Interference between non-overlapping wave-packets of a single photon

Summary form only given. Consider an experiment where a single photon is split into two wave-packets by a beam splitter and where the two wave packets are made to overlap in a specific region in space. If the two wave-packets arrive at the same time, an interference pattern can be recorded by a classical detector such as a photographic plate. If however, the difference in arrival time between the two wave-packets is made to be larger than the coherence time of the wave packets, the interference pattern, as recorded by the detector, will disappear. It has been argued that if the classical detector is replaced by a material that can remember the phase of the electromagnetic field, i.e. a material with a long homogeneous dephasing time, it would be possible to record the interference between the two wave-packets even if the time difference between them is much larger than the coherence time. We denote this single-photon self-interference. The interference pattern would take the form of a frequency dependent population grating in the material and could be detected by diffracting a light pulse on this grating. The delayed single-photon self-interference experiment has several unique features. It is a four-wave mixing experiment where the two first pulses share a total of only one photon. Thus interaction between these two pulses and the material, normally considered as a nonlinear multiphoton process, is here carried out by a single photon. We have performed experiments with multiphoton excitation pulses and extrapolated the data to the single photon level. These experiments support the conclusion from the theoretical calculations that delayed single-photon self-interference could be observed.