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[Phys-L] Re: Nobel: Glauber; Hall, Hänsch



As I understand it, "Glauber" state is the same as "coherent state". It
is the state created by the exponentiation of the creation operator for a
1-particle state.
Regards,
Jack
p.s. I've known Glauber since we both lectured at the Boulder Summer
School in the 60's. I think that his Nobel was too-longed-delayed. He
also invented the idea of "shadowing" in collisions of elementary
particles with nuclei.




On Thu, 6 Oct 2005, John Denker wrote:

Does anybody know of a good tutorial on Glauber states?

I've googled 'till I can't google no more, and haven't found anything very
useful ... just some hand-wavy stuff that pretty much misses the point,
plus some non-tutorial stuff that assumes you already have a strong
background in the area.

It is perfectly possible to get a PhD in physics from a brand-name institution
without ever learning about Glauber states ... which I find rather shocking.

Glauber states are wonderful. They are what allow you to establish the
correspondence limit involving:
-- quantum harmonic oscillator: energy eigenstates, raising and lowering
operators, and
-- classical harmonic oscillator: sinusoidal oscillations.


As a rule, I consider that I don't really understand a system unless I know
how the classical limit emerges from the QM description.

Since harmonic oscillators figure prominently in so much of modern physics
(everything from sound waves to electronics to quantum field theory), we
are playing for pretty high stakes here!

Here's the basic idea: Draw the phase space of the harmonic oscillator,
with axes x and p. The QM ground state is, roughly speaking, a little blob
of size sqrt(hbar) that sits at the origin. It is the simplest Glauber state.
A general Glauber state is congruent to the ground state, displaced some
distance from the origin, and orbiting the origin at angular frequency
omega. A system initially in a Glauber state will remain in a Glauber
state forever.

Since the Glauber state is congruent to the ground state, it is classified
as a _minimum uncertainty_ state.

The classical limit is obtained when the amplitude of the Glauber state
(i.e. its distance from the origin) is huge compared to its diameter
(i.e. sqrt(hbar)). For instance, the classical 115V sine wave that the
power company sells you can be described in these terms.

If you want to see the math, you can refer to
http://manitoba.ks.uiuc.edu/Services/Class/PHYS480/qm_PDF/chp4.pdf
section 4.7 ("quasi-classical states...")

=====


Also note that Glauber states are the starting point for any discussion
of _squeezed states_, which are even more wonderful.

For instance, in QM class measurement is described in terms of eigenvalues
and idempotent operators ... but when I go into the lab to make a measurement,
I typically use a voltmeter. What is the connection here? What does a
voltage eigenstate look like?

Answer: Voltage eigenstates don't strictly exist, except in the classical
limit. The best approximation thereto is a squeezed state.

I get _zero_ hits from
http://www.google.com/search?q=voltage-eigenstate
which is pretty sad. It means people have not been doing a very good job of
connecting fundamental physics to the real world.

There are some offline reference that address this, e.g.
http://prola.aps.org/abstract/PRA/v29/i3/p1419_1


--
"Trust me. I have a lot of experience at this."
General Custer's unremembered message to his men,
just before leading them into the Little Big Horn Valley