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arXiv:quant-ph/9907055 · Physical Review A

Mutual coherence of optical and matter waves

Gilberto Aparecido Prataviera, Elena V. Goldstein, Pierre Meystre

Published Dec 1, 1999• 8 citations
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Abstract

We propose a scheme to measure the cross correlations and mutual coherence of optical and matter fields. It relies on the combination of a matter-wave detector operating by photoionization of the atoms and a traditional absorption photodetector. We show that the double-detection signal is sensitive to cross-correlation functions of light and matter waves.

DOI
10.1103/physreva.60.4846

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We propose a scheme to measure the cross correlations and mutual coherence of optical and matter fields. It relies on the combination of a matter-wave detector operating by photoionization of the atoms and a traditional absorption photodetector. We show that the double-detection signal is sensitive to cross-correlation functions of light and matter waves.
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.
We introduce a new approach to photodetection, based on absorbers (atoms, molecules, or dopant donors in semiconductors) that are kept in a steady superposition of two bound states having different spatial symmetries (e.g., s and p0). We consider the illumination of such absorbers by a superposition of two fields that are mutually orthogonal by virtue of polarization or frequency, and measurements of the resulting photocurrent along the direction of polarization of one of the fields. In contrast to conventional photon counters, the directional photocurrent generated in the considered scheme measures only the phase-sensitive cross products of the mutually orthogonal field amplitudes, without responding to the photon flux of each mode separately. If the light is a superposition of a one- or two-mode squeezed vacuum field and a nearly coherent (local-oscillator) field orthogonal to the former, then cross correlations between two such photocurrents yield the autocorrelation function of the squeezed-field quadrature without terms related to the noise of the local oscillator (although shot noise still affects the degree of accuracy to which the autocorrelation is measured).
The generation of an entangled coherent state is one of the most important ingredients of quantum information processing using coherent states. Recently, numerous schemes to achieve this task have been proposed. In order to generate travelling-wave entangled coherent states, cross-phase-modulation, optimized by optical Kerr effect enhancement in a dense medium in an electromagnetically induced transparency (EIT) regime, seems to be very promising. In this scenario, we propose a fully quantized model of a double-EIT scheme recently proposed [D. Petrosyan and G. Kurizki, Phys. Rev. A 65, 33 833 (2002)]: the quantization step is performed adopting a fully Hamiltonian approach. This allows us to write effective equations of motion for two interacting quantum fields of light that show how the dynamics of one field depends on the photon-number operator of the other. The preparation of a Schr\"odinger cat state, which is a superposition of two distinct coherent states, is briefly exposed. This is based on nonlinear interaction via double EIT of two light fields (initially prepared in coherent states) and on a detection step performed using a 50:50 beam splitter and two photodetectors. In order to show the entanglement of an entangled coherent state, we suggest to measure the joint quadrature variance of the field. We show that the entangled coherent states satisfy the sufficient condition for entanglement based on quadrature variance measurement. We also show how robust our scheme is against a low detection efficiency of homodyne detectors.