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arXiv:cond-mat/0405222 · Physical Review Letters

High Sensitivity Phonon Spectroscopy of Bose-Einstein Condensates using Matter-Wave Interference

Nadav Y. Katz, Roee Ozeri, Jeff Steinhauer, Nir Davidson, C. Tozzo, F. Dalfovo

Published Nov 24, 2004• 22 citations
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Abstract

We study low-momentum excitations of a Bose-Einstein condensate using a novel matter-wave interference technique. In time-of-flight expansion images we observe strong matter-wave fringe patterns. The fringe visibility is a sensitive spectroscopic probe of in-trap phonons and is explained by use of a Bogoliubov excitation projection method applied to the rescaled order parameter of the expanding condensate. Gross-Pitaevskii simulations agree with the experimental data and confirm the validity of the theoretical interpretation. We show that the high sensitivity of this detection scheme gives access to the quantized quasiparticle regime.

DOI
10.1103/physrevlett.93.220403

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We study low-momentum excitations of a Bose-Einstein condensate using a novel matter-wave interference technique. In time-of-flight expansion images we observe strong matter-wave fringe patterns. The fringe visibility is a sensitive spectroscopic probe of in-trap phonons and is explained by use of a Bogoliubov excitation projection method applied to the rescaled order parameter of the expanding condensate. Gross-Pitaevskii simulations agree with the experimental data and confirm the validity of the theoretical interpretation. We show that the high sensitivity of this detection scheme gives access to the quantized quasiparticle regime.
We study low momentum excitations of a Bose-Einstein condensate using a novel matter-wave interference technique.In time-of-flight expansion images we observe strong matter-wave fringe patterns.The fringe contrast is a sensitive spectroscopic probe of in-trap phonons and is explained by use of a Bogoliubov excitation projection method applied to the rescaled order parameter of the expanding condensate.Gross-Pitaevskii simulations agree with the experimental data and confirm the validity of the theoretical interpretation.We show that the high sensitivity of this detection scheme gives access to the quantized quasiparticle regime.
Phonon like excitations can be imprinted into a trapped Bose-Einstein condensate of cold atoms using light scattering. If the condensate is suddenly let to freely expand, the initial phonons lose their collective character by transferring their energy and momentum to the motion of individual atoms. The basic mechanisms of this evaporation process are investigated by using the Gross-Pitaevskii theory and dynamically rescaled Bogoliubov equations. Different regimes of evaporation are shown to occur depending on the phonon wavelength. Distinctive signatures of the evaporated phonons are visible in the density distribution of the expanded gas, thus providing a new type of spectroscopy of Bogoliubov excitations.
The visibility of the density interference pattern of two Bose-Einstein condensates, which are produced in traps and overlap after the trapping potential is switched off, is investigated. Coherent wave packets are used to describe the order parameter in a second-quantization formalism. This results in a decrease of the visibility of the interference fringes with increasing time delay between the formation of the condensates and the observation of interference. In the two limiting cases of ideal and very dense gases the correlation time increases, τ →∞, and the result is identical to that obtained using an approach based on the Gross-Pitaevskii equation. Under the conditions of the experiment performed by M. R. Andrews, C. G. Townsend, H. J. Miesner et al. , Science 275 , 6367 (1997), the computed correlation time τ ≈0.2 s is much longer than the confinement time of the condensate, and it is possible to observe the predicted decrease of visibility of the interference fringes of the density of the atoms.
In a Bose-Einstein condensate, the excitation of a Bogoliubov phonon with low momentum (e.g., by a two-photon Bragg process) is strongly suppressed due to destructive interference between two indistinguishable excitation pathways. Here we show that scattering of this sound excitation into a double-momentum mode is strongly enhanced due to constructive interference. This enhancement yields an inherent amplification of second-order sound excitations of the condensate, as we confirm experimentally. We further show that due to parity considerations, this effect is extended to higher-order excitations.
We experimentally verified our prior theoretical work [J. Opt. Soc. Am. B 39, 3012 (2022)] by employing matter-wave interference to measure the ultranarrow momentum width of an optically trapped Bose-Einstein condensate (BEC) in situ. Splitting the BEC wave packet into various diffraction orders through double stand-wave pulses, we calibrated the momentum width by fitting the oscillation curve of the population of the zero-momentum state. The observed interference fringes exhibited slight deviations from our simplified theory. We numerically calculated the Gross-Pitaevskii equation and utilized Wigner function to gain insight into the impact of the external trap potential and nonlinear term of BEC. We found that the discrepancy was caused by the combined effects of the mean-field interaction and spatial density modulation of BEC. This quantum thermometry is straightforward to apply and is especially well suited for temperature calibration in deep cooling experiments. For atomic samples at the pK level after deep cooling, interatomic interactions can be safely disregarded, enabling momentum-width calibration in a single shot.