Marcos Gil de Oliveira

The authors calculate correlations between Hawking radiation, its partner wave inside the horizon, and greybody factors near an acoustic horizon in a driven-dissipative fluid of light. Resolving the correlations in the frequency domain allows one to weigh the contributions of each pair to the total output quantum state

We investigate theoretically and experimentally the optical second harmonic generation (SHG) with a twisted Gaussian Schell model (TGSM) beam as the fundamental field. We use Type-II phase matching and analyze the cross spectral density (CSD) of the SHG output beam when the input fundamental is prepared with a TGSM structure. We analyze two synthetization methods for preparing the TGSM fundamental beam and we find that for one method the SHG is also a TGSM beam. For the other method, we find that the SHG is not a TGSM beam and presents an anomalous CSD possessing a dip instead of a peak in the transverse spatial structure. Moreover, we show that the dip depth is directly related to the twisted phase parameter, being absent for a non twisted GSM beam. Our results show that the SHG from a fundamental TGSM beam can result in a doubled frequency TGSM or in a non-TGSM beam depending on the synthetization method.

The Weyl-Wigner representation of quantum mechanics allows one to map the density operator in a function in phase space - the Wigner function - which acts like a probability distribution. In the context of statistical mechanics, this mapping makes the transition from the classical to the quantum regimes very clear, because the thermal Wigner function tends to the Boltzmann distribution in the high temperature limit. We approximate this quantum phase space representation of the canonical density operator for general temperatures in terms of classical trajectories, which are obtained through a Wick rotation of the semiclassical approximation for the Weyl propagator. A numerical scheme which allows us to apply the approximation for a broad class of systems is also developed. The approximation is assessed by testing it against systems with one and two degrees of freedom, which shows that, for a considerable range of parameters, the thermodynamic averages are well reproduced.