Transverse Breathing Mode of an Elongated Bose-Einstein Condensate

Chevy, Frédéric; Bretin, Vincent; Rosenbusch, P.; Madison, Kirk W.; Dalibard, Jean

doi:10.1103/physrevlett.88.250402

Cited by 161 publications

(197 citation statements)

References 35 publications

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“…5. There is an additional frequency shift due to nonzero temperature [4][5][6][7] which is estimated to be negligible given our low temperatures and interaction strength [43]. Even though we can neglect temperature effects in the measurements presented here, our method of excitation of the quadrupole mode may be used to study these effects in further detail in regimes of stronger interactions.…”

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confidence: 99%

“…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.…”

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confidence: 99%

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

Pollack

Dries²,

Hulet³

et al. 2010

Phys. Rev. A

101

113

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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. 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...

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confidence: 99%

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confidence: 99%

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

Pollack

Dries²,

Hulet³

et al. 2010

Phys. Rev. A

101

113

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“…The observations of low-lying excitations [1,2,3], including the scissor mode [4], were an important step toward the characterization of these systems. Collective excitations were also studied at finite temperature [5,6,7,8] investigating frequency shifts and damping rates. All the experiments so far reported were performed on Bose-Einstein condensates magnetically trapped in pure harmonic potentials.…”

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confidence: 99%

Collective Excitations of a Trapped Bose-Einstein Condensate in the Presence of a 1D Optical Lattice

et al. 2003

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We study low-lying collective modes of a horizontally elongated 87 Rb condensate produced in a 3D magnetic harmonic trap with the addition of a 1D periodic potential which is provided by a laser standing-wave along the horizontal axis. While the transverse breathing mode results unperturbed, quadrupole and dipole oscillations along the optical lattice are strongly modified. The measurement of frequencies of collective modes was immediately recognized to be a fundamental and precise tool to investigate the quantum macroscopic behaviour of atomic Bose-Einstein condensates. The observations of low-lying excitations [1,2,3], including the scissor mode [4], were an important step toward the characterization of these systems. Collective excitations were also studied at finite temperature [5,6,7,8] investigating frequency shifts and damping rates. All the experiments so far reported were performed on Bose-Einstein condensates magnetically trapped in pure harmonic potentials.More recently, condensates trapped in periodic potentials have attracted much interest demonstrated by the flourishing of both theoretical and experimental papers in this field. BEC trapped in a periodic potential is particularly interesting as a possible system for the investigation of pure quantum effects. Many results have been reported e.g. interference of atomic de Broglie waves tunneling from a vertical array of BECs [9], observation of squeezed states in a BEC [10], realization of a linear array of Josephson junctions [11] with BECs, observation of Bloch oscillations [12] and culminating with the observation of the quantum phase transition from a superfluid to a Mott insulator [13]. Recently, the general interest of this field has been extended to a careful study of the loading of BECs in an optical lattice [14] and to the observation of collapse and revival of the matter wave field of a BEC [15]. In this context, the characterization of collective modes of a condensate in the presence of an optical lattice motivated the development of a new theoretical treatment [16] based on a generalization of the hydrodynamic equation of superfluids for a weakly interacting Bose gas [17,18] to include the effects of the periodic potential. The collective modes of a trapped BEC are predicted to be significantly modified by the presence of an optical lattice. Precise measurements of the low-lying collective frequency would verify the validity of the mass renormalization theory [16].In this Letter we quantitatively investigate the modification of the low-lying excitation spectrum of a harmonically trapped BEC, due to the presence of a 1D optical lattice. In particular we measure the frequencies of the quadrupole and transverse breathing modes as a function of the optical lattice depth. The experimental observations are compared with the predictions of the model reported in [16] consisting in a frequency shift of the collective modes characterized by a motion along the lattice axis, whereas the frequency of collective modes involving an atomic flow transverse...

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“…In this regard, the results in [37] are also of interest, where propagation and absorption of the transverse breathing mode of an elongated BEC were investigated experimentally in 87 Rb vapour. The authors of the mentioned study, attempting to measure the damping rate of these modes at the temperature approximately equal to 40 ÷ 60 nK, had found that the behaviour of the perturbation amplitude in this temperature region differs significantly from the behaviour of the amplitude of a damped sinusoidal signal.…”

Section: Resultsmentioning

confidence: 99%

“…We also would like to draw attention to the fact that temperature range 40 ÷ 60 nK corresponds to the values of quantity a in terms of the present paper that are in the 0.7 ÷ 1.0 range. The value of a is naturally calculated according to formula (4.9) and using the values of the physical characteristics of the system [37]. In other words, in the mentioned case [37], it deals with the nearest neighbourhood of the point a ≈ 0.847 where the nonanalytic dependence of the dispersion characteristics on temperature is revealed.…”

Section: Resultsmentioning

confidence: 99%

Mechanism of collisionless sound damping in dilute Bose gas with condensate

Slyusarenko¹,

Kruchkov²

2013

Condens. Matter Phys.

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We develop a microscopic theory of sound damping due to Landau mechanism in dilute gas with Bose condensate. It is based on the coupled evolution equations of the parameters describing the system. These equations have been derived in earlier works within a microscopic approach which employs the Peletminskii-Yatsenko reduced description method for quantum many-particle systems and Bogoliubov model for a weakly nonideal Bose gas with a separated condensate. The dispersion equations for sound oscillations were obtained by linearization of the mentioned evolution equations in the collisionless approximation. They were analyzed both analytically and numerically. The expressions for sound speed and decrement rate were obtained in high and low temperature limiting cases. We have shown that at low temperature the dependence of the obtained quantities on temperature significantly differs from those obtained by other authors in the semi-phenomenological approaches. Possible effects connected with non-analytic temperature dependence of dispersion characteristics of the system were also indicated.

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Transverse Breathing Mode of an Elongated Bose-Einstein Condensate

Cited by 161 publications

References 35 publications

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

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

Collective Excitations of a Trapped Bose-Einstein Condensate in the Presence of a 1D Optical Lattice

Mechanism of collisionless sound damping in dilute Bose gas with condensate

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