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arXiv:physics/9710043 · Physical Review Letters

Atomic Detection and Matter-Wave Coherence

Elena V. Goldstein, Pierre Meystre

Published Jun 8, 1998• 23 citations
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Abstract

We analyze several models of atomic detectors in the context of the measurement of coherence properties of matter waves. In particular, we show that an ionization scheme measures normally ordered correlation functions of the Schr\"odinger field, in analogy with the optical situation. However, it exhibits a sensitivity to exchange processes that is normally absent in optics.

DOI
10.1103/physrevlett.80.5036

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We analyze several models of atomic detectors in the context of the measurement of coherence properties of matter waves. In particular, we show that an ionization scheme measures normally ordered correlation functions of the Schr"odinger field, in analogy with the optical situation. However, it exhibits a sensitivity to exchange processes that is normally absent in optics.
We use an operational approach to discuss ways to measure the higher-order cross correlations between optical and matter-wave fields. We pay particular attention to the fact that atomic fields actually consist of composite particles that can easily be separated into their basic constituents by a detection process such as photoionization. In the case of bosonic fields, that we specifically consider here, this leads to the appearance in the detection signal of exchange contributions due to both the composite bosonic field and its individual fermionic constituents. We also show how time-gated counting schemes allow to isolate specific contributions to the signal, in particular involving different orderings of the Schr\"odinger and Maxwell fields.
In analogy to Glauber's analysis of optical coherence, we adopt an operational approach to introduce different classes of atomic coherence associated with different types of measurements. For the sake of concreteness we consider specifically fluorescence, nonresonant imaging, and ionization. We introduce definitions of coherence appropriate to them, which we call electronic, density, and field coherence, respectively. We illustrate these concepts in various descriptions of Bose-Einstein condensation, showing that each of these descriptions makes different implicit assumptions on the coherence of the system. We also study the impact of elastic collision on the field and density coherence properties of atom lasers.
In analogy to Glauber's analysis of optical coherence, we adopt an operational approach to introduce different classes of atomic coherence associated with different types of measurements. For the sake of concreteness we consider specifically fluorescence, nonresonant imaging, and ionization. We introduce definitions of coherence appropriate to them, which we call electronic, density, and field coherence, respectively. We illustrate these concepts in various descriptions of Bose-Einstein condensation, showing that each of these descriptions makes different implicit assumptions on the coherence of the system. We also study the impact of elastic collision on the field and density coherence properties of atom lasers.
One of the seminal advances in quantum optics was the understanding that a quantised description of ensembles of photons is best characterised by correlation functions. Correlations are also a fundamental property of matter waves, and the single wavefunction that describes a Bose-Einstein condensate (BEC) is in principle characterised by long range coherence to all orders (i.e. a universal correlation value of unity). Here we measure the higher order correlation properties of ultra-cold matter waves and use them to probe the coherence of the gas.
One of the seminal advances in quantum optics was the understanding that a quantised description of ensembles of photons is best characterised by correlation functions. Correlations are also a fundamental property of matter waves, and the single wavefunction that describes a Bose-Einstein condensate (BEC) is in principle characterised by long range coherence to all orders (i.e. a universal correlation value of unity). Here we measure the higher order correlation properties of ultra-cold matter waves and use them to probe the coherence of the gas.