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arXiv:1306.4086 · New Journal of Physics

Interaction of a Bose–Einstein condensate and a superconductor via eddy currents

Igor Sapina, Thomas Dahm

Published Jul 17, 2013• 6 citations
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Abstract

We study center-of-mass oscillations of a dipolar Bose–Einstein condensate in the vicinity of a superconducting surface. We show that the magnetic field of the magnetic dipoles induces eddy currents in the superconductor, which act back on the Bose–Einstein condensate. This leads to a shift of its oscillation frequency and to an anharmonic coupling of the Bose–Einstein condensate with the superconductor. The anharmonicity creates a coupling to one of the collective modes of the condensate that can be resonantly enhanced if the parameters of the condensate are chosen properly. This provides a new physical mechanism to couple a Bose–Einstein condensate and a superconductor, which becomes significant for 52 Cr, 168 Er or 164 Dy condensates in superconducting microtraps.

DOI
10.1088/1367-2630/15/7/073035

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We study center-of-mass oscillations of a dipolar Bose–Einstein condensate in the vicinity of a superconducting surface. We show that the magnetic field of the magnetic dipoles induces eddy currents in the superconductor, which act back on the Bose–Einstein condensate. This leads to a shift of its oscillation frequency and to an anharmonic coupling of the Bose–Einstein condensate with the superconductor. The anharmonicity creates a coupling to one of the collective modes of the condensate that can be resonantly enhanced if the parameters of the condensate are chosen properly. This provides a new physical mechanism to couple a Bose–Einstein condensate and a superconductor, which becomes significant for 52 Cr, 168 Er or 164 Dy condensates in superconducting microtraps.
We study the dynamics of a dipolar Bose-Einstein condensate, like, for example, a 52Cr^{52}\mathrm{Cr}52Cr or 164Dy^{164}\mathrm{Dy}164Dy condensate, interacting with a superconducting surface. The magnetic dipole moments of the atoms in the Bose-Einstein condensate induce eddy currents in the superconductor. The magnetic field generated by eddy currents modifies the trapping potential such that the center-of-mass oscillation frequency is shifted. We numerically solve the Gross-Pitaevskii equation for this system and compare the results with analytical approximations. We present an approximation that gives excellent agreement with the numerical results. The eddy currents give rise to anharmonic terms, which leads to the excitation of shape fluctuations of the condensate. We discuss how the strength of the excitation of such modes can be increased by exploiting resonances, and we examine the strength of the resonances as a function of the center-of-mass oscillation amplitude of the condensate. Finally, we study different orientations of the magnetic dipoles and discuss favorable conditions for the experimental observation of the eddy-current effect.
The subject of the present thesis is the study of the interaction between a Bose-Einstein condensate (BEC) and a superconductor.The BEC performs center-of-mass oscillations perpendicular to the superconducting surface.Each atom in the BEC carries a magnetic dipole moment, which induces eddy currents in the surface.These eddy currents are a source of a magnetic field which modifies the potential in which the BEC is trapped.This leads to a change of the dynamical behavior of the BEC.In particular the BEC center-of-mass oscillation frequency is shifted compared to the case without the surface interaction.Additionally, the potential generated by the superconductor excites shape oscillations of the BEC.To investigate these effects, the Gross-Pitaevskii equation for a dipolar BEC close to a superconducting surface is solved numerically.Also analytical approximations are presented and compared to the numerically obtained results.It is shown that the interaction with the superconducting surface generates a frequency shift, that is large enough to be detected in an experiment.Furthermore, different methods to identify the eddy current effect are presented.It is also discussed how the effects on the BEC can be enhanced by choosing the proper dipole orientation and by adjusting the geometry of the setup.The BEC shape oscillations can be additionally enhanced by making use of a resonance phenomenon.4 Center-of-mass frequency shift 4.1 Frequency shift within TF approximation . . . . . . . . . .4.1.1Frequency shift based on a Thomas-Fermi ellipsoid 4.1.2Frequency shift based on the column density model 4.2 Numerical results for the frequency shift . . . . . . . . . . .4.3 Different polarizations of the BEC . . . . . . . . . . . . . .4.3.1 Polarization in the y-direction . . . . . . . . . . . .4.3.2Polarization in the x-direction (perpendicular to the surface) . . . . . . . . . . .
The collective excitations of a one-dimensional dipolar Bose—Einstein condensate trapped in an anharmonic potential are investigated theoretically. Using the variational approach, we obtain the coupled equations of motion for the center-of-mass coordinate of the condensate and its width. In particular, analytical expressions for the low-lying excitation modes are given. The results show that dipole-dipole interactions reduce the frequency shift induced by quartic distortion. The interplay between dipole-dipole interactions and anharmonic distortion for the collapse and revival of the collective excitations originating from the nonlinear coupling between the two modes are also discussed.
We have studied the internal and external dynamics of a Bose-Einstein condensate in an anharmonic magnetic waveguide. An oscillating condensate experiences a strong coupling between the center of mass motion and the internal collective modes. Because of the anharmonicity of the magnetic potential, not only the center of mass motion shows harmonic frequency generation, but also the internal dynamics exhibit nonlinear frequency mixing. Thereby, the condensate shows shape oscillations with an extremely large change in the aspect ratio of up to a factor of 10. We describe the data with a theoretical model to high accuracy. For strong excitations we test the experimental data for indications of a chaotic behavior.
We study the influence of dipole–dipole interaction on the formation of vortices in a rotating dipolar Bose–Einstein condensate (BEC) of 52 Cr and 164 Dy atoms in quasi two-dimensional geometry. By numerically solving the corresponding time-dependent mean-field Gross–Pitaevskii equation, we show that the dipolar interaction enhances the number of vortices, while a repulsive contact interaction increases the stability of the vortices. Furthermore, an ordered vortex lattice of a relatively large number of vortices is found in a strongly dipolar BEC.
The sss-wave interaction is usually the dominant form of interactions in atomic Bose-Einstein condensates (BECs). Recently, Feshbach resonances have been employed to reduce the strength of the sss-wave interaction in many atomic species. This opens the possibilities to study magnetic dipole-dipole interactions (MDDIs) in BECs, where the novel physics resulting from long-range and anisotropic dipolar interactions can be explored. Using a variational method, we study the effect of MDDIs on the statics and dynamics of atomic BECs with tunable sss-wave interactions for a variety of species, including both nonalkali metals with large magnetic dipole moments (52{}^{52}52Cr, 164{}^{164}164Dy, 168{}^{168}168Er) and alkali metals (with much smaller magnetic dipole moments). A parameter of magnetic Feshbach resonances, ${\ensuremath{\epsilon}}_{dd,\text{max}}$, is used to quantitatively indicate the feasibility of experimentally observing MDDI effects in different atomic species. We find that strong MDDI effects should be observable in both in-trap and time-of-flight behaviors, not only for the strongly magnetic dipolar species but also for the alkali-metal BECs of 7{}^{7}7Li, 39{}^{39}39K, and 133{}^{133}133Cs. In addition, we predict several effects which should be experimentally observable. Our results provide a helpful guide for experimentalists to realize and study atomic dipolar quantum gases.