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arXiv:cond-mat/0206308 · Physical Review A

Bose-Einstein condensates in strong electric fields: Effective gauge potentials and rotating states

Janik Kailasvuori, T. H. Hansson, G. M. Kavoulakis

Published Nov 11, 2002• 3 citations
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Abstract

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.

DOI
10.1103/physreva.66.053603

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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.
Here it is shown that a condensate of electrically polarized bosons subject to a radial magnetic field must rotate due to the Aharonov-Bohm effect. As in mechanically rotated superfluids, rotation is accompanied by penetration of vortices into the condensate at some critical magnetic field. In the case of a Bose-condensed exciton cloud in a double-quantum well, a necessary electric polarization is provided with spatial separation of electrons and holes forming excitons. Penetration of vortices strongly affects the intensity and the angular distribution of photoluminescence from the exciton cloud. This effect can be used for an experimental manifestation of exciton Bose condensation.
Quantum mechanically, static or applied gauge fields manifest themselves by directly coupling to a system's phase. Artificial gauge field techniques manipulate the phase of a Bose-Einstein condensate's order parameter, yielding effects present in condensed matter systems subject to magnetic fields, electric fields, or spin-orbit coupling. In this chapter, we explore the impact of these artificial gauge fields on Bose- Einstein condensates and explain the consequences. Several analogues to traditional condensed matter systems are enabled by these techniques, including the Hall effect, superfluid vortex nucleation in systems with artificial magnetic fields, and magnetic-like phase transitions in systems with spin-orbit coupling. Introduction Since the first experiments with Bose-Einstein condensates (BECs), researchers have exploited the universality of physical laws to draw analogies between the behavior of ultracold quantum gases and systems ranging from material to astrophysical. These analogous situations are deliberately engineered, giving cold-atom “quantum simulators” [1] that exhibit behavior either observed or predicted in analogous quantum systems. Superfluidity was one of the first many-body quantum phenomena demonstrated in BECs. For example, several experiments showed superfluid behavior by rapidly rotating the condensates and observing the formation of vortices [2, 3, 4, 5] – quantized point-defects in the BEC's order parameter. In the rotating frame of these experiments, this nucleation of vortices could be understood as the consequence of an artificial magnetic field [6] that arises via the formal equivalence of the rotating-frame Coriolis force and the Lorentz force, which we describe in Section 15.4.1. Together with other measurements, these results proved to be in excellent agreement with the predictions of the Gross-Pitaevskii equation (GPE) [7], a decades-old idealization of superfluid helium. Buoyed by the prospect for studying magnetic field–driven strongly correlated systems using these nearly ideal quantum gases, proposals for alternate techniques to simulate gauge fields were developed. These methods primarily employ an internal state–selective atom–light coupling, where the photon momentum provides the forces necessary to mimic a Lorentz force [8, 9, 10, 11, 12, 13, 14, 15, 16]. The first demonstration of this type of technique used a spatially dependent Ramantransition scheme to effect a magnetic field [17], and experiments demonstrating artificial electric fields [18] and spin-orbit coupling [19, 20, 21, 22, 23, 24] soon followed.
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.
We investigate the rotational properties of a Bose-Einstein condensate (BEC) in an effective magnetic field. The corresponding gauge potential is optically generated, and based on the adiabatic motion of the atoms. We demonstrate that the nucleation of vortices is seeded by instabilities in surface excitations and show that this picture also holds when the applied effective magnetic field is not homogeneous. The eventual configuration of vortices in the cloud depends on the geometry of the applied field.
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.