### Violating classical inequalities

There can be much confusion in contemporary scientific discussions about the distinction between quantum and classical effects. It can be surprising to realize how many supposed “quantum” effects are in fact adequately described by classical models based on coupled oscillators and classical fields, for example.

Fortunately there are measurable quantities which are bounded by mathematical inequalities for any possible model based on classical variables. A famous example are the Bell inequalities. More generally, the two-time second-order correlation function of a classical field is bounded by Cauchy-Schwartz inequalities. Violating one of these inequalities in a measurement is a direct evidence of non-classical physics.

In our group, we want to measure second-order correlation functions of the photons scattered by Raman-active phonons in order to show the non-classical nature of the vibrational modes. Moreover, using a pump-probe scheme, we will be able to follow the quantum dynamics in real time and to measure the decoherence of specific phonon quantum states. The figure below is a simulation of the expected results of such a measurement, using a methodology developped in a recent paper.