Violation of the Cauchy-Schwarz inequality in the macroscopic regime. A. M. Marino, V. Boyer and P. D. Lett in Phys. Rev. Lett. 100:233601 (2008). What the paper says!?
This paper reports violation of CSI through the intensity correlations of intensity-difference squeezed beams produced by four-wave mixing. This is for bright-modes so in the macroscopic regimes (not the photon counting regime), that are displaced from the $S_{ab}$ squeezing operators applied to a coherent state (for the probe) and vacuum (for the conjugate).
They are making the daring implication of being the first to check cleanly violation of non-classical correlations in a macroscopic system:
to date, most of these experiments have been carried out in the regime in which particles are detected one at a time. It is thus interesting to study whether or not the quantum signature given by these tests is still present in the limit in which the system becomes macroscopic.
The most others are their Refs. [10-11] (see also [6-9] for, apparently, theory)
They claim 8-standard deviation but the effect looks quite weak (only one point, furthermore) and after treatment, see their Fig. 2.
While this is not directly related to our violation in space, this makes interesting points for other aspects, in particular the effect of squeezed+coherent state admixtures
The bright correlated beams that are obtained from the seeded 4WM process consist of a large coherent part plus quantum-correlated fluctuations.
—for which the paper by Carmichael et al.[1] seems particularly relevant—as well as frequency filtering, see their Fig. 4. We are in fact citing them with Sánchez Muñoz et al.[2] but for violation of CSI, not for anything frequency related. The good reference for that is Li et al.[3].
Regarding bright beams, the CSI in this case becomes: $$\epsilon_{ab}\le\frac{\epsilon_{aa}+\epsilon_{bb}}{2}\,,$$ where $g^{(2)}_{ij}\equiv 1+\epsilon_{ij}$ separates the coherent from fluctuation parts, as we do with Zubizarreta Casalengua et al.[4]. This is proved here.
They make this very interesting comment, but leave it hanging there (so I'd need to check Ref. [2]):
In addition, the CSI has some interesting implications about the nature of the field, which can be obtained from its relation to the quasiprobability functions, as described in Ref. [2].
- ↑ Giant violations of classical inequalities through conditional homodyne detection of the quadrature amplitudes of light. H. J. Carmichael, H. M. Castro-Beltran, G. T. Foster and L. A. Orozco in Phys. Rev. Lett. 85:1855 (2000).
- ↑ Violation of classical inequalities by photon frequency filtering. C. Sánchez Muñoz, E. del Valle, C. Tejedor and F.P. Laussy in Phys. Rev. A 90:052111 (2014).
- ↑ Violation of a classical Cauchy-Schwarz inequality in photon noise spectra. Y.-Q. Li, P. J. Edwards, X. Huang and Y. Wang in J. Opt. B: Quantum Semiclass. Opt. 2:292 (2000).
- ↑ Two photons everywhere. E. Zubizarreta Casalengua, F. P. Laussy and E. del Valle in Phil. Trans. R. Soc. A 382:20230315 (2024).