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


"Timo Nieminen" <timo@xxxxxxxxxxxxxxxxx> wrote in message
news:Pine.LNX.4.50.0506201012460.13251-100000@xxxxxxxxxxxx
On Sun, 19 Jun 2005, Ron Baker, Pluralitas! wrote:

> On Sun, 19 Jun 2005, Ron Baker, Pluralitas! wrote:
>
>> "Timo Nieminen" <timo@xxxxxxxxxxxxxxxxx> wrote:
>> > On Sun, 19 Jun 2005, Ron Baker, Pluralitas! wrote:
>> >>
>> >> 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.
>>
>> Did you read the article?
>> "Under the influence of ordinary laboratory radiation
>> sources, these transitions would exhibit ~10^6-10^7 oscillations
>> during their transition period." They were refering to the transition,
>> not the level lifetime.
>
> Well, they're talking about an atom driven by an external field, not
> spontaneous emission.

Right.

> However, what they call the transition period is the
> time from when the atom (or population of atoms) is known to be in the
> upper state to when the atom (or population) is known to be in the lower
> state, ie 1/2 a Rabi cycle.

Interesting. It seems to me that spontaneous emission could
be somewhat similar. An excited state could be a quasi-stable
state. A thermal 'photon' comes along and bumps the electron
a little off the quasi-stable state onto a figurative energy
slope leading down to the lower state. It (its charge distribution)
is wobbling now so it is radiating, causing to wobble more, etc.

>
> This is the time during which the transition must happen. That the authors
> call it the "transition time" doesn't mean that the actual transition
> takes that long.

Yeah, but golly gee, how can you say that?
It is the very picture of a radiation process happening
over time. It gives an oscillating dipole charge distribution
of the exact frequency coresponding to the difference in the energy
levels. It matches the classical EM
wave generation scenario so well. It matches and it seems
to be natural, using standard QM, and not a force fit.

>
> A little more on this below.
>
> [moved]
>> > 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.
>>
>> So if sometimes it is quick it is always quick?
>
> If sometimes it is quick, it isn't something that *must* take a long time.

OK.

> If it is sometimes quick, it doesn't take a time comparable to the total
> time during which the transition happens.

I don't see the need or reason to differentiate between
the emission and the transition (unless someone insists that
a photon is a point or a billiard ball).

Maybe the transition is quick when the right combination
of thermal photons disturb it strongly, strongly launching
it on the slope toward the lower energy.
Maybe it is slow when a single 'photon' nudges it
onto the slope.

>
> There's an interesting thing in spectral line broadening. Consider
> broadening of a spectral line by electron collision - the atom is sitting
> nicely in one state, and an electron comes close enough to disturb it,
> upsetting the phase-coherence between before and after the collision.
> Basically, this reduces the lifetime of the level, and increases the width
> of the line spectrum. So, giving the atom less time in which to emit or
> absorb a photon increases the line width.

Which I think is quite in line with what I just wrote above.

>
> If we consider photon emission to be instantaneous, then there is no
> mystery - the increased line width results from the reduced time as a
> direct consequence of the Heisenberg uncertainty relation.

(If it is instananeous isn't the line width infinite?)

> If we consider
> the emission of radiation to be purely classical and continuous, there is
> also no mystery, since the Fourier transform of a damped oscillation with
> random collisions randomising the phase gives the same spectrum.

Makes sense.

>
> If instead we consider the photon to be emitted over some finite time, how
> does the collision disturb the process of photon emission? If the
> collision occurs 1/2 way during the "transition time", do you get 1/2 a
> photon?

You get a mixture maybe?

> But the average energy of the photons is still the same; there is
> just more variation in the energy of the detected photons. The rate of
> emission of photons is still pretty much the same.
>
>> But what do you consider a photon to be?
>> Is it a point particle somehow associated with a wave function?
>> How big is a photon?
>
> The safe but unrevealing answer is "the quantum of excitation of EM
> fields".

That works for me.

> It wouldn't be wrong either to call it "the mathematical
> description of exchange of energy, momentum, and angular momentum between
> EM fields and matter".

Sounds accurate if a little 'political', ie carefully covering certain
aspects and avoiding others.

> And one could even say "particle of light", as long
> as it is understood that "particle" means "quantum particle" and not
> "classical particle" - but then one is just repeating the first of these
> statements!

:) Right. And the very mention of 'particle' seems
misleading to me.

> A point particle in that to the best of spatial and
> temporal resolution, if one tries to find the size of a photon by
> detecting it, the size is zero.

Hmm. That doesn't make sense to me. Doesn't a 'photon'
act like a wave in any experiment that would measure
its extent? If that is the case how would it make sense to
say that it has 0 extent?

>
> Some further reading for you:
>
> D. G. C. Jones
> "Teaching modern physics - misconceptions of the photon that can
> damage understanding"
> Physics Education 26, 93-98 (1991)

Hmm. http://www.iop.org/EJ/article/0031-9120/26/2/002/pe910202.pdf
$30

>
> A. Aspect, P. Grangier, and G. Roger
> "Dualité onde-particule pour un photon unique"
> Journal of Optics (Paris) 20(3), 119-129 (1989)

Hmm. My French is a little rusty.

>
> Ole Keller
> "Near-field optics: The nightmare of the photon"
> Journal of Chemical Physics 112(18), 7856-7863 (2000)

....

>
> Ole Keller
> "Space-time description of photon emission from an atom"
> Physical Review A 62, 022111 (2000)
>
> Richard Kidd, James Ardini, and Anatol Anton
> "Evolution of the modern photon"
> American Journal of Physics 57(1), 27-35 (1989)
>
> Michael G. Raymer
> "Observations of the modern photon"
> American Journal of Physics 58(1), 11 (1990)
> (a comment on the previous paper, with further references)
>
> W. E. Lamb, Jr.
> "Anti-photon"
> Applied Physics B - Lasers and Optics 60, 77-84 (1995)
>
> Enjoy!

Hmm. I will save this and search for those articles
as the time becomes favorable.

>
>> >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.
>>
>> Right. Well, not directly.
>> When you say 'localization it time' would you be refering or
>> relating that to the center of the wave function, or the extent
>> of the wave function, or something else?
>
> Knowing something about when the photon is emitted. Eg, if at time A, the
> atomic wavefunction such that the atom must be in the upper state, and at
> time B, such that the atom must be in the lower state, the photon must
> be emitted between times A and B. At the atom, then, the photon
> wavefunction is non-zero only between A and B - the photon is localised
> in time.

Is the transition instantaneous at some time between A and B?
If it is instantaneous then B-A can go to zero and the
line width is infinite, isn't it?

If the line width is finite then the wavefunction must have
temporal extent, right?
It must also travel at c, so it must have longitudinal extent
too, right?
Given those things, if the transition is instantaneous then
that wave function must appear over that spacial extent
instantaneously, right?
And is the spacial and temporal extent over which that wave
function instantaneously appears
determined by B-A, i.e. how quickly we measured the
state of the atom?


--
rb




.

Relevant Pages

  • Re: Will Radio Engineering be QMs worst nightmare?
    ... > absorbtion and emission are instantaneous. ... >> Rotate the laser around the axis of emission. ... Are you still saying that the transition ... The instant that the photon exists. ...
    (sci.physics)
  • Re: "A single atom can undergo only one transition at a time"
    ... just one atom sitting there doing all the spectroscopy. ... absorb many photons over time - after the 1s->2p transition, ... > only "one photon" will be absorbed or emitted. ...
    (sci.chem)
  • Re: Will Radio Engineering be QMs worst nightmare?
    ... >> strongly driven transition (or rather, ... >> occurred or not) to see if an atom was in a particular state. ... >>, the photon is ... It's not at all unusual for a level lifetime ...
    (sci.physics)
  • Re: Will Radio Engineering be QMs worst nightmare?
    ... >>> This article suggests that for stimulated emission they can ... >> The time during which the transition can happen is not necessarily the ... Well, they're talking about an atom driven by an external field, not ... absorb a photon increases the line width. ...
    (sci.physics)
  • Re: Will Radio Engineering be QMs worst nightmare?
    ... Therefore the energy is not a constant of motion during the transition ... >>> If the line width is finite then the wavefunction must have ... we don't see a line width for a single photon. ... > to have no temporal extent? ...
    (sci.physics)