Re: Speed limit at C a misconception?

Skywise schrieb:

> Ok (I think).

In the paper you refer to (doi:10.1063/1.2033147), the authors create a
very narrowband (few MHz) gain or loss for a signal pulse in an optical
fiber by a Brillouin scattering process with a strong counterpropagating
pump wave.

The strongly frequency dependent transmission of the fiber then leads to a
huge dispersion which produces the extraordinary group velocities they
observe. This is nothing new by itself (the effect has been described in
the sixties of the last century or even earlier).

The novelity is that they can produce this strongly frequency dependent
transmission in a standard optical fiber, not using specific transitions
of doped crystals or atomic vapors.

> So how does this work with a single photon?

In principle: Yes.

The process that they use does not conserve the photon number, since either
strong absorption or gain is involved.

Let's first clarify what it means if we talk about a single photon in a
gaussian pulse. Such a state means that we have a coherent superposition
of exactly one photon being in one of many plane wave modes with
wavevector so that the total pulse is gaussian.

That means, that if we analyze such a pulse with a photon counter, there is
a certain small probability to measure the photon very early at the
beginning of the pulse, a much bigger probability to actually find a
photon at the center of the pulse and a small probability to find the
photon at the tail of the gaussian.

So even if we sent this pulse through a vacuum channel to an detector,
there is no violation of causality if we detect the photon at the exit
before the center of the pulse entered.


Lets now assume that such a "gaussian photon" enters their pumped fiber.
Then at the end a smaller (bigger) number of photons also in a gaussian
pulse exits earlier (later) than one would expect with the pump wave
absent.

Note 1) There is not a problem with energy conservation since energy can
exchanged with the pump wave.

Note 2) The wave vector dependent absorption leads to either an attenuation
(amplification) of the head or the tail of the gaussian: the probability
of detecting a photon in the tail is reduced because of attenuation (or
the probability of finding a photon in the tail is enhanced by adding
additional photons to that part of the pulse). This leads to a shift of
the center of the gaussian which means acceleration (slowdown).

So, there is no magic :-)

Best regards,
Jürgen

--
GPG key:
http://pgp.mit.edu:11371/pks/lookup?search=J%FCrgen+Appel&op=get
.

Relevant Pages

  • Re: Speed limit at C a misconception?
    ... very narrowband gain or loss for a signal pulse in an optical fiber by a Brillouin scattering process with a strong counterpropagating pump wave. ... The process that they use does not conserve the photon number, ... wavevector so that the total pulse is gaussian. ... a certain small probability to measure the photon very early at the ...
    (sci.optics)
  • Re: Length definition in SR - can anyone explain
    ... This posting is a question about lengths. ... I'm in an inertial frame. ... The moving observer measures the length of one pulse to be much less ... about the range of speeds my photon emitting device can have and the ...
    (sci.physics.relativity)
  • Re: what really are Gravitons?
    ... does not know the difference between an electro-magnetic pulse ... try not to mix up a photon and a pulse of electromagnetic ... certain is that these quanta can jiggle electrons and that said jiggling ... Cycles for your benefit? ...
    (sci.physics.relativity)
  • Re: The end of Bohrs complementarity principle?
    ... Surely there is no crying need for a particle to ... "Since the photon emission is triggered by the external laser pulse, ... to probe the pulse shape by performing repeated measurements on subsequent ...
    (sci.physics)
  • Re: Length definition in SR - can anyone explain
    ... I'm in an inertial frame. ... The moving observer measures the length of one pulse to be ... about the range of speeds my photon emitting device can have and the ... how a moving frame moving with V relative to a laser source measures ...
    (sci.physics.relativity)