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Optics Express

Non-classical states of the electromagnetic field in cavity QED

L. G. Lutterbach, L. Davidovich

Published Aug 17, 1998• 15 citations
Publisher

Abstract

We propose simple experiments in cavity quantum electrodynamics leading, for the first time, to the measurement of negative values of the Wigner function of an electromagnetic field. We also show that the realization of a controlled-not gate within the framework of cavity QED is a special case of our proposal, and is equivalent to the measurement of the Wigner function of a one-photon field at the origin of phase space.

DOI
10.1364/oe.3.000147

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We propose simple experiments in cavity quantum electrodynamics leading, for the first time, to the measurement of negative values of the Wigner function of an electromagnetic field. We also show that the realization of a controlled-not gate within the framework of cavity QED is a special case of our proposal, and is equivalent to the measurement of the Wigner function of a one-photon field at the origin of phase space.
We show that the technique of Ramsey interferometry may be used to completely determine the quantum state of an electromagnetic field in a cavity. Our method, which allows the direct measurement of the Wigner function of the field, is a useful tool for probing the quantum-classical transition and, in particular, the decoherence between coherent superpositions of distinguishable coherent states of the electromagnetic field in the cavity. We also show that the realization of a controlled-not gate within framework of cavity QED is a special case of our proposal, and leads to the measurement of a negative value for the Wigner function of an electromagnetic field.
Recent experiments in cavity QED have allowed the monitoring of the decoherence process, which is at the heart of the quantum theory of measurement and plays an essential role in the classical limit of quantum mechanics. It is shown here that the technique of Ramsey interferometry, central to those experiments, may be used to determine completely the quantum state of an electromagnetic field in a cavity. This new method, which allows the direct measurement of the Wigner function of the field, is a useful tool for probing the quantum-classical transition and, in particular, the decoherence of superpositions of distinguishable coherent states of the electromagnetic field in the cavity. It is also shown that the realization of a controlled-not gate within the framework of cavity QED is a special case of this proposal, and is related to the measurement of the Wigner function of a one-photon state.
Following a proposal by two of us [L. G. Lutterbach and L. Davidovich, Phys. Rev. Lett. 78, 2547 (1997)], we have measured the Wigner function at the origin of phase space for a single photon field. Its value is negative, exhibiting the nonclassical nature of this state. The experiment is based on the absorption-free detection of the microwave field stored in a superconducting cavity [G. Nogues et al., Nature (London) 400, 239 (1999)]. Extension to a measurement of the Wigner function over the complete phase space is discussed.
These lectures review some basic techniques of quantum optics, related to the description of the quantized electromagnetic field in phase space and of the interaction between atoms and photons in cavities. The Wigner function is introduced, and some of the methods for measuring this distribution are reviewed. The combination of phase space methods with cavity QED techniques is shown to lead to experiments which are closely connected to fundamental problems regarding the classical limit of quantum mechanics and the quantum theory of measurement.