Rotational dynamics of vortices in confined Bose-Einstein condensates

McGee, S. A.; Holland, Murray

doi:10.1103/physreva.63.043608

Cited by 47 publications

(77 citation statements)

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“…[55] for more details). As discussed above, the presence of the harmonic trap induces vortex precession [375][376][377][378][379][380][381][382]. Therefore, in order to pin/drag the vortex at an off-center position, the pinning force exerted by the impurity has to be stronger than the vortex precession force induced by the harmonic trap and the impurity has to be deep enough to avoid emission of sound waves [451].…”

Section: Localized Potentialsmentioning

confidence: 99%

“…These gradients can be induced by an external potential or the presence of another vortex. The effect of vortex precession induced by the external trap has been extensively studied [375][376][377][378][379][380][381][382]. The motion induced on a vortex by another vortex is equivalent to the one observed in fluid vortices whereby vortices with same charge travel parallel to each other at constant speed, while vortices of opposite charges rotate about each other at constant angular speed.…”

Section: Vortices and Vortex Latticesmentioning

confidence: 99%

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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: Localized Potentialsmentioning

confidence: 99%

Section: Vortices and Vortex Latticesmentioning

confidence: 99%

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

2008

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“…In the context of BECs, this approach was first applied with great success to the low-lying normal modes of a trapped stationary (nonrotating) condensate (Pérez-García et al, 1996). Subsequently, its application to a single straight vortex in a disk-shaped condensate yields an explicit prediction for the angular precession of such a trapped vortex (Lundh and Ao, 2000;McGee and Holland, 2001;Svidzinsky and Fetter, 2000a). In this case, the position r 0 of the off-center vortex serves as an appropriate parameter, and the Lagrangian formalism shows that the precession rate is proportional to (the negative of) the slope of the appropriate curve in Fig.…”

Section: Dynamical Motion Of a Trapped Vortexmentioning

confidence: 99%

Rotating trapped Bose-Einstein condensates

2008

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After reviewing the ideal Bose-Einstein gas in a box and in a harmonic trap, I discuss the effect of interactions on the formation of a Bose-Einstein condensate (BEC), along with the dynamics of small-amplitude perturbations (the Bogoliubov equations). When the condensate rotates with angular velocity Ω, one or several vortices nucleate, with many observable consequences. With more rapid rotation, the vortices form a dense triangular array, and the collective behavior of these vortices has additional experimental implications. For Ω near the radial trap frequency ω ⊥ , the lowest-Landau-level approximation becomes applicable, providing a simple picture of such rapidly rotating condensates. Eventually, as Ω → ω ⊥ , the rotating dilute gas is expected to undergo a quantum phase transition from a superfluid to various highly correlated (nonsuperfluid) states analogous to those familiar from the fractional quantum Hall effect for electrons in a strong perpendicular magnetic field.

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“…Simulations performed for the cylindrically symmetric system show that an off-axis vortex tends to precess in the positive direction and the frequency of precession is an increasing function of the precession radius [12]. However, numerical simulations of the GP equation show that the repulsion between the two vortices in a vortex pair renders the frequency of precession to be a decreasing function of the precession radius.…”

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confidence: 99%

Splitting of a doubly quantized vortex through intertwining in Bose-Einstein condensates

et al. 2003

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The stability of doubly quantized vortices in dilute Bose-Einstein condensates of 23 Na is examined at zero temperature. The eigenmode spectrum of the Bogoliubov equations for a harmonically trapped cigar-shaped condensate is computed and it is found that the doubly quantized vortex is spectrally unstable towards dissection into two singly quantized vortices. By numerically solving the full three-dimensional time-dependent Gross-Pitaevskii equation, it is found that the two singly quantized vortices intertwine before decaying. This work provides an interpretation of recent experiments [A. E. Leanhardt et al. Phys. Rev. Lett. 89, 190403 (2002) The stability of single-quantum vortices has been studied extensively after such vortices were first observed in dilute alkali atom Bose-Einstein condensates (BECs) [1]. Since a single-valued complex order parameter describes the state of the condensate, its phase must undergo a 2πn change along a loop encircling a vortex, where n is the quantum number of the vortex. However, the creation of multiquantum vortices is impossible just by rotating the harmonic trapping potential at a high frequency, since the existence of many singly quantized vortices is energetically more favorable than a single multiquantum vortex [2]. Indeed, vortex lattices composed of single-quantum vortices were observed in such experiments [3].Verifying the proposal of topological phase engineering by Nakahara et al. [4], Leanhardt et al. [5] have recently succeeded in creating vortices simply by reversing the bias magnetic field used to trap the condensate. The vortices created display winding numbers with n = 2 (4π phase winding) or with n = 4 (8π phase winding), depending on the hyperfine spin states used for 23 Na condensates. It was confirmed that the axial angular momentum per particle is 2h (4h) for the doubly (quartically) quantized vortex.In this experiment, after creating a vortex it is held for ∼ 20 ms, watching the vortex core to split into singlequantum vortices. However, no splitting was observed in this time span. Since a doubly quantized vortex is expected to decay spontaneously into two singly quantized vortices owing to energetics, this observation seems to be puzzling. This motivates our investigation of the detailed dynamics of the decay process of multiply quantized vortices in view of the present experimental situation. In dilute BECs, these were the first experimentally realized double-quantum vortices which are known to exist in other superfluids, such as superfluid 3 He-A [6]. Therefore, we have a unique opportunity to examine the physics of multiply quantized vortices.There are several theoretical investigations on the instability of the doubly quantized vortex: The instability due to the bound state in the vortex core was pointed out by Rokhsar [7], who claimed that the decay of vortex states requires the presence of thermal atoms. On the other hand, Pu et al. [8] found that even in the absence of thermal atoms, i.e. in the non-dissipative system, appearance of the modes with...

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Rotational dynamics of vortices in confined Bose-Einstein condensates

Cited by 47 publications

References 13 publications

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

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

Rotating trapped Bose-Einstein condensates

Splitting of a doubly quantized vortex through intertwining in Bose-Einstein condensates

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