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ABSTRACT: A quantized vortex dipole is the simplest vortex molecule, comprising two
counter-circulating vortex lines in a superfluid. Although vortex dipoles are
endemic in two-dimensional superfluids, the precise details of their dynamics
have remained largely unexplored. We present here several striking observations
of vortex dipoles in dilute-gas Bose-Einstein condensates, and develop a
vortex-particle model that generates vortex line trajectories that are in good
agreement with the experimental data. Interestingly, these diverse trajectories
exhibit essentially identical quasi-periodic behavior, in which the vortex
lines undergo stable epicyclic orbits.
04/2011;
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ABSTRACT: We study the existence and stability properties of clusters of alternating
charge vortices in 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.
12/2010;
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ABSTRACT: We investigate the effects of anisotropy on the stability and dynamics of
vortex cluster states which arise in Bose-Einstein condensates. Sufficiently
strong anisotropies are shown to stabilize states with arbitrary numbers of
vortices that are highly unstable in the isotropic limit. Conversely,
anisotropy can be used to destabilize states which are stable in the isotropic
limit. Near the linear limit, we identify the bifurcations of vortex states
including their emergence from linear eigenstates, while in the strongly
nonlinear limit, a particle-like description of the dynamics of the vortices in
the anisotropic trap is developed. Both are in very good agreement with
numerical results. Collective modes of stabilized many vortex cluster states
are demonstrated.
11/2010;
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ABSTRACT: In the present work, we offer a unifying perspective between the dark soliton stripe and the vortex multipole (dipole, tripole, aligned quadrupole, quintopole, etc.) states that emerge in the context of quasi-two-dimensional Bose-Einstein condensates. In particular, we illustrate that the multivortex states with the vortices aligned along the (former) dark soliton stripe sequentially bifurcate from the latter state in a supercritical pitchfork manner. Each additional bifurcation adds an extra mode to the dark soliton instability and an extra vortex to the configuration; moreover, the bifurcating states inherit the stability properties of the soliton prior to the bifurcation. The critical points of this bifurcation are computed analytically via a few-mode truncation of the system, which clearly showcases the symmetry-breaking nature of the corresponding bifurcation. We complement this small(-er) amplitude, few mode bifurcation picture, with a larger amplitude, particle-based description of the ensuing vortices. The latter enables us to characterize the equilibrium position of the vortices, as well as their intrinsic dynamics and anomalous modes, thus providing a qualitative description of the nonequilibrium multivortex dynamics.
Phys. Rev. A. 07/2010; 82(1).
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ABSTRACT: We explore the stability and dynamics of dark-bright solitons in
two-component elongated Bose-Einstein condensates by developing effective 1D
vector equations as well as solving the corresponding 3D Gross-Pitaevskii
equations. A strong dependence of the oscillation frequency and of the
stability of the dark-bright (DB) soliton on the atom number of its components
is found. Spontaneous symmetry breaking leads to oscillatory dynamics in the
transverse degrees of freedom for a large occupation of the component
supporting the dark soliton. Moreover, the interactions of two DB solitons are
investigated with special emphasis on the importance of their relative phases.
Experimental results showcasing dark-bright soliton dynamics and collisions in
a BEC consisting of two hyperfine states of $^{87}$Rb confined in an elongated
optical dipole trap are presented.
05/2010;
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ABSTRACT: We utilize the combination of two standard trapping techniques, a magnetic trap and an optical trap in a Raman setup, to propose a versatile and tunable trap for cold atoms. The created potential provides several advantages over conventional trapping potentials. One can easily convert the type of the trap, e.g., from a single well to a double well trap. Atoms in different internal states can be trapped in different trap types, thereby enabling the realization of experiments with multi-component Bose-Einstein condensates. Moreover, one can achieve variations of the trapping potential on small length scales without the need of microstructures. We present the potential surfaces for different setups, demonstrate their tunability, give a semi-analytical expression for the potential, and propose experiments which can be realized within such a trap. Comment: 10 pages, 9 figures
03/2010;
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ABSTRACT: We study the statics and dynamics of dark solitons in a cigar-shaped Bose-Einstein condensate confined in a double-well potential. Using a mean-field model with a non-cubic nonlinearity, appropriate to describe the dimensionality crossover regime from one to three dimensional, we obtain branches of solutions in the form of single- and multiple-dark soliton states, and study their bifurcations and stability. It is demonstrated that there exist dark soliton states which do not have a linear counterpart and we highlight the role of anomalous modes in the excitation spectra. Particularly, we show that anomalous mode eigenfrequencies are closely connected to the characteristic soliton frequencies as found from the solitons' equations of motion, and how anomalous modes are related to the emergence of instabilities. We also analyze in detail the role of the height of the barrier in the double well setting, which may lead to instabilities or decouple multiple dark soliton states. Comment: 35 pages, 12 figures
02/2010;
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ABSTRACT: In this work, the spectral properties of a singly-charged vortex in a In this
work, the spectral properties of a singly-charged vortex in a Bose-Einstein
condensate confined in a highly anisotropic (disk-shaped) harmonic trap are
investigated. Special emphasis is given on the analysis of the so-called
anomalous (negative energy) mode of the Bogoliubov spectrum. We use analytical
and numerical techniques to illustrate the connection of the anomalous mode to
the precession dynamics of the vortex in the trap. Effects due to inhomogeneous
interatomic interactions and dissipative perturbations motivated by finite
temperature considerations are explored. We find that both of these effects may
give rise to oscillatory instabilities of the vortex, which are suitably
diagnosed through the perturbation-induced evolution of the anomalous mode, and
being monitored by direct numerical simulations.
11/2009;
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ABSTRACT: In this work, we consider quasi-one-dimensional Bose–Einstein condensates (BECs), with spatially varying collisional interactions, trapped in double-well potentials. In particular, we study a setup in which such a “collisionally inhomogeneous” BEC has the same (attractive–attractive or repulsive–repulsive) or different (attractive–repulsive) types of interparticle interactions. Our analysis is based on the continuation of the symmetric ground state and anti-symmetric first excited state of the non-interacting (linear) limit into their nonlinear counterparts. The collisional inhomogeneity produces a saddle–node bifurcation scenario between two additional solution branches; as the inhomogeneity becomes stronger, the turning point of the saddle–node tends to infinity and eventually only the two original branches remain, which is completely different from the standard double-well phenomenology. Finally, one of these branches changes its monotonicity as a function of the chemical potential, a feature especially prominent, when the sign of the nonlinearity changes between the two wells. Our theoretical predictions, are in excellent agreement with the numerical results.
Physica D: Nonlinear Phenomena. 12/2008;
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ABSTRACT: We demonstrate that atoms in magnetically insensitive hyperfine states (m=0) can be trapped efficiently by a Bose-Einstein Condensate of the same atomic species occupying a different hyperfine state. The latter is trapped magnetically. Hyperfine-state–changing collisions, and therefore loss of the trapped (m=0) atoms, are shown to be strongly inhibited in case of a low density of the confined atomic cloud. We monitor the transition from a "soft" to a "hard" effective potential by studying the backaction of the trapped (m=0) atoms onto the condensate which provides their confinement. The controlled outcoupling of the trapped atoms by shaping the condensate wave function is explored. We observe a pulsed emission of atoms from the trapping region reminiscent of an atom laser.
EPL (Europhysics Letters) 11/2008; 84(4):40011. · 2.17 Impact Factor
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ABSTRACT: We study the dynamics of bright and dark matter-wave solitons in the presence of a spatially varying nonlinearity. When the spatial variation does not involve zero crossings, a transformation is used to bring the problem to a standard nonlinear Schrödinger form, but with two additional terms: an effective potential one and a non-potential term. We illustrate how to apply perturbation theory of dark and bright solitons to the transformed equations. We develop the general case, but primarily focus on the non-standard special case whereby the potential term vanishes, for an inverse square spatial dependence of the nonlinearity. In both cases of repulsive and attractive interactions, appropriate versions of the soliton perturbation theory are shown to accurately describe the soliton dynamics.
Physics Letters A. 11/2008;
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ABSTRACT: The electronic spectrum of a Rydberg atom immersed in a Bose-Einstein condensate is investigated. The Heisenberg equations of motions for the condensate and the Rydberg atom are derived. Neglecting the back action of the Rydberg atom onto the condensate decouples the equations describing the condensate and Rydberg atom. In this case the spectral structure of the Rydberg atom is completely determined by an effective potential which depends on the density distribution of the condensate. We study the spectral properties for the situation of an isotropic harmonic and anharmonic as well as axially symmetric confinement. In the latter case an intriguing analogy with Rydberg atoms in magnetic fields is encountered.
Phys. Rev. A. 08/2007; 76(2).
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ABSTRACT: Motivated by recent experiments studying the dynamics of config-urations bearing a small number of vortices in atomic Bose-Einstein conden-sates (BECs), we illustrate that such systems can be accurately described by ordinary differential equations (ODEs) incorporating the precession and inter-action dynamics of vortices in harmonic traps. This dynamics is tackled in detail at the ODE level, both for the simpler case of equal charge vortices, and for the more complicated (yet also experimentally relevant) case of op-posite charge vortices. In the former case, we identify the dynamics as being chiefly quasi-periodic (although potentially periodic), while in the latter, irreg-ular dynamics may ensue when suitable external drive of the BEC cloud is also considered. Our analytical findings are corroborated by numerical computa-tions of the reduced ODE system.
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ABSTRACT: We explore the stability and dynamics of dark–bright (DB) solitons in two-component elongated Bose–Einstein condensates by developing effective one-dimensional vector equations and solving the three-dimensional Gross–Pitaevskii equations. A strong dependence of the oscillation frequency and of the stability of the DB soliton on the atom number of its components is found; importantly, the wave may become dynamically unstable even in the 1D regime. As the atom number in the dark-soliton-supporting component is further increased, spontaneous symmetry breaking leads to oscillatory dynamics in the transverse degrees of freedom. Moreover, the interactions of two DB solitons are investigated with an emphasis on the importance of their relative phases. Experimental results showcasing multiple DB soliton oscillations and a DB–DB collision in a Bose–Einstein condensate consisting of two hyperfine states of 87Rb confined in an elongated optical dipole trap are presented.
Physics Letters A.
