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Re: Is photon a wave packet ?



Hi,
I am not sure why you believe that a single
photon must be monochromatic. It is true that the
often formalism deals with it that way. If there
is just a single frequency associated with a
photon, how long must it be? From the Fourier
analysis I think you get infinite. If there is no
uncertainty in the energy, what is the uncertainty
in when the photon was somewhere. Again infinite.
( These two questions are related.)

One can experimentally measure the length of a
single photon. Use an interferometer, such as a
Michelson, and a light source that emits a single
transition (use filters or gratings as needed),
and that emits at a single photon rate. The
interference pattern falls apart if the difference
of the two optical paths lengths exceeds the
length of a photon because it can no longer
interfere with itself. Thus photons have a finite
length and the photons are not truly
monochromatic.

We, physicists, almost always work in systems of
energy eigenstates, but it is not required. A
single isolated, at rest, atom emits a photon with
a energy spread associated with the natural line
width of the transition. This is related to the
lifetime of the excited state. There is an
uncertainty in the energy of the photon until an
energy measurement is made.

Thanks
Roger Haar

***********************************************
Qiang Lu wrote:

Hello friends,

I have two questions.
One, if a single photon has the property of wave?
The single photon means an excited atom emits a single photon.
Two, if a single photon is a wave packet? i.e. if a single photon has
a width of frequency, but not monochromatic?
In quantum field theory

2
/ _
| \
A_{\mu}(x)= | d^3 k / (a_{k,i} A_{\mu}(k,i;x) + a*_{k,i} A*_{\mu}(k,i;x)
| -
/ i=1

Here creation operator a_{k,i} creats an single photon with
polarization i and frequency k. Thus for a single photon, it must be
absolutely monochromatic. While for wave packet, it is a fourier
expansion of variable frequency, may be k+-dk. For a wave packet the
frequency has a width dk, but not a define and single freqency.
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k-dk k k+dk
From this point of wiew, one may say that a single photon is not a
packet. That is why I asked if a single photon is a wave packet?

--
Best regards,
Qiang