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arXiv:cond-mat/0412672 · Physical Review A

High-contrast interference in a thermal cloud of atoms

Daniel E. Miller, J. R. Anglin, J. R. Abo-Shaeer, K. Xu, J. K. Chin, Wolfgang Ketterle

Published Apr 29, 2005• 34 citations
arXivHTMLPDF

Abstract

The coherence properties of a gas of bosonic atoms above the Bose-Einstein-condensation transition temperature were studied. Bragg diffraction was used to create two spatially separated wave packets, which interfere during expansion. Given sufficient expansion time, high fringe contrast could be observed in a cloud of arbitrary temperature. Fringe visibility greater than 90% was observed, which decreased with increasing temperature, in agreement with a simple model. When the sample was ``filtered'' in momentum space using long, velocity-selective Bragg pulses, the contrast was significantly enhanced in contrast to predictions.

DOI
10.1103/physreva.71.043615

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The coherence properties of a gas of bosonic atoms above the Bose-Einstein-condensation transition temperature were studied. Bragg diffraction was used to create two spatially separated wave packets, which interfere during expansion. Given sufficient expansion time, high fringe contrast could be observed in a cloud of arbitrary temperature. Fringe visibility greater than 90% was observed, which decreased with increasing temperature, in agreement with a simple model. When the sample was ``filtered'' in momentum space using long, velocity-selective Bragg pulses, the contrast was significantly enhanced in contrast to predictions.
The role of source cloud spatial coherence in a Mach-Zehnder-type atom interferometer is experimentally investigated. The visibility and contrast of a Bose-Einstein condensate (BEC) and three thermal sources with varying spatial coherence are compared as a function of interferometer time. At short times, the fringe visibility of a BEC source approaches 100100%100 nearly independent of $\ensuremath{\pi}$ pulse efficiency, while thermal sources have fringe visibilities limited to the $\ensuremath{\pi}$ pulse efficiency. More importantly for precision measurement systems, the BEC source maintains interference at interferometer times significantly beyond the thermal source.
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.
Interference between two freely expanding Bose-Einstein condensates has been observed. Two condensates separated by approximately 40 micrometers were created by evaporatively cooling sodium atoms in a double-well potential formed by magnetic and optical forces. High-contrast matter-wave interference fringes with a period of approximately 15 micrometers were observed after switching off the potential and letting the condensates expand for 40 milliseconds and overlap. This demonstrates that Bose condensed atoms are "laser-like"; that is, they are coherent and show long-range correlations. These results have direct implications for the atom laser and the Josephson effect for atoms.
We present a cold-atom gravimeter operating with a sample of Bose-condensed 87{}^{87}87Rb atoms. Using a Mach-Zehnder configuration with the two arms separated by a two-photon Bragg transition, we observe interference fringes with a visibility of ($83\ifmmode\pm\else\textpm\fi{}6$)% at T=3T=3T=3 ms. We exploit large momentum transfer (LMT) beam splitting to increase the enclosed space-time area of the interferometer using higher-order Bragg transitions and Bloch oscillations. We also compare fringes from condensed and thermal sources and observe a reduced visibility of ($58\ifmmode\pm\else\textpm\fi{}4$)% for the thermal source. We suspect the loss in visibility is caused partly by wave-front aberrations, to which the thermal source is more susceptible due to its larger transverse momentum spread. Finally, we discuss briefly the potential advantages of using a coherent atomic source for LMT, and we present a simple mean-field model to demonstrate that with currently available experimental parameters, interaction-induced dephasing will not limit the sensitivity of inertial measurements using freely falling, coherent atomic sources.
We construct a Mach-Zehnder interferometer using Bose-Einstein condensed rubidium atoms and optical Bragg diffraction. In contrast to interferometers based on normal diffraction, where only a small percentage of the atoms contribute to the signal, our Bragg diffraction interferometer uses all the condensate atoms. The condensate coherence properties and high phase-space density result in an interference pattern of nearly 100% contrast. The two arms of the interferometer may be completely separated in space, making it an ideal tool that can be used to detect vortices or other topological condensate phases.
Bose–Einstein condensates of particles behave in many ways like coherent radiation fields, and the realization of Bose–Einstein condensation in dilute gases has opened up the experimental study of many aspects of interactions between coherent matter waves. In addition, the existence of these dilute trapped quantum gases has prompted a re-examination of a number of theoretical issues. This field is a vast one, and in this chapter we shall touch briefly on selected topics. In Sec. 13.1 we describe the classic interference experiment, in which two clouds of atoms are allowed to expand and overlap. Rather surprisingly, an interference pattern is produced even though initially the two clouds are completely isolated. We shall analyse the reasons for this effect. The marked decrease in density fluctuations in a Bose gas when it undergoes Bose–Einstein condensation is demonstrated in Sec. 13.2. Gaseous Bose–Einstein condensates can be manipulated by lasers, and this has made possible the study of coherent matter wave optics. We describe applications of these techniques to observe solitons, Bragg scattering, and non-linear mixing of matter waves in Sec. 13.3. The atom laser and amplification of matter waves is taken up in Sec. 13.4. How to characterize Bose–Einstein condensation microscopically is the subject of Sec. 13.5, where we also consider fragmented condensates. Interference of two condensates One of the striking manifestations of the wave nature of Bose–Einstein condensates is the observation of an interference pattern when two condensed and initially separated clouds are allowed to overlap. An example is shown in Fig. 13.1.