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Physical Review A

Finding the Elementary Excitations of Bose-Condensed Neutral Atoms in a Trap

Mark Edwards, P. A. Ruprecht, Keith R. Burnett

Published Jan 1, 1996• 1 citation

Abstract

We describe a method for finding the excitation frequencies of a Bosecondensed collection of trapped, neutral atoms. These excitations are the equivalents of the collisionless phonons in a homogeneous gas. Numerical results for a small assembly of trapped atoms are also presented. We discuss how one may be able to use these excitations as diagnostics of Bose condensates formed, for example, in evaporative cooling of alkali atoms. I. INTRODUCTION Now that Bose-Einstein condensation (BEC) has been achieved in a magnetic, alkalivapor trap [1], we soon hope to be able to look at its dynamical behavior. The approach used to produce this condensate combined laser- and evaporative-cooling techniques [2,3]. By the standards of most condensed-matter experiments, however, the trap used in this experiment was very small and the condensate formed in it correspondingly very inhomogeneous. Planning and analyzing experiments to probe this novel condensate requires a theory of how it responds to ext...

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We describe a method for finding the excitation frequencies of a Bosecondensed collection of trapped, neutral atoms. These excitations are the equivalents of the collisionless phonons in a homogeneous gas. Numerical results for a small assembly of trapped atoms are also presented. We discuss how one may be able to use these excitations as diagnostics of Bose condensates formed, for example, in evaporative cooling of alkali atoms. I. INTRODUCTION Now that Bose-Einstein condensation (BEC) has been achieved in a magnetic, alkalivapor trap [1], we soon hope to be able to look at its dynamical behavior. The approach used to produce this condensate combined laser- and evaporative-cooling techniques [2,3]. By the standards of most condensed-matter experiments, however, the trap used in this experiment was very small and the condensate formed in it correspondingly very inhomogeneous. Planning and analyzing experiments to probe this novel condensate requires a theory of how it responds to ext...

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.

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 investigate the response of a Bose-Einstein condensate of trapped, neutral atoms to weak and strong sinusoidal perturbation of the trapping potential both by solving the Bogoliubov equations and by direct integration of the time-dependent, driven Ginzburg-Pitaevskii-Gross equation. We find that the distortion of the condensate is maximal when the frequency of the perturbation equals one of the mode positions of the condensate's excitation spectrum. On resonance, the condensate exhibits a strong nonlinear response that can be used as a clear signature of the mode frequency in an experiment where the trap potential is weakly perturbed. For strong driving, we find evidence for an array of nonlinear effects such as harmonic generation and frequency mixing. These phenomena are the matter-wave analogs of conventional nonlinear optics and should be straightforward to study in evaporatively cooled samples of alkali-metal atoms. \textcopyright{} 1996 The American Physical Society.

Bose-Einstein condensation (BEC) in a gas has now been achieved. Alkali atoms (

^{87}Rb

,

^{23}Na

and

^{7}Li

) have been cooled to the point of condensation (temperature of 100 nK) using laser cooling and trapping, followed by magnetic trapping and evaporative cooling. This important experimental result has also renewed the interest on theoretical studies of BEC. In this contribution we discuss the statistical mechanics of the trapped BEC at zero temperature. In particular, we study the stability of the condensate by using a variational method with local and non-local interaction between the particles.

The recent developments in the study of Bose-Einstein condensation of neutral atoms are described. These studies aim to observe this phenomenon in a Bose gas where the quantum statistics of the particles, rather than the interactions between them, dominate the transition. The latest techniques use a combination of laser and evaporative cooling to get to the very low temperatures, in the nanokelvin regime, that are required to see condensation. In recent experiments at the Joint Institute for Laboratory Astrophysics of the University Colorado and the National Institute of Standards and Technology, Bose-condensed assemblies of rubidium atoms have been produced and their properties investigated. The relationship of this work to other phenomena in condensed matter and quantum field theory is discussed.

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.