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Damping and frequency shift in the oscillations of two colliding Bose-Einstein condensates

Michele Modugno, C. Fort, INGUSCIO, MASSIMO, P. Maddaloni, F. Minardi

Published Jan 1, 2001• 1 citation
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Abstract

We have investigated the center-of-mass oscillations of a Rb87 Bose-Einstein condensate in an elongated magneto-static trap. We start from a trapped condensate and we transfer part of the atoms to another trapped level, by applying a radio-frequency pulse. The new condensate is produced far from its equilibrium position in the magnetic potential, and periodically collides with the parent condensate. We discuss how both the damping and the frequency shift of the oscillations are affected by the mutual interaction between the two condensates, in a wide range of trapping frequencies. The experimental data are compared with the prediction of a mean-field model.

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We experimentally and theoretically investigate the dynamics of two trapped condensates in a magnetostatic trap. The two condensates, being in different internal Zeeman state (|F=2,m=2〉 and |F=2,m=1〉), experience external parabolic potentials that differ by both curvature and equilibrium position.The dynamics of the system, exhibiting large amplitude oscillations of the |F=2,m=1〉 condensate, is affected in a profound manner by the periodical intercondensates collisions.In particular, we show that both an amplitude damping and a frequency shift occur. Measuring the former allows to study the elastic scattering, whose suppression is a manifestation of the Bose condensates superfluidity, while the latter gives access to the cross scattering length a21.

AIP conference proceedings•Jan 1, 2001•0 citations
We have investigated the center-of-mass oscillations of a Rb87 Bose-Einstein condensate in an elongated magneto-static trap. We start from a trapped condensate and we transfer part of the atoms to another trapped level, by applying a radio-frequency pulse. The new condensate is produced far from its equilibrium position in the magnetic potential, and periodically collides with the parent condensate. We discuss how both the damping and the frequency shift of the oscillations are affected by the mutual interaction between the two condensates, in a wide range of trapping frequencies. The experimental data are compared with the prediction of a mean-field model.
Two 87Rb{}^{87}\mathrm{Rb}87Rb condensates ( F=2F\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2F=2, mf=2{m}_{f}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2mf​=2, and mf=1{m}_{f}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1mf​=1) are produced in highly displaced harmonic traps and the collective dynamical behavior is investigated. The mutual interaction between the two condensates is evidenced in the center-of-mass oscillations as a frequency shift of 6.4(3)6.4(3)%6.4(3). Calculations based on a mean-field theory well describe the observed effects of periodical collisions both on the center-of-mass motion and on the shape oscillations.
We study the dynamics of two interacting Bose-Einstein condensates, by numerically solving two coupled Gross-Pitaevskii equations at zero temperature. We consider the case of a sudden transfer of atoms between two trapped states with different magnetic moments: the two condensates are initially created with the same density profile, but are trapped into different magnetic potentials, whose minima are vertically displaced by a distance much larger than the initial size of both condensates. Then the two condensates begin to perform collective oscillations, undergoing a complex evolution, characterized by collisions between the two condensates. We investigate the effects of their mutual interaction on the center-of-mass oscillations and on the time evolution of the aspect ratios. Our theoretical analysis provides a useful insight into the recent experimental observations by Maddaloni et al. [Phys. Rev. Lett. 85, 2413 (2000)].
We experimentally and theoretically investigate the dynamics of two trapped condensates in a magnetostatic trap. The two condensates, being in different internal Zeeman state (/F = 2, m = 2) and /F = 2,m = i]), experience external parabolic potentials that differ by both curvature and equilibrium position. The dynamics of the system, exhibiting large amplitude oscillations of the /F = 2,nt = 1] condensate, is affected in a profound manner by the periodical inter condensates collisions. In particular, we show that both an amplitude damping and a frequency shift occur. Measuring the former allows to study the elastic scattering, whose suppression is a manifestation of the Bose condensates superfluidity, while the latter gives access to the cross scattering length alpha.
We calculate the effect of the interaction between an optically active material and a Bose-Einstein condensate on the collective oscillations of the condensate. We provide explicit expressions for the frequency shift of the center-of-mass oscillation in terms of the potential generated by the substrate and of the density profile of the gas. The form of the potential is discussed in detail and various regimes (van der Waals--London, Casimir-Polder, and thermal regimes) are identified as a function of the distance of atoms from the surface. Numerical results for the frequency shifts are given for the case of a sapphire dielectric substrate interacting with a harmonically trapped condensate of 87Rb^{87}\mathrm{R}\mathrm{b}87Rb atoms. We find that at distances of $4--8\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{m}$, where thermal effects become visible, the relative frequency shifts produced by the substrate are of the order ${10}^{\ensuremath{-}4}$ and hence accessible experimentally. The effects of nonlinearities due to the finite amplitude of the oscillation are explicitly discussed. Predictions are also given for the radial breathing mode.
We experimentally investigate the collective excitation of 87 Rb Bose–Einstein condensates confined in a cigar-shaped magnetic trap (QUIC trap). Using a method of magnetic perturbation, the center-of-mass oscillation of the condensate is excited, so that the radial trapping frequency of the QUIC trap can be precisely determined. A high-order excitation, characterized by a fast shape oscillation, also occurs simultaneously, with a noticeable damping in the oscillation amplitude compared with the oscillation of the center of mass. The measured oscillation frequencies, associated with these two low-energy excitation modes, agree well with theoretical predictions based on the Gross–Pitaevskii equation.
We experimentally and theoretically investigate the dynamics of two trapped condensates in a magnetostatic trap. The two condensates, being in different internal Zeeman state (|F=2,m=2〉 and |F=2,m=1〉), experience external parabolic potentials that differ by both curvature and equilibrium position.The dynamics of the system, exhibiting large amplitude oscillations of the |F=2,m=1〉 condensate, is affected in a profound manner by the periodical intercondensates collisions.In particular, we show that both an amplitude damping and a frequency shift occur. Measuring the former allows to study the elastic scattering, whose suppression is a manifestation of the Bose condensates superfluidity, while the latter gives access to the cross scattering length a21.