Measuring the temporal wavefnction of a photon

Homodyne tomography provides information about the signal state of the electromagnetic field in the mode of the local oscillator. If the signal state is known to be the signal photon, the mode of that photon can be determined by searching for the temporal shape of the local oscillator pulse such that the observed single-photon efficiency is maximized. However, if the bandwidth of the temporal mode of the photon is sufficiently narrow in comparison with those of the detector and the acquisition system, the same task can be solved with a continuous local oscillator, thereby greatly simplifying the experimental procedure. Complete information about the mode can be obtained from the autocorrelation statistics of the homodyne photocurrent acquired at several different local oscillator frequencies. We present a theory and experiment to demonstrate the capabilities of this technique. A heralded single photon is obtained from a pair generated via four-wave mixing in an atomic vapor and the required bandwidth is achieved by spectral filtering of the trigger channel by means of a narrowband optical cavity.