Dynamics of a single ring of vortices in two-dimensional trapped Bose-Einstein condensates

Kim, Jong-kwan; Fetter, Alexander L.

doi:10.1103/physreva.70.043624

Cited by 33 publications

(56 citation statements)

References 32 publications

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“…(5). It is valid even for the exact GP solution having a net circulation of N 0 in the low-density hole region and N r vortex singularities arranged on a ring of radius R. The remaining part v 1 = v 1rr + v 1φφ has the Fourier expansion [9] …”

Section: Energymentioning

confidence: 99%

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Transition to the giant vortex state in a harmonic-plus-quartic trap

Zaremba

2006

Phys. Rev. A

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We consider a rapidly rotating Bose-condensed gas in an harmonic plus quartic trap. At sufficiently high rotation rates the condensate acquires an annular geometry with the superposition of a vortex lattice. With increasing rotation rate the lattice evolves into a single ring of vortices. Of interest is the transition from this state to the giant vortex state in which the circulation is carried by only a central vortex. By analyzing the Gross-Pitaevskii energy functional variationally, we have been able to map out the phase boundary between these two states as a function of the rotation rate and the various trapped gas parameters. The variational results are in good qualitative agreement with those obtained by means of a direct numerical solution of the Gross-Pitaevskii equation.

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Section: Energymentioning

confidence: 99%

“…where v 0 is the azimuthally averaged part of the velocity field which is given by [9] v 0 (r) = N 0 r θ(R − r)…”

Section: Energymentioning

confidence: 99%

Transition to the giant vortex state in a harmonic-plus-quartic trap

Zaremba

2006

Phys. Rev. A

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“…Differences between incompressible [22] or ThomasFermi [23] and LLL vortex dynamics are already apparent in the case of m vortices symmetrically arranged and equidistant with respect to the centre of the trap. Up to a phase, the vortices are in the directions of the mth roots of unity in the ζ-plane, and hence the wave-function is of the form φ(z) ∼ (a 0 (t) + a m (t)z m ).…”

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confidence: 99%

Anomalous Hydrodynamics and Normal Fluids in Rapidly Rotating Bose-Einstein Condensates

2006

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In rapidly rotating bose systems we show that there is a region of anomalous hydrodynamics whilst the system is still condensed, which coincides with the mean field quantum Hall regime. An immediate consequence is the absence of a normal fluid in any conventional sense. However, even the superfluid hydrodynamics is not described by conventional Bernoulli and continuity equations. We show there are kinematic constraints which connect spatial variations of density and phase, that the positions of vortices are not the simplest description of the dynamics of such a fluid (despite their utility in describing the instantaneous state of the condensate) and that the most compact description allows solution of some illuminating examples of motion. We demonstrate, inter alia, a very simple relation between vortices and surface waves. We show the surface waves can form a "normal fluid" which absorbs energy and angular momentum from vortex motion in the trap. The time scale of this process is sensitive to the initial configuration of the vortices, which can lead to long-lived vortex patches -perhaps related to those observed at JILA. The area of rapidly rotating Bose Einstein condensates was one of the first to produce predicted phenomena quite distinct to the analogous condensed matter system, 4 He. Initially an instability was found[1] to a noncondensed, Laughlin, state for repulsive effective interactions between the atoms with sufficiently high angular momentum, and the production[1] of a fragmented condensate in the rotating attractive case. Both of these novel features occur in a regime where the atoms reside in restricted set of single particle states, the "Lowest Landau level" (LLL), defined below. Subsequently it has been understood that when the atoms reside in the Lowest Landau level at intermediate amounts of angular momentum mean field theory provides a good description (Mean field quantum Hall regime or MFQHR). In that regime the ground state is a vortex lattice [3,4] and it has been shown that other phases occur en route to the Laughlin state in the correlated domain [5,6,7] as the amount of angular momentum in increased. The nature of these transitions in the thermodynamic limit [8] and in finite systems remains a very active area of research, extending now into anisotropic traps [9,10].Following the pioneering studies [11,12] of the vortex lattice, current experiments are in [13] or near [14,15] the mean field quantum Hall regime. The correlated regime is still to be investigated. The experiments find that the vortex lattice becomes very soft with an increasingly lengthy period for recovery after disruption. In this Letter we show the underlying hydrodynamics in the LLL is very unconventional and will be a contributory factor to understanding these experimental observations. There has been considerable theoretical discussion [8,16] about the conventional or unconventional nature of excitations in the vortex lattice; this Letter provides a formulation of the hydrodynamics underlying such excitations.The defi...

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“…In a harmonic trap, a dark soliton tends to oscillate axially at a fixed proportion of the trap frequency [27][28][29][30] while a vortex precesses about the trap center at a frequency with a non-trivial dependence on its position and system parameters [31][32][33][34][35]. Remarkably, however, dark solitons and vortices show many analogous behaviors -underpinned by their common nature as phase defects -such as their spontaneous creation under the Kibble-Zurek mechanism [36][37][38], their emergence during the breakdown of superflow [11,16,22,[39][40][41], their instability to acceleration [42,43] and their interaction with phonons [44,45].…”

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confidence: 99%

Transition from vortices to solitonic vortices in trapped atomic Bose-Einstein condensates

Tsatsos¹,

Edmonds²,

Parker³

2016

Phys. Rev. A

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Motivated by recent experiments we study theoretically the dynamics of vortices in the crossover from two to one-dimension in atomic condensates in elongated traps. We explore the transition from the dynamics of a vortex to that of a dark soliton as the one-dimensional limit is approached, mapping this transition out as a function of the key system parameters. Moreover, we probe this transition dynamically through the hysteresis under time-dependent deformation of the trap at the dimensionality crossover. When the solitonic regime is probed during the hysteresis, significant angular momentum is lost from the system but, remarkably, the vortex can re-emerge.

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Dynamics of a single ring of vortices in two-dimensional trapped Bose-Einstein condensates

Cited by 33 publications

References 32 publications

Transition to the giant vortex state in a harmonic-plus-quartic trap

Transition to the giant vortex state in a harmonic-plus-quartic trap

Anomalous Hydrodynamics and Normal Fluids in Rapidly Rotating Bose-Einstein Condensates

Transition from vortices to solitonic vortices in trapped atomic Bose-Einstein condensates

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