Single-photon Fock state

Abstract The spatiotemporal optical mode of the single-photon Fock state prepared by conditional measurements on a biphoton is investigated and found to be identical to that of a classical wave due to a nonlinear interaction of the pump wave and Klyshko s advanced wave. We discuss the applicability of this identity in various experimental settings. 

This method has recently been utilized by the Konstanz quantum optics group, who has prepared the signal photon in a well-defined, highly pure spatiotemporal mode which can be matched with, coupled into, or caused to interfere with, a classical laser mode. Based on this achievement, we have demonstrated homodyne tomography of the single-photon Fock state [Lvovsky 2001]... 

As an example, consider the simple case of two single-mode fields of equal frequencies and polarizations. Assume that there are initially n photons in field 1 and m photons in the field 2, and that the state vectors of the fields are the Fock states /j) = n) and v /2) = m). The initial state of the two fields is the direct product of the single-field states, v /) = n) m). Inserting Eq. (27) into Eq. (28) and taking the expectation value with respect to the initial state of the fields, we find... 

Cavity QED has led to many new effects, including the realization of a quantmn phase gate (Turchette et al. 1995), the creation of Fock states of the radiation field (Varcoe et al. 2000), and a demonstration of quantum nondemolition detection of single photons (Nogues et al. 1999). Ye et al. (1999) have noted that all serious schemes for quantum computation and communication via cavity QED rely on developing techniques for atom confinement. This explains the importance of the experiments on the trapping of single atoms under conditions of cavity QED. 

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