Can Single Photon Beams Exhibit Coherence?

[Joseph14]

For any light beam it is normal to characterize the coherence length and time. This is done by measuring the ability light to interfere with itself.

Does it make sense to talk about the coherence of a single photon beam, such as the one used in the double slit experiment? Can a single photon beam be incoherent? I imagine this could be tested using a mach-zehnder interferometer.

 

[PhilDSP]

A single photon could have a coherence relationship to a varying background field. As an analogy you might look at G. P. Thomson's electron beam experiments where single electrons were fired into a very thin gold foil. The arrangement of the atoms in the foil lattice produced a varying field that interfered with the electron. The result was the creation of visible rings (EM fluctuations) spreading out from the impact point.

 

[Cthugha]

A single photon state will show ideal first-order coherence in both temporal and spatial domains. In fact, this holds true for any arbitrary pure-state excitation of a single mode and any statistical-mixture state, in which a single mode of the radiation field is excited.

This is discussed for example in chapter 9 of Loudon's "The quantum theory of light" and to some lesser degree in the book about "Mesoscopic quantum optics" by Yoshi Yamamoto and Atac Imamoglu.

It is also discussed in depth in "U. Titulaer and R. Glauber, Density operators for Coherent Fields", Phys Rev, Vol 145, (1966), pp. 1041, but that paper is not an easy read.

However, all single photon states will of course only show first-order, but no second or higher-order coherence. In addition one should also add that real single photon sources are not necessarily creating real Fock states in the sense theory proclaims. Most will produce single photons over a narrow range of energies varying from one photon to the next.