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arXiv:1004.2887 · Physical Review A

Collective excitation of a Bose-Einstein condensate by modulation of the atomic scattering length

S. E. Pollack, D. Dries, Randall G. Hulet, K. M. F. Magalhães, E. A. L. Henn, E. R. F. Ramos, M. A. Caracanhas, Vanderlei Salvador Bagnato

Published May 24, 2010• 105 citations
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Abstract

We excite the lowest-lying quadrupole mode of a Bose-Einstein condensate by modulating the atomic scattering length via a Feshbach resonance. Excitation occurs at various modulation frequencies, and resonances located at the natural quadrupole frequency of the condensate and at the first harmonic are observed. We also investigate the amplitude of the excited mode as a function of modulation depth. Numerical simulations based on a variational calculation agree with our experimental results and provide insight into the observed behavior.

DOI
10.1103/physreva.81.053627

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We excite the lowest-lying quadrupole mode of a Bose-Einstein condensate by modulating the atomic scattering length via a Feshbach resonance. Excitation occurs at various modulation frequencies, and resonances located at the natural quadrupole frequency of the condensate and at the first harmonic are observed. We also investigate the amplitude of the excited mode as a function of modulation depth. Numerical simulations based on a variational calculation agree with our experimental results and provide insight into the observed behavior.
In a recent experiment, a Bose-Einstein condensate of 7{}^{7}7Li has been excited by a harmonic modulation of the atomic sss-wave scattering length via Feshbach resonance. By combining an analytical perturbative approach with extensive numerical simulations, we analyze the emerging nonlinear dynamics of the system on the mean-field Gross-Pitaevskii level at zero temperature. Resulting excitation spectra are presented and prominent nonlinear features are found: mode coupling, higher harmonics generation, and significant shifts in the frequencies of collective modes. We indicate how nonlinear dynamical properties could be made clearly observable in future experiments and compared to our results.
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We consider a superfluid cloud composed of a Bose-Einstein condensate oscillating within a magnetic trap (dipole mode) where, due to the existence of a Feshbach resonance, an effective periodic time-dependent modulation in the scattering length is introduced. Under this condition, collective excitations such as the quadrupole mode can take place. We approach this problem by employing both the Gaussian and the Thomas-Fermi variational Ans\"atze. The resulting dynamic equations are analyzed by considering both linear approximations and numerical solutions, where we observe coupling between dipole and quadrupole modes. Aspects of this coupling related to the variation of the dipole oscillation amplitude are analyzed. This may be a relevant effect in situations where oscillation in a magnetic field in the presence of a bias field BBB takes place, and should be considered in the interpretation of experimental results.
We demonstrate novel methods for exciting the collective oscillations of Bose–Einstein condensates without directly deforming the confinement potential. The collective excitations were induced through the radio-frequency (rf) forced evaporative cooling of 87 Rb atoms confined in a magnetic trap. We studied two methods, the first involving a sinusoidal amplitude modulation of the rf field, and the other a fast sweep of the rf frequency, both performed during evaporation. An almost-pure low-energy quadrupole oscillation mode was observed with both methods. In the case of the rf-amplitude modulation (fast rf-frequency sweep), the collective excitations are likely to be induced by the periodic (bulk) emission of atoms from the trap. We also observed substantial loss of atoms from the trap when the rf amplitude was modulated with a frequency near the axial-trap frequency. This allows a precise determination of the magnetic-trap frequency.
Finite-temperature simulations are used to study quadrupole excitations of a trapped Bose-Einstein condensate. We focus specifically on the m = 0 mode, where a long-standing theoretical problem is to account for an anomalous variation of the mode frequency with temperature. We explain this behavior in terms of the excitation of two separate modes, corresponding to the coupled motion of the condensate and the thermal cloud. The relative amplitude of the modes depends sensitively on the temperature and on the frequency of the harmonic drive used to excite them. Good agreement with experiment is found for appropriate drive frequencies.
We analytically and numerically study nonlinear dynamics in Bose–Einstein condensates (BECs) induced either by a harmonic modulation of the interaction or by the geometry of the trapping potential. To analytically describe BEC dynamics, we use a perturbative expansion based on the Poincaré–Lindstedt analysis of a Gaussian variational ansatz, whereas in the numerical approach we use numerical solutions of both a variational system of equations and the full time-dependent Gross–Pitaevskii equation. The harmonic modulation of the atomic s-wave scattering length of a BEC of 7 Li was achieved recently via Feshbach resonance, and such a modulation leads to a number of nonlinear effects, which we describe within our approach: mode coupling, higher harmonics generation and significant shifts in the frequencies of collective modes. In addition to the strength of atomic interactions, the geometry of the trapping potential is another key factor for the dynamics of the condensate, as well as for its collective modes. The asymmetry of the confining potential leads to important nonlinear effects, including resonances in the frequencies of collective modes of the condensate. We study in detail such geometric resonances and derive explicit analytic results for frequency shifts for the case of an axially symmetric condensate with two- and three-body interactions. Analytically obtained results are verified by extensive numerical simulations.