Vortex Formation by Merging of Multiple Trapped Bose-Einstein Condensates

Scherer, David R.; Weiler, Chad; Neely, Tyler W.; Anderson, Brian P.

doi:10.1103/physrevlett.98.110402

Cited by 203 publications

(211 citation statements)

References 78 publications

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“…It is also possible to nucleate vortices by dragging a moving impurity through the condensate for speeds above a critical velocity (depending on the local density and also the shape of the impurity) [352][353][354][355][356][357][358][359]. Yet another possibility to nucleate vortices can be achieved by separating the condensate in different fragments and allowing them to collide [360][361][362]. The profile of a vortex in a two dimensional setting (see left panel of Fig.…”

Section: Vortices and Vortex Latticesmentioning

confidence: 99%

Nonlinear waves in Bose–Einstein condensates: physical relevance and mathematical techniques

2008

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Abstract. The aim of the present review is to introduce the reader to some of the physical notions and of the mathematical methods that are relevant to the study of nonlinear waves in Bose-Einstein Condensates (BECs). Upon introducing the general framework, we discuss the prototypical models that are relevant to this setting for different dimensions and different potentials confining the atoms. We analyze some of the model properties and explore their typical wave solutions (plane wave solutions, bright, dark, gap solitons, as well as vortices). We then offer a collection of mathematical methods that can be used to understand the existence, stability and dynamics of nonlinear waves in such BECs, either directly or starting from different types of limits (e.g., the linear or the nonlinear limit, or the discrete limit of the corresponding equation). Finally, we consider some special topics involving more recent developments, and experimental setups in which there is still considerable need for developing mathematical as well as computational tools.PACS numbers: 03.75. Kk, 03.75.Lm, 05.45 • EP: Ermakov-Pinney (Equation)• GP: Gross-Pitaevskii (Equation)• KdV: Korteweg-de Vries (Equation)• LS: Lyapunov-Schmidt (Technique)• MT: Magnetic Trap• NLS: Nonlinear Schrödinger (Equation)• NPSE: Non-polynomial Schrödinger Equation IntroductionThe phenomenon of Bose-Einstein condensation is a quantum phase transition originally predicted by Bose [1] and Einstein [2,3] in 1924. In particular, it was shown that below a critical transition temperature T c , a finite fraction of particles of a boson gas (i.e., whose particles obey the Bose statistics) condenses into the same quantum state, known as the Bose-Einstein condensate (BEC). Although BoseEinstein condensation is known to be a fundamental phenomenon, connected, e.g., to superfluidity in liquid helium and superconductivity in metals (see, e.g., Ref.[4]), BECs were experimentally realized 70 years after their theoretical prediction: this major achievement took place in 1995, when different species of dilute alkali vapors confined in a magnetic trap (MT) were cooled down to extremely low temperatures [5][6][7], and has already been recognized through the 2001 Nobel prize in Physics [8,9]. This first unambiguous manifestation of a macroscopic quantum state in a manybody system sparked an explosion of activity, as reflected by the publication of several thousand papers related to BECs since then. Nowadays there exist more than fifty experimental BEC groups around the world, while an enormous amount of theoretical work has followed and driven the experimental efforts, with an impressive impact on many branches of Physics.From a theoretical standpoint, and for experimentally relevant conditions, the static and dynamical properties of a BEC can be described by means of an effective mean-field equation known as the Gross-Pitaevskii (GP) equation [10,11]. This is a variant of the famous nonlinear Schrödinger (NLS) equation [12] (incorporating an external potential used to confine th...

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Section: Vortices and Vortex Latticesmentioning

confidence: 99%

Nonlinear waves in Bose–Einstein condensates: physical relevance and mathematical techniques

2008

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“…Recent proposals include the generation of honeycomb vortex-antivortex lattices through linear interference of three expanding BECs 5 . Such lattices have never been observed experimentally, although related techniques have been used to nucleate vortices in BECs 6 or vortex solitons in non-linear media that have been used as waveguides 7 and photonic crystals 8 .…”

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Geometrically locked vortex lattices in semiconductor quantum fluids

et al. 2012

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Macroscopic quantum states can be easily created and manipulated within semiconductor microcavity chips using exciton-photon quasiparticles called polaritons. Besides being a new platform for technology, polaritons have proven to be ideal systems to study out-of-equilibrium condensates. Here we harness the photonic component of such a semiconductor quantum fluid to measure its coherent wavefunction on macroscopic scales. Polaritons originating from separated and independent incoherently pumped spots are shown to phase-lock only in high-quality microcavities, producing up to 100 vortices and antivortices that extend over tens of microns across the sample and remain locked for many minutes. The resultant regular vortex lattices are highly sensitive to the optically imposed geometry, with modulational instabilities present only in square and not triangular lattices. Such systems describe the optical equivalents to one-and two-dimensional spin systems with (anti)-ferromagnetic interactions controlled by their symmetry, which can be reconfigured on the fly, paving the way to widespread applications in the control of quantum fluidic circuits.

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“…Vortices have been realized experimentally in Bose-Einstein condensates (BECs), obtained when bosons are cooled down to almost-zero temperatures [12][13][14][15][16][17][18][19][20][21][22]. These vortices are expected to offer interesting applications in interferometry [23] and as a means to study the behavior of random polynomial roots [24].…”

Section: Introductionmentioning

confidence: 99%

Symmetry breaking and singularity structure in Bose-Einstein condensates

et al. 2012

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We determine the trajectories of vortex singularities that arise after a single vortex is broken by a discretely symmetric impulse in the context of Bose-Einstein condensates in a harmonic trap. The dynamics of these singularities are analyzed to determine the form of the imprinted motion. We find that the symmetry-breaking process introduces two effective forces: a repulsive harmonic force that causes the daughter trajectories to be ejected from the parent singularity and a Magnus force that introduces a torque about the axis of symmetry. For the analytical noninteracting case we find that the parent singularity is reconstructed from the daughter singularities after one period of the trapping frequency. The interactions between singularities in the weakly interacting system do not allow the parent vortex to be reconstructed. Analytic trajectories were compared to the actual minima of the wave function, showing less than 0.5% error for an impulse strength of v = 0.00005. We show that these solutions are valid within the impulse regime for various impulse strengths using numerical integration of the Gross-Pitaevskii equation. We also show that the actual duration of the symmetry-breaking potential does not significantly change the dynamics of the system as long as the strength is below v = 0.0005

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Vortex Formation by Merging of Multiple Trapped Bose-Einstein Condensates

Cited by 203 publications

References 78 publications

Nonlinear waves in Bose–Einstein condensates: physical relevance and mathematical techniques

Nonlinear waves in Bose–Einstein condensates: physical relevance and mathematical techniques

Geometrically locked vortex lattices in semiconductor quantum fluids

Symmetry breaking and singularity structure in Bose-Einstein condensates

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