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Physical Review A

Electric and magnetic monopoles in rotating Bose-Einstein condensates

C. R. Bennett, Leda G. Boussiakou, M. Babiker

Published Nov 14, 2001• 8 citations
Publisher

Abstract

We show that by virtue of the R\"ontgen interaction, a vortex of order n in a Bose-Einstein condensate (BEC), in which the constituent atoms are characterized by an electric dipole, gives rise to a magnetic monopole distribution, which correctly preserves magnetic charge neutrality. If, on the other hand, the BEC atoms are characterized by a magnetic dipole, we show that the Aharonov-Casher interaction term leads to the prediction of an electric charge distribution associated with the vortex state, which too, exhibits electric charge neutrality. Our theory displays an exact symmetry between the electric and magnetic aspects of the problem and can thus be presented in a unified fashion. Illustrations are given for finite-size atomic gas BECs, superfluid helium, and spin-polarized hydrogen BECs in the $n=1$ vortex state.

DOI
10.1103/physreva.64.061602

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We show that by virtue of the R"ontgen interaction, a vortex of order n in a Bose-Einstein condensate (BEC), in which the constituent atoms are characterized by an electric dipole, gives rise to a magnetic monopole distribution, which correctly preserves magnetic charge neutrality. If, on the other hand, the BEC atoms are characterized by a magnetic dipole, we show that the Aharonov-Casher interaction term leads to the prediction of an electric charge distribution associated with the vortex state, which too, exhibits electric charge neutrality. Our theory displays an exact symmetry between the electric and magnetic aspects of the problem and can thus be presented in a unified fashion. Illustrations are given for finite-size atomic gas BECs, superfluid helium, and spin-polarized hydrogen BECs in the n=1n=1n=1 vortex state.
A theory determining the electric and magnetic properties of vortex states in Bose–Einstein condensates (BECs) is presented. The principal ingredient is the Lagrangian of the system, which we derive correct to the first order in the atomic centre-of-mass velocity. For the first time using centre-of-mass coordinates, a gauge transformation is performed and relevant relativistic corrections are included. The Lagrangian is symmetric in the electric and magnetic aspects of the problem and includes two key interaction terms, namely the Aharanov–Casher and the Röntgen interaction terms. The constitutive relations, which link the electromagnetic fields to the matter fields via their electric polarization and magnetization, follow from the Lagrangian as well as the corresponding Hamiltonian. These relations, together with a generalized Gross–Pitaevskii equation, determine the magnetic (electric) monopole charge distributions accompanying an order n vortex state when the constituent atoms are characterized by an electric dipole (magnetic dipole). Field distributions associated with electric dipole active (magnetic dipole active) BECs in a vortex state are evaluated for an infinite- and a finite-length cylindrical BEC. The predicted monopole charge distributions, both electric and magnetic, automatically satisfy the requirement of global charge neutrality and the derivations highlight the exact symmetry between the electric and magnetic properties. Order of magnitude estimates of the effects are given for an atomic gas BEC, superfluid helium and a spin-polarized hydrogen BEC.
A theory determining the electric and magnetic properties of vortex states in Bose-Einstein condensates (BECs) is presented. The principal ingredient is the Lagrangian of the system, which we derive correct to the first order in the atomic centre-of-mass velocity. For the first time using centre-of-mass coordinates, a gauge transformation is performed and relevant relativistic corrections are included. The Lagrangian is symmetric in the electric and magnetic aspects of the problem and includes two key interaction terms, namely the Aharanov-Casher and the Röntgen interaction terms. The constitutive relations, which link the electromagnetic fields to the matter fields via their electric polarization and magnetization, follow from the Lagrangian as well as the corresponding Hamiltonian. These relations, together with a generalized Gross-Pitaevskii equation, determine the magnetic (electric) monopole charge distributions accompanying an order n vortex state when the constituent atoms are characterized by an electric dipole (magnetic dipole). Field distributions associated with electric dipole active (magnetic dipole active) BECs in a vortex state are evaluated for an infinite- and a finite-length cylindrical BEC. The predicted monopole charge distributions, both electric and magnetic, automatically satisfy the requirement of global charge neutrality and the derivations highlight the exact symmetry between the electric and magnetic properties. Order of magnitude estimates of the effects are given for an atomic gas BEC, superfluid helium and a spin-polarized hydrogen BEC.
Magnetically trapped atoms in Bose-Einstein condensates are spin polarized. Since the magnetic field is inhomogeneous, the atoms acquire Berry phases of the Aharonov-Bohm type during adiabatic motion. In the presence of an electric field, there is an additional Aharonov-Casher effect. Taking into account the limitations on the strength of the electric fields due to the polarizability of the atoms, we investigate the extent to which these effects can be used to induce rotation in a Bose-Einstein condensate.
We classify all possible fractional charge vortices of charge less than unity in spin-1 and spin-2 polar and cyclic Bose-Einstein condensates (BECs) with zero magnetization. Statics and dynamics of these vortices in quasi-two-dimensional spinor BECs are studied employing an accurate numerical solution and a Lagrange variational approximation. The results for density and collective-mode oscillation are illustrated using the fractional-charge BEC vortex of 23Na^{23}\mathrm{Na}23Na and 87Rb^{87}\mathrm{Rb}87Rb atoms with realistic interaction and trapping potential parameters.
When a Bose–Einstein condensate is set to rotate, superfluid vortices will be formed, which finally condense into a vortex lattice as the rotation frequency further increases. We show that the dipole-dipole interactions renormalize the short-range interaction strength and result in a distinction between interactions of parallel-polarized atoms and interactions of antiparallel-polarized atoms. This effect may lead to a spontaneous breakdown of the rapidly rotating Bose condensate into a novel anti-ferromagnetic-like vortex lattice. The upward-polarized Bose condensate forms a vortex lattice, which is staggered against a downward-polarized vortex lattice. A phase diagram related to the coupling strength is obtained.