Rotation of an atomic Bose–Einstein condensate with and without a quantized vortex

Corro, I.; Parker, N. G.; Martin, A. M.

doi:10.1088/0953-4075/40/18/004

Cited by 10 publications

(27 citation statements)

References 35 publications

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“…At the high frequency end these crescents merge to form a main region of instability, characterised by large eigenvalues. At the low frequency end the crescents become vanishingly thin and are characterised by very small eigenvalues which are at least one order of magnitude smaller than in the main instability region [19]. As such these regions will only induce instability in the condensate if they are traversed very slowly.…”

Section: Dynamical Stability Of Stationary Solutionsmentioning

confidence: 99%

“…Furthermore, they predict these modes become unstable for certain ranges of rotation frequency [15,16]. Comparison with experiments [13,14] and full numerical simulations of the GPE [17,18,19] have clearly shown that the instabilities are the first step in the entry of vortices into the condensate and the formation of a vortex lattice. Crucially, the hydrodynamic equations give a clear explanation of why vortex lattice formation in s-wave BECs was only observed to occur at a much greater rotation frequency than that at which they become energetically favorable.…”

Section: Introductionmentioning

confidence: 94%

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Exact solutions and stability of rotating dipolar Bose-Einstein condensates in the Thomas-Fermi limit

et al. 2009

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We present a theoretical analysis of dilute gas Bose-Einstein condensates with dipolar atomic interactions under rotation in elliptical traps. Working in the Thomas-Fermi limit, we employ the classical hydrodynamic equations to first derive the rotating condensate solutions and then consider their response to perturbations. We thereby map out the regimes of stability and instability for rotating dipolar Bose-Einstein condensates and, in the latter case, discuss the possibility of vortex lattice formation. We employ our results to propose several routes to induce vortex lattice formation in a dipolar condensate.

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Section: Dynamical Stability Of Stationary Solutionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 94%

Exact solutions and stability of rotating dipolar Bose-Einstein condensates in the Thomas-Fermi limit

et al. 2009

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“…The seeding of vortices, at higher rotation frequencies, arises when one or more of these modes becomes unstable [181,182]. Evidence for this comes from comparison between experiments [40,183] and full numerical simulations of the GPE [184][185][186][187].…”

Section: Stationary Solutions Of Rotating Dipolar Condensates In Ellimentioning

confidence: 99%

“…The relative smallness of the eigenvalues in this region indicates that instabilities grow over a much longer time-scale as compared to the main region of instability. For non-dipolar BECs this was numerically investigated by solving the GPE [187]. These numerical results showed that the narrow instability regions have negligible effect when ramping Ω at rates greater than As the size of the scalar matrix operator (80) is increased to N 4, 5, = … , the higher lying modes develop real eigenvalues as Ω is increased.…”

Section: Dynamical Stability Of Stationary Solutionsmentioning

confidence: 99%

Vortices and vortex lattices in quantum ferrofluids

Martin

Marchant

O’Dell

et al. 2017

J. Phys.: Condens. Matter

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The experimental realization of quantum-degenerate Bose gases made of atoms with sizeable magnetic dipole moments has created a new type of fluid, known as a quantum ferrofluid, which combines the extraordinary properties of superfluidity and ferrofluidity. A hallmark of superfluids is that they are constrained to rotate through vortices with quantized circulation. In quantum ferrofluids the long-range dipolar interactions add new ingredients by inducing magnetostriction and instabilities, and also affect the structural properties of vortices and vortex lattices. Here we give a review of the theory of vortices in dipolar Bose-Einstein condensates, exploring the interplay of magnetism with vorticity and contrasting this with the established behaviour in non-dipolar condensates. We cover single vortex solutions, including structure, energy and stability, vortex pairs, including interactions and dynamics, and also vortex lattices. Our discussion is founded on the mean-field theory provided by the dipolar Gross-Pitaevskii equation, ranging from analytic treatments based on the Thomas-Fermi (hydrodynamic) and variational approaches to full numerical simulations. Routes for generating vortices in dipolar condensates are discussed, with particular attention paid to rotating condensates, where surface instabilities drive the nucleation of vortices, and lead to the emergence of rich and varied vortex lattice structures. We also present an outlook, including potential extensions to degenerate Fermi gases, quantum Hall physics, toroidal systems and the Berezinskii-Kosterlitz-Thouless transition.

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“…At low synthetic magnetic fields the crescents become vanishingly small, with eigenvalues several orders of magnitude smaller than in the main instability region. These regions induce instability if they are traversed very slowly [26]. B * z(b) ( ) and the stability of the stationary solutions of the upper branch are key to understanding the response of the BEC to the adiabatic introduction of orB * z .…”

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confidence: 99%

Synthetic magnetohydrodynamics in Bose-Einstein condensates and routes to vortex nucleation

et al. 2011

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Engineering of synthetic magnetic flux in Bose-Einstein condensates [Lin et al., Nature (London) 462, 628 (2009)] has prospects for attaining the high vortex densities necessary to emulate the fractional quantum Hall effect. We analytically establish the hydrodynamical behavior of a condensate in a uniform synthetic magnetic field, including its density and velocity profile. Importantly, we find that the onset of vortex nucleation observed experimentally corresponds to a dynamical instability in the hydrodynamical solutions and reveal other routes to instability and anticipated vortex nucleation.One of the driving forces behind quantum degenerate gas research is the emulation of many-body condensed matter phenomenon [1]. For quantum degenerate Bose gases, achievements include the observation of Bloch oscillations [2] and the Mott insulator superfluid transition [3]. Considerable attention has also been applied to the achievement of the fractional quantum Hall (FQH) regime in rotating Bose-Einstein condensates (BECs) [4]. To obtain quantum Hall physics time reversal symmetry must be broken. In solid state devices this is done through the relatively simple process of applying a magnetic field. Since the atoms in a BEC are neutral an alternative method needs to be applied to break time reversal symmetry. In the context of FQH physics considerable focus has been applied to the breaking of time reversal symmetry through rotation.For BECs in rotating traps the nucleation of vortices has been observed by several groups [5]. Theoretical superfluid hydrodynamical studies, in the Thomas-Fermi (TF) regime, have proved effective in calculating the rotation frequency at which vortices are nucleated by dynamical instability [6,7]. Such studies, which have been extended to dipolar BECs [8], agree with numerical predictions from the Gross-Pitaevskii equation [6,7,[9][10][11][12]. However, to reach the FQH regime the number of vortices needs to be significantly larger than the number of bosons in the BEC. Typically, experiments are carried out in parabolic traps, defined by average in-plane trapping frequency ω ⊥ . When the rotation frequency, z , is equal to ω ⊥ the BEC becomes untrapped. Hence, the attainment of the FQH regime, which requires z → ω ⊥ , is an extremely challenging task. An alternative approach is to generate a synthetic vector potential [13], which breaks the time reversal symmetry of the problem, producing a synthetic magnetic field [14][15][16][17][18][19][20].The recent work of Lin et al.[20] has demonstrated the effectiveness of such an approach, in a 87 Rb BEC, through the experimental realization of a synthetic vector potential in the Landau gauge: A * = A * xX , corresponding to a synthetic magnetic field B * = ∇ × A * . The authors showed that vortices were nucleated at a critical synthetic magnetic field. Here we generalize the TF methodology used to successfully calculate the onset of vortex nucleation in rotating systems [6,7] to the case of synthetic magnetic fields in harmonically confined BECs. W...

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Rotation of an atomic Bose–Einstein condensate with and without a quantized vortex

Cited by 10 publications

References 35 publications

Exact solutions and stability of rotating dipolar Bose-Einstein condensates in the Thomas-Fermi limit

Exact solutions and stability of rotating dipolar Bose-Einstein condensates in the Thomas-Fermi limit

Vortices and vortex lattices in quantum ferrofluids

Synthetic magnetohydrodynamics in Bose-Einstein condensates and routes to vortex nucleation

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