Quite often one can see descriptions saying that the coherence time of single photons corresponds to the length of the single photon wavepacket (for example Jelezko et al, PRA 67 041802(R) (2003) http://pra.aps.org/abstract/PRA/v67/i4/e041802). I find it hard to come to terms with this picture. There are some threads discussing related topics but I find that none of them really helps a lot. I will try to describe my trouble and hopefully someone can join the discussion:(adsbygoogle = window.adsbygoogle || []).push({});

Consider a single photon emitted from the decay of a simple two-level system with radiative lifetime T. The probability amplitude of detecting the photon I usually picture as a sharp wavefront propagating out from the emitter, with an exponential tail decaying as exp(-t/T) (or spatially exp(-r/cT)). I can understand the direct correspondence between the length of a wavepacket such as this and the spectral distribution of the photon, but what about cases when dephasing of the excited state is present? Dephasing limits the coherence time of the emitted photons in solid state systems, and single photon interferometry is often used as a probe of the dephasing of the emitter, for example in the paper linked above. What if the dephasing is such that the energy level of the excited state is modulated during the emission of the wavepacket? This would would obviously broaden the linewidth and shorten the coherence time of the photon, and – in my world – correspond to a frequency modulated wavepacket in the time domain. But how is this compatible with the notion that shorter coherence time equals shorter wavepacket?

Looking forward to hearing your comments and ideas.

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# Photon coherence time as the wavepacket length and dephasing

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