Thursday, June 07, 2012

Light Shows Non-Classical Properties, But I Don't Get It

OK, this is where you can help me understand this paper in the context of the press report.

This is the paper:

E. Kot et al., "Breakdown of the Classical Description of a Local System", Phys. Rev. Lett., v.08, p.233601 (2012).

Abstract: We provide a straightforward demonstration of a fundamental difference between classical and quantum mechanics for a single local system: namely, the absence of a joint probability distribution of the position x and momentum p. Elaborating on a recently reported criterion by Bednorz and Belzig [ Phys. Rev. A 83 052113 (2011)] we derive a simple criterion that must be fulfilled for any joint probability distribution in classical physics. We demonstrate the violation of this criterion using the homodyne measurement of a single photon state, thus proving a straightforward signature of the breakdown of a classical description of the underlying state. Most importantly, the criterion used does not rely on quantum mechanics and can thus be used to demonstrate nonclassicality of systems not immediately apparent to exhibit quantum behavior. The criterion is directly applicable to any system described by the continuous canonical variables x and p, such as a mechanical or an electrical oscillator and a collective spin of a large ensemble.

From a quick reading of the paper, they are trying to show this:

Classically, the phase space distribution Wðxi; piÞ is the joint probability of finding the system in an infinitesimal area around x = x_i, p = p_i, and hence it obeys all the requirements of a probability distribution including being a non-negative function. As mentioned, in the case of a quantum phase space formulation, introduced by Wigner [9], the Heisenberg uncertainty renders this definition meaningless, as a joint probability distribution for x and p does not exist. The phase space distribution is only defined through the single coordinate (marginal) distributions, projected from the distribution function [10] and this relaxation of constraints allows for negative values of the function in areas smaller than hbar. This negativity is not directly observable due to the vacuum fluctuations preventing simultaneous measurement of x and p. However, one can still infer the phase space distribution from measurements of only a single observable at a time and detect such negativities, thereby illuminating the failure of classical theory.
I think they showed this in Fig. 2.

Fine. However, here's the press release of this work. The lead author was interviewed, and said this:

Based on a series of experiments in the quantum optics laboratories, they examined the state of light. In classical physics, light possesses both an electric and a magnetic field.

“What our study demonstrated was that light can have both an electric and a magnetic field, but not at the same time. We thus provide a simple proof that an experiment breaks the classical principles. That is to say, we showed light possesses quantum properties, and we can expand this to other systems as well” says Eran Kot.
Electric and magnetic field? Not at the same time? What did I miss? The press release doesn't seem to have any resemblance (at least in terms of the experiment and what is being measured) with the actual paper. Can someone clarify this for me?



Peter said...

From page 3, "The equivalence
between a single mode electromagnetic field and a harmonic oscillator allows us to describe the EM field by a phase space of a single degree of freedom." The electric field is generally taken to be the canonical momentum for the gauge-dependent electromagnetic potential, but one can also work with the nontrivial commutation relations of the observable fields, E and B. Use of a single mode, both in frequency and polarization, keeps things relatively simple, in the usual quantum optics fashion.

How does that seem?

ZapperZ said...

I suppose that is the possible connection. I need to digest this a bit more.


Boaz said...

I didn't read the paper yet, but I've been trying to understand the use of Wigner functions in describing x-rays in synchrotron radiation facilities. I asked this question on Stack Exchange. Maybe the answers will be useful to you also. (I think Peter gave one of them!)

Boaz said...

Here's a recent paper on this for synchrotron radiation:
However, its not dealing with single photon states...
so I'd have to say I'm also still a little confused.