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

Bijnen, van Rmw Rick; Dow, AJ; O’Dell, D. H. J.; Parker, N. G.; Martin, A. M.

doi:10.1103/physreva.80.033617

Cited by 33 publications

(74 citation statements)

References 53 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Both the thermodynamic threshold for vortices to be favoured, as well as the process by which vortices nucleate [165][166][167] into the condensate, are sensitive to dipolar interactions; this will be analysed in detail below.…”

Section: Summary Of Vortex Generation Methodsmentioning

confidence: 99%

“…This is done by considering small perturbations in the BEC density and phase of the form n n n eq δ = + and S S S eq δ = + . By linearizing the dipolar hydrodynamic equations (61) and (62), the dynamics of such perturbations can be described as [165][166][167], To investigate the stability of the BEC the eigenfunctions and eigenvalues of the operator in equation (80) can be examined. Dynamical instability arises when one or more eigenvalues λ possess a positive real part.…”

Section: Dynamical Stability Of Stationary Solutionsmentioning

confidence: 99%

“…Figure 18 [167] shows examples of these routes. Specifically, figure 18 shows the static solutions v α of equation (77) as a function of Ω ( figure 18(a) .…”

Section: Routes To Instability and Vortex Lattice Formationmentioning

confidence: 99%

See 2 more Smart Citations

Vortices and vortex lattices in quantum ferrofluids

Martin

Marchant

O’Dell

et al. 2017

J. Phys.: Condens. Matter

View full text Add to dashboard Cite

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.

show abstract

Section: Summary Of Vortex Generation Methodsmentioning

confidence: 99%

Section: Dynamical Stability Of Stationary Solutionsmentioning

confidence: 99%

See 1 more Smart Citation

Vortices and vortex lattices in quantum ferrofluids

Martin

Marchant

O’Dell

et al. 2017

J. Phys.: Condens. Matter

View full text Add to dashboard Cite

show abstract

“…At temperatures T much smaller than the critical temperature T c , the properties of BEC in a rotating frame with long-range dipole-dipole interaction (DDI) are well described by the macroscopic complex-valued wave function ψ = ψ(x, t) whose evolution is governed by the three-dimensional (3D) Gross-Pitaevskii equation (GPE) with an angular momentum rotation term and long-range DDI [1,10,20,26,30,31,41,47,49,54]. In dimensionless form, the 3D GPE has the form (1.1) i∂ t ψ(x, t) = − 1 2…”

mentioning

confidence: 99%

A Simple and Efficient Numerical Method for Computing the Dynamics of Rotating Bose--Einstein Condensates via Rotating Lagrangian Coordinates

Bao¹,

Marahrens²,

Tang³

et al. 2013

SIAM J. Sci. Comput.

View full text Add to dashboard Cite

Abstract. We propose a simple, efficient, and accurate numerical method for simulating the dynamics of rotating Bose-Einstein condensates (BECs) in a rotational frame with or without longrange dipole-dipole interaction (DDI). We begin with the three-dimensional (3D) Gross-Pitaevskii equation (GPE) with an angular momentum rotation term and/or long-range DDI, state the twodimensional (2D) GPE obtained from the 3D GPE via dimension reduction under anisotropic external potential, and review some dynamical laws related to the 2D and 3D GPEs. By introducing a rotating Lagrangian coordinate system, the original GPEs are reformulated to GPEs without the angular momentum rotation, which is replaced by a time-dependent potential in the new coordinate system. We then cast the conserved quantities and dynamical laws in the new rotating Lagrangian coordinates. Based on the new formulation of the GPE for rotating BECs in the rotating Lagrangian coordinates, a time-splitting spectral method is presented for computing the dynamics of rotating BECs. The new numerical method is explicit, simple to implement, unconditionally stable, and very efficient in computation. It is spectral-order accurate in space and second-order accurate in time and conserves the mass on the discrete level. We compare our method with some representative methods in the literature to demonstrate its efficiency and accuracy. In addition, the numerical method is applied to test the dynamical laws of rotating BECs such as the dynamics of condensate width, angular momentum expectation, and center of mass, and to investigate numerically the dynamics and interaction of quantized vortex lattices in rotating BECs without or with the long-range DDI. 1. Introduction. Bose-Einstein condensation (BEC), first observed in 1995 [4,18,23], has provided a platform to study the macroscopic quantum world. Later, with the observation of quantized vortices [2,19,34,35,37,39,50], rotating BECs have been extensively studied in the laboratory. The occurrence of quantized vortices is a hallmark of the superfluid nature of BECs. In addition, condensation of bosonic atoms and molecules with significant dipole moments whose interaction is both nonlocal and anisotropic has recently been achieved experimentally in trapped 52 Cr and 164 Dy gases [1,22,27,32,33,36,48].At temperatures T much smaller than the critical temperature T c , the properties of BEC in a rotating frame with long-range dipole-dipole interaction (DDI) are well

show abstract

“…Vortices have not been experimentally realized in dipolar BECs yet, but they are a most appealing phenomenon and there is intensive theoretical research on them [5,6,7,8,9,10,11].…”

Section: Introductionmentioning

confidence: 99%

Energy barriers for vortex nucleation in dipolar condensates

et al. 2010

View full text Add to dashboard Cite

We consider singly-quantized vortex states in a condensate of 52 Cr atoms in a pancake trap. We obtain the vortex solutions by numerically solving the Gross-Pitaevskii equation in the rotating frame with no further approximations. The behavior of the condensate is studied under three different situations concerning the interactions: only s-wave, s-wave plus dipolar and only dipolar. The energy barrier for the nucleation of a vortex is calculated as a function of the vortex displacement from the rotation axis in the three cases. These results are compared to those obtained for contact interaction condensates in the Thomas-Fermi approximation, and to a pseudo-analytical model, showing this latter a very good agreement with the numerical calculation.

show abstract

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

Cited by 33 publications

References 53 publications

Vortices and vortex lattices in quantum ferrofluids

Vortices and vortex lattices in quantum ferrofluids

A Simple and Efficient Numerical Method for Computing the Dynamics of Rotating Bose--Einstein Condensates via Rotating Lagrangian Coordinates

Energy barriers for vortex nucleation in dipolar condensates

Contact Info

Product

Resources

About