Re: Will Radio Engineering be QM's worst nightmare?

On Sun, 19 Jun 2005, Ron Baker, Pluralitas! wrote:

> "Timo Nieminen" <uqtniemi@xxxxxxxxxxxxxxxxx> wrote:
> > On Sat, 18 Jun 2005, Ron Baker, Pluralitas! wrote:
> >
> >> "Timo Nieminen" <uqtniemi@xxxxxxxxxxxxxxxxx> wrote:
> >>>
> >>> I don't know of any RF tests of this, but detection statistics of low
> >>> photon-number sources supports this routinely. Measurement of the
> >>> suddenness of radiation of photons by atoms is less every-day, but to
> >>> the
> >>> best of time-resolution, radiation is instant.
> >>
> >> Can you cite a reference on that?
> >
> > I can assume you mean the latter part? No specific references at hand; I
> > haven't seriously read up on that since 1988. State-of-the art back used a
> > strongly driven transition (or rather, whether a strong transition
> > occurred or not) to see if an atom was in a particular state. Then you
> > check out a weak transition from the upper state to a third state. There
> > might be much better stuff done in the 15+ years since. My point was
> > simply that, compared to the level lifetime of an atomic energy state
> > (which is what determines the length of the wavetrain), the photon is
> > emitted in a very short time.
> >
> > If you're interested in the old papers, "quantum jump" might be a good
> > keyword.
>
> The papers cited below imply that the transition is far
> from instantaneous.
>
> This article suggests that for stimulated emission they can
> be on the order of 10^6 wavelengths in length.
> http://jchemed.chem.wisc.edu/JCEWWW/Articles/DynaPub/DynaPub.html#ref16

The time during which the transition can happen is not necessarily the
time taken by the transition. It's not at all unusual for a level lifetime
to be about 10^6 optical periods long. My point was that experiments that
were intended to see whether or not the transition is fast compared to
lifetime or not observed that it was. A quick googling finds:

http://www.iop.org/EJ/article/0305-4470/30/9/006/ja30009l6.html

which looks like it cites the original mid-80s experiments.

> This article on spontaneous emission relates it to line width
> That translates to an order of thousands of wavelengths.
> http://www.optics.rochester.edu/~stroud/cqi/rochester/URsub1.pdf#search='quantum%20emission%20photon%20wave%20function%20transition%20emission'

Localisation of a photon does not tell you the size of a photon, or
localisation in time does not tell you the time taken by the transition
that produces the photon. Line width does tell you about localisation in
time, so it's important to the topic of that paper. I don't see where the
paper addresses the point of how rapid the transition is when it occurs.

I often see a classical derivation of natural line width that assumes that
the atom is a classical damped oscillator, emitting an exponentially
decaying wave. The Fourier transform of that waveform, with suitable
approximations, yields the Lorentzian natural line profile. A simple
semi-classical approach, assuming a two-level atom initially in the upper
state, with a certain lifetime, gives, without approximation, the same
lineshape. Basically, the probability of occupancy of the upper state
decays exponentially, and the Fourier transform of this gives the
distribution of photon energies about the transition energy. The
difference between the two pictures is that in the first, the radiation is
a continuous process, and in the 2nd, it is an instantaneous process. In
the 2nd, if a measurement made to see what state the atom is in is made at
a time much less than the lifetime, there is a small but finite
probability of finding the atom in the lower state. If the atom is found
to be in the lower state, then there must have been emission of a photon,
even in that small time.

--
Timo Nieminen - Home page: http://www.physics.uq.edu.au/people/nieminen/
Shrine to Spirits: http://www.users.bigpond.com/timo_nieminen/spirits.html
.

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