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arXiv:0811.3296 · Physical Review Letters

Gauge-Field Rotation of an Electrically Polarized Bose Condensate by a Radial Magnetic Field

Edouard B Sonin

Published Mar 13, 2009• 13 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.102.106407

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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.
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.
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 demonstrate that a spin-orbit-coupled Bose-Einstein condensate can be effectively rotated by adding a real magnetic field to inputting gauge angular momentum, which is distinctly different from the traditional ways of rotation by stirring or Raman laser dressing to inputting canonical angular momentum. The gauge angular momentum is accompanied by the spontaneous generation of equal and opposite canonical angular momentum in the ground states, and it leads to the nucleation of quantized vortices. We explain this by indicating that the effective rotation with the vortex nucleation results from the effective magnetic flux induced by the gauge potential, which is essentially different from the previous scheme of creating vortices by synthetic magnetic fields. In the weakly interacting regime, symmetrically placed domains separated by vortex lines as well as half-integer giant vortices are discovered. With relatively strong interatomic interaction, we predict a structure of coaxially arranged annular vortex arrays, which is in stark contrast to the familiar Abrikosov vortex lattice. The developed way of rotation may be extended to a more general gauge system.
We consider quantum phase transitions in a system of bright dipolar excitons which can form bound pairs (dipolar biexcitons). The biexciton energy is tuned from negative to positive values through the scattering threshold. At sufficiently large density an exciton superfluid transforms into a superfluid of biexcitons. With the average relative momenta of excitons in the pairs being beyond the light cone, the transition is accompanied by a reduction of the photoluminescence intensity. Effective magnetic fields due to the long-range exchange splitting of exciton states shift the position of the gap in the elementary excitation spectrum to a circle of degenerate minima in the $\mathbit{k}$ space. Closing the gap results in the formation of exciton stripes polarized linearly along the direction of their translational symmetry. In the biexciton energy vs density phase diagram the novel phase intervenes between the dark biexciton and radiative exciton superfluids. We conclude that formation of a BCS-like biexciton condensate induces correlated alignment of the effective magnetic fields and excitonic spins. We outline important differences in the predicted mechanism from the phenomenon of spin-orbit-coupled Bose-Einstein condensation.
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.
We numerically simulate vortex nucleation in a Bose-Einstein Condensate (BEC) subject to an effective magnetic field. The effective magnetic field is generated from the interplay between light with a non-trivial phase structure and the BEC, and can be shaped and controlled by appropriate modifications to the phase and intensity of the light. We demonstrate that the nucleation of vortices is seeded by instabilities in surface excitations which are coupled to by an asymmetric trapping potential (similar to the case of condensates subject to mechanical rotation) 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.