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

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. Collective excitation of a Bose-Einstein condensate (BEC) is an essential diagnostic tool for investigating properties of the ultracold quantum state. Fundamental information about condensate dynamics can be determined from observations of collective modes [1][2][3], including the effects of temperature [4][5][6], and the dimensionality of the system [7]. In addition, the interplay between these modes and external agents, such as random potentials [8,9], lattices [10,11], as well as other atoms [12][13][14][15][16], can be investigated. Examining the excitation spectrum of the BEC allows for a detailed comparison with theoretical models [17][18][19][20] and related quantum systems such as superfluid helium [21,22] and superconductors [23,24].Generically, a collective excitation is generated by the modification of the trapping potential of the condensate [25]. One convenient method is to apply a sudden magnetic field gradient, thereby shifting the center of the trap and exciting a dipole oscillation about the trap center. One may also suddenly change the curvature of the trap to excite quadrupole modes. The lowest-lying m = 0 quadrupole mode is characterized by out-of-phase axial and radial oscillations.If the condensate is not the only occupant of the trap (i.e., there exists a thermal component or another species of atoms) then the other atoms may also be excited through these processes. The evolution of a collective excitation can therefore be complicated because the multiple components may affect damping or induce frequency shifts of the oscillation [12][13][14][15][16]. Therefore, modulating the trap, although an extremely useful tool for an isolated condensate, can be cumbersome when the system to be studied is multispecied. An alternative approach is to excite the condensate alone, leaving the other occupants of the trap untouched.In this work, we demonstrate the excitation of the lowestlying quadrupole mode in a BEC of 7 Li by modulating the atomic scattering length via a magnetic Feshbach resonance. In contrast to abruptly changing the scattering length [26], sinusoidal modulation enables the controlled excitation of a single mode at a specific frequency. In addition, by using this method, a coexisting thermal component will be minimally excited by the mean-field coupling to the normal gas [27,28]. In the case of a multispecies experiment, resonant modulation of the scattering length of one species will not necessarily excite the others, depending on the details of other F...

Tuning the quantum phase transition of bosons in optical lattices via periodic modulation of thes-wave scattering length

“…In the following we study a system of spinless bosons in a homogeneous lattice of arbitrary dimension D with a periodically modulated s-wave scattering length [22,23], which can be experimentally achieved, for instance, in the vicinity of a broad Feshbach resonance [24]. This periodically driven quantum many-body system is described by the time-dependent Hamiltonian…”

“…(23) follow from applying Rayleigh-Schrödinger perturbation theory by using a suitable diagrammatic representation [37,40]. By denoting the creation (annihilation) operator with an arrow line pointing into (out of) the site, each perturbative contribution of α (n) 2p can be sketched as an arrow-line diagram, which is composed of n oriented internal lines connecting the vertices and two external arrow lines.…”

“…Another method to periodically drive an ultracold quantum gas system relies on a periodic modulation of the s-wave scattering length [22,23], which can be experimentally achieved, for instance, in the vicinity of a broad Feshbach resonance [24]. For a harmonically trapped Bose-Einstein condensate this induces various phenomena of nonlinear dynamics as, for instance, mode coupling, higher harmonics generation, and significant shifts in the frequencies of collective modes (see, for instance, Ref.…”

Coupling collective modes in a trapped superfluid

“…In general, the macroscopic oscillations of the density n = |ψ| 2 represent the so-called collective modes. In this paper, we concentrate our attention on two of the most investigated modes: the dipole mode [13] and the quadrupole mode [12].…”

“…Beyond the linear approximation, theoretical studies of such collective oscillations point out the significant dependence of the frequencies on the oscillation amplitudes [4], which can be enhanced by manipulating the trap anisotropy in such a way that the normal modes become resonant [11]. In recent work [12], we have experimentally demonstrated the excitation of quadrupole modes when a modulation was introduced in the scattering length, using an oscillating magnetic field near a Feshbach resonance in a 7 Li Bose-Einstein condensate held in an optical trap. In particular, excitations were investigated with respect to their response to the modulation frequency, thus allowing the measurement of the resonance curve.…”