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Physical Review Letters

Collective Excitations of a Bose-Einstein Condensate in a Dilute Gas

D. S. Jin, J. R. Ensher, M. R. Matthews, Carl Wieman, Eric Cornell

Published Jul 15, 1996• 708 citations
Publisher

Abstract

We observe phononlike excitations of a Bose-Einstein condensate (BEC) in a dilute atomic gas. ${}^{87}$Rb atoms are optically trapped and precooled, loaded into a magnetic trap, and then evaporatively cooled through the BEC phase transition to form a condensate. We excite the condensate by applying an inhomogeneous oscillatory force with adjustable frequency and symmetry. We have observed modes with different angular momenta and different energies and have studied how their characteristics depend on interaction energy. We find that the condensate excitations persist longer than their counterparts in uncondensed clouds.

DOI
10.1103/physrevlett.77.420

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We observe phononlike excitations of a Bose-Einstein condensate (BEC) in a dilute atomic gas. 87{}^{87}87Rb atoms are optically trapped and precooled, loaded into a magnetic trap, and then evaporatively cooled through the BEC phase transition to form a condensate. We excite the condensate by applying an inhomogeneous oscillatory force with adjustable frequency and symmetry. We have observed modes with different angular momenta and different energies and have studied how their characteristics depend on interaction energy. We find that the condensate excitations persist longer than their counterparts in uncondensed clouds.
Collective excitations of a dilute Bose condensate have been observed. These excitations are analogous to phonons in superfluid helium. Bose condensates were created by evaporatively cooling magnetically trapped sodium atoms. Excitations were induced by a modulation of the trapping potential, and detected as shape oscillations in the freely expanding condensates. The frequencies of the lowest modes agreed well with theoretical predictions based on mean-field theory. Before the onset of Bose-Einstein condensation, we observed sound waves in a dense ultracold gas.
We extend to finite temperature the study of collective excitations of a Bose-Einstein condensate in a dilute gas of 87Rb{}^{87}\mathrm{Rb}87Rb. Measurements of two modes with different angular momenta show unexpected temperature-dependent frequency shifts, with very different behavior for the two symmetries; in addition there is a sharp feature in the temperature dependence of one mode. The damping of these excitations exhibits dramatic temperature dependence, with condensate modes at temperatures near the transition damping even faster than analogous noncondensate oscillations.
Bose–Einstein condensation represents a quintessential manifestation of quantum mechanics at macroscopic scales, where a dilute gas of bosonic atoms undergoes a phase transition to form a coherent matter wave. This study presents a comprehensive theoretical investigation of collective excitations and critical phenomena in interacting Bose–Einstein condensates (BECs). Beginning with the Gross–Pitaevskii equation , we develop the Bogoliubov theory of excitations yielding the spectrum , where is the free-particle energy and characterizes contact interactions. The spectrum reveals phonon behavior at low momenta with sound velocity , transitioning to free-particle dispersion at momenta exceeding the inverse healing length . Collective modes in harmonically trapped condensates are analyzed in the Thomas–Fermi regime, yielding breathing mode frequency and quadrupole frequency . Damping mechanisms including Landau damping ( ) and Beliaev damping ( ) are characterized. The Lee–Huang–Yang correction extends the equation of state beyond mean field. Critical phenomena near are analyzed within the 3D XY universality class, with critical exponents , , and the interaction-induced shift with . All predictions show excellent agreement with experimental measurements on ultracold atomic gases.
In this work we study a Bose-Einstein condensate of 87Rb under the effects of an oscillatory excitation. The condensate is produced through forced evaporative cooling by radio-frequency in a harmonic magnetic trap. The excitation is generated by an oscillatory quadrupole field superimposed on the trapping potential. For a fixed value of the frequency of the excitation we observe the production of different regimes in the condensate as a function of two parameters of the excitation: the time and the amplitude. For the lowest values of these parameters we observe a bending of the main axis of the condensate. This demonstrates that the excitation is able to transfer angular momentum into the sample. By increasing the time or the amplitude of the excitation we observe the nucleation of an increasing number of quantized vortices. If the value of the parameters of the excitation is increased even further the vortices evolve into a different regime which we have identified as quantum turbulence. In this regime, the vortices are tangled among each other, generating a highly irregular array. For the highest values of the excitation the condensate breaks into pieces surrounded by a thermal cloud. This constitutes a different regime which we have identified as granulation. We present numerical simulations together with other theoretical considerations which allow us to interpret our observations. In this thesis we also describe the construction of a second experimental setup whose objective is to study magnetic properties of a Bose-Einstein condensate of 87Rb. In this new system the condensate is produced in a hybrid trap which combines a magnetic trap with an optical dipole trap. Bose-Einstein condensation has been already achieved in the new apparatus; experiments will be performed in the near future.
Bose–Einstein condensation in a gas has now been achieved. Atoms are cooled to the point of condensation using laser cooling and trapping, followed by magnetic trapping and evaporative cooling. These techniques are explained, as well as the techniques by which we observe the cold atom samples. Three different signatures of Bose–Einstein condensation are described. A number of properties of the condensate, including collective excitations, distortions of the wave function by interactions, and the fraction of atoms in the condensate versus temperature, have also been measured.
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.