensate, on transverse trapping frequency and on the length of the condensate. The energy width of the collective mode is taken into account in our calculation. With little approximation, our theoretic calculation results agree well with the experimental ones and are helpful for deducing the damping mechanics and the inter-particle interaction.

Emergence and stability of vortex clusters in Bose–Einstein condensates: A bifurcation approach near the linear limit

We study the existence and stability properties of clusters of alternating charge vortices in repulsive Bose–Einstein condensates. It is illustrated that such states emerge from cascades of symmetry-breaking bifurcations that can be analytically tracked near the linear limit of the system via weakly nonlinear few-mode expansions. We present the resulting states that emerge near the first few eigenvalues of the linear limit, and illustrate how the nature of the bifurcations can be used to understand their stability. Rectilinear, polygonal and diagonal vortex clusters are only some of the obtained states while mixed states, consisting of dark solitons and vortex clusters, are identified as well. We also explore the evolution of unstable states and their transient dynamics exploring configurations of nearby bifurcation branches.

Macroscopic quantum control of exact many-body coherent states

We demonstrate that the idea of quantum control can be generalized to construct the exact many-body coherent state (MBCS) in a trapped Bose-Einstein condensate (BEC) of N atoms. Such a MBCS possesses the form of the single-particle coherent state, which does not deform in propagation and is stable for a repulsive BEC. The results suggest an experimental scheme for resonantly generating and coherently controlling the MBCSs.

Distribution of eigenfrequencies for oscillations of the ground state in the Thomas-Fermi limit

In this work, we present a systematic derivation of the distribution of eigenfrequencies for oscillations of the ground state of a repulsive Bose-Einstein condensate in the semi-classical (Thomas-Fermi) limit. Our calculations are performed in 1-, 2- and 3-dimensional settings. Connections with the earlier work of Stringari, with numerical computations, and with theoretical expectations for invariant frequencies based on symmetry principles are also given.

Particle-Hole Asymmetry and Brightening of Solitons in a Strongly Repulsive Bose-Einstein Condensate

We study solitary wave propagation in the condensate of a system of hard-core bosons with nearest-neighbor interactions. For this strongly repulsive system, the evolution equation for the condensate order parameter of the system, obtained using spin-coherent state averages, is different from the usual Gross-Pitaevskii equation (GPE). The system is found to support two kinds of solitons when there is a particle-hole imbalance: a dark soliton that dies out as the velocity approaches the sound velocity and a new type of soliton which brightens and persists all the way up to the sound velocity, transforming into a periodic wave train at supersonic speed. Analogous to the GPE soliton, the energy-momentum dispersion for both solitons is characterized by Lieb II modes.

Laser-Manipulating Macroscopic Quantum States of a Bose–Einstein Condensate Held in a Kronig–Penny Potential

We investigate the boundary value problem (BVP) of a quasi-one-dimensional Gross–Pitaevskii equation with the Kronig–Penney potential (KPP) of period d, which governs a repulsive Bose–Einstein condensate. Under the zero and periodic boundary conditions, we show how to determine n exact stationary eigenstates {Rn} corresponding to different chemical potentials {μn} from the known solutions of the system. The n-th eigenstate Rn is the Jacobian elliptic function with period 2d/n for n = 1,2,…, and with zero points containing the potential barrier positions. So Rn is differentiable at any spatial point and Rn2 describes n complete wave-packets in each period of the KPP. It is revealed that one can use a laser pulse modeled by a δ potential at site xi to manipulate the transitions from the states of {Rn} with zero point x ≠ xi to the states of {Rn} with zero point x = xi. The results suggest an experimental scheme for applying BEC to test the BVP and to observe the macroscopic quantum transitions.

Modulational instability in two-component discrete media with cubic-quintic nonlinearity

The effect of cubic-quintic nonlinearity and associated intercomponent couplings on the modulational instability (MI) of plane-wave solutions of the two-component discrete nonlinear Schrödinger (DNLS) equation is considered. Conditions for the onset of MI are revealed and the growth rate of small perturbations is analytically derived. For the same set of initial parameters as equal amplitudes of plane waves and intercomponent coupling coefficients, the effect of quintic nonlinearity on MI is found to be essentially stronger than the effect of cubic nonlinearity. Analytical predictions are supported by numerical simulations of the underlying coupled cubic-quintic DNLS equation. Relevance of obtained results to dense Bose-Einstein condensates (BECs) in deep optical lattices, when three-body processes are essential, is discussed. In particular, the phase separation under the effect of MI in a two-component repulsive BEC loaded in a deep optical lattice is predicted and found in numerical simulations. Bimodal light propagation in waveguide arrays fabricated from optical materials with non-Kerr nonlinearity is discussed as another possible physical realization for the considered model.

Interaction between two bright solitons in the coupled defocusing nonlinear Schrödinger equation: application to Bose–Einstein condensation

The interaction of two bright matter solitons in two-component repulsive Bose–Einstein condensates with interspecies attraction is investigated using the variational approach. The effective interaction potential of the two solitons is obtained. It is shown that the interaction between the two solitons is a short-range attractive force. The relative motion of the two solitons and the oscillating angular frequency are also obtained.

Quantum squeezing effects in creating triatomic molecules from ultracold atoms

We study the quantum dynamics of coherent creation of triatomic molecules from a repulsive atomic Bose-Einstein condensate. In a single-mode approach with short pulse duration we consider the squeezing effects for homonuclear and heteronuclear trimers by taking into account an optical photoassociation. The possibility of manipulating the quantum statistical properties of the trimer fields provides an appealing research area for current molecular matter-wave optics.

Matter sound waves in two-component Bose–Einstein condensates

The creation and propagation of sound waves in two-component Bose–Einstein condensates (BECs) are investigated and a new method of wave generation in binary BEC mixtures is proposed. The method is based on a fast change of the inter-species interaction constant and is illustrated for two experimental settings: a drop-like condensate immersed into a second large repulsive condensate, and a binary mixture of two homogeneous repulsive BECs. A mathematical model based on the linearized coupled Gross–Pitaevskii equations is developed and explicit formulae for the space and time dependence of sound waves are provided. Comparison of the analytical and numerical results shows excellent agreement, confirming the validity of the proposed approach.

Double-barrier potentials for matter-wave gap solitons

We investigate collisions of solitons of the gap type, supported by a lattice potential in repulsive Bose-Einstein condensates, with an effective double-barrier potential that resembles a Fabry-Perot cavity. We identify conditions under which the trapping of the entire incident soliton in the cavity is possible. Collisions of the incident soliton with an earlier trapped one are considered too. In the latter case, many outcomes of the collisions are identified, including merging, release of the trapped soliton with or without being replaced by the incoming one, and trapping of both solitons.