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Optics and Photonics News

Characterizing Atom Sources with Quantum Coherence

Sean S. Hodgman, R. G. Dall, Andrew Manning, Mattias Johnsson, K. G. H. Baldwin, Andrew G. Truscott

Published Dec 1, 2011• 2 citations
Publisher

Abstract

Researchers can characterize atom \nsources by coherence properties, \nviewed either in the wave or particle \npicture, in analogy with quantum optics. \nFirst-order coherence measures amplitude \nfluctuations related to, for example, \nfringe visibility in an interferometer. \nSecond-order coherence measures intensity \nvariations as manifested in laser \nlight speckle.

DOI
10.1364/opn.22.12.000037

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Researchers can characterize atom \nsources by coherence properties, \nviewed either in the wave or particle \npicture, in analogy with quantum optics. \nFirst-order coherence measures amplitude \nfluctuations related to, for example, \nfringe visibility in an interferometer. \nSecond-order coherence measures intensity \nvariations as manifested in laser \nlight speckle.
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Interferometers provide a highly sensitive means to investigate and exploit the coherence properties of light in metrology applications. However, interferometers come in various forms and exploit different properties of the optical states within. In this paper, we introduce a classification scheme that characterizes any interferometer based on the number of involved nonlinear elements by studying their influence on single-photon and photon-pair states. Several examples of specific interferometers from these more general classes are discussed, and the theory describing the expected first-order and second-order coherence measurements for single-photon and single-photon-pair input states is summarized and compared. These theoretical predictions are then tested in an innovative experimental setup that is easily able to switch between implementing an interferometer consisting of only one or two nonlinear elements. The resulting singles and coincidence rates are measured in both configurations and the results are seen to fit well with the presented theory. The measured results of coherence are tied back to the presented classification scheme, revealing that our experimental design can be useful in gaining insight into the properties of the various interferometeric setups containing different degrees of nonlinearity.
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.
We investigate how the temporal coherence interference properties of light in a Michelson-Morley interferometer (MMI), using only a single-photon detector, can be understood in a quantum-optics framework in a straightforward and pedagogical manner. For this purpose we make use of elementary quantum field theory and Glaubers theory for photon detection in order to calculate the expected interference pattern in the MMI. If a thermal reference source is used in the MMI local oscillator port in combination with a thermal source in the signal port, the interference pattern revealed by such an intensity measurement shows a distinctive dependence on the differences in the temperature of the two sources. The MMI can therefore be used in order to perform temperature measurements. A related method was actually used to carry out high precision measurements of the cosmic micro-wave background radiation on board of the COBE satellite. The theoretical framework allows us to consider any initial quantum state. The interference of single photons as a tool to determine the angular peak-frequency of a one-photon pulse interfering with a single-photon reference pulse is, e.g., considered. A similar consideration for coherent laser pulses leads to a different response in the detector. The MMI experimental setup is therefore in a sense an example of an optical device where one can exhibit the difference between classical and quantum-mechanical light using only intensity measurements.
Bohr’s principle of complementarity has a long history and it is an important topic in quantum theory, among which the famous example is the duality relation. The relation between visibility C and distinguishability D, <?CDATA C2+D2≤1{C}^{2}+{D}^{2}\le 1C2+D2≤1?> C 2 + D 2 ≤ 1 , has long been recognized as the only representative of the duality relation. However, recent researches have shown that this inequality is not good enough because it is not tight for multipath interferometers. Meanwhile, a tight bound for the multipath interferometer has been put forward. Here we design and experimentally implement a three-path interferometer coupling with path indicator states. The wave property of photons is characterized by l 1-norm coherence measure, and the particle property is based on distinguishability of the indicator states. The new duality relation of the three-path interferometer is demonstrated in our experiment, which bounds the union of a right triangle and a part of elliptical area inside the quadrant of a unit circle. Data analysis confirms that the new bound is tight for photons in three-path interferometers.