Re: Quantum question?

[David Bowman <David_Bowman@GEORGETOWNCOLLEGE.EDU>]

Regarding the exchange between Leigh and Ben:

> > > A single photon doesn't have a linewidth. Linewidth pertains to the
> > > distribution of energies in an ensemble of photons.
> >
> > Not true. A photon could only have zero line width if it was a
> > sine wave of infinite length. How this effect compares in importance
> > with thermal broadening, for instance, depends on the situation.
>
> You overinterpret my statement. I didn't say that a photon could
> have zero linewidth. I said that linewidth is not an attribute
> of a photon. I have no idea what is meant by a photon of infinite
> length. Coherence length (which is what I guess you mean) is not
> an attribute of a single photon either. It, too, pertains to an
> ensemble of photons.

It seems this all depends, to some extent, on just what one means by the
term 'photon'.  In one case one could (and often does) call a photon an
elementary exitation of the pure noninteracting Maxwell field.  If this
is the case then such things must have (assuming a universe of infinite
extent) an infinite extent in both space and time since they *do* have
precisely defined energy and momentum.  Such things are mathematical
constructs of theory and are not realizable in a laboratory.  OTOH, one
could (and often does) define a photon as being the relatively localized
corpusles of propagating electromagnetic energy that are emitted and
absorbed in various quantum transitions that occur by virtue of the
interaction of the Maxwell field with the quantum dynamical system of
interest.  These latter-type photons *are* things that one observes in
the lab.  These latter-type photons are are of finite extent in space and
time and have a finite width of energy and momentum.  Their width in
these parameters is related to the lifetime of the metastable states that
produced them.  It is certainly possible to consider one of these
latter-type photons as being coherent superposition of many of the
former-type single-photon states.

It should be noted that for a state of exactly 1 (or exactly any other
well-defined integer number) of the latter-type photons this
superposition of the former-type photon states has a completely undefined
phase as a solution of Maxwell's equations, and is completely incoherent
in terms of the phase of its electric and magnetic fields (and
potentials).  OTOH, a state that is characterized by a well-defined
coherent phase for its electic and magnetic fields is very ill-defined
regarding the number of photons (of *either* definitional type) present.
This is a consequence of the fact that the phase of the electromagnetic
field is in a conjugate uncertainty relationship with the total number
of photons present in the state where the phase and the photon number
are subject to a version of the uncertainty principle.  This situation
tends to produce certain complications for the proper description and
understanding of the famous two-slit diffraction experiment for photons
when the intensity is lowered approximately to the point of individual
photons travelling through the apparatus.

David Bowman
David_Bowman@georgetowncollege.edu