Sonic Hawking Radiation from a blackhole laser

Abstract

The quantum thermal radiation from a black hole (BH) known as “Hawking Radiation” or “Black Hole Evaporation” results from studying quantum fields in the curved space-time of the horizon of a BH. Experimentally, the radiation is difficult if not impossible to be detected from a real black hole with a mass much higher than that of our sun, since the Radiation temperature is substantially below that of microwave background radiation. However, in 1981 Unruh showed an analogy between the propagation of sound waves in any convergent fluid flow and that of the quantum field in a gravitational field. He showed that if the background fluid is accelerated to higher than the speed of sound then it can develop a horizon (point of no return) for the sound waves. This is the so-called the sonic BH. This horizon will emit thermal radiation in terms of sound wave quanta (phonons) in an analogy to the thermal radiation of black holes (Analogue Hawking Radiation) (AHR). Bose-Einstein Condensates (BECs) can be used as a background fluid developing a sonic horizon for the phonon modes propagating through its background due to the very low temperature of the BEC. Recently in 2014, Steinhauer has reported the observation of self-Amplifying Hawking radiation from the realization of an accelerated BEC. The experiment reported an exponentially growing signal of modes trapped between a BH and white hole (WH) horizon, where the white hole is the point where sound cannot enter. Experimental signatures of AHR are a growing oscillating perturbation of the condensate mean density and a characteristic pattern in density-density correlation functions. However, the former mentioned oscillations may result from the dynamical instabilities of the classical mean field density. In this work, we were able to reproduce the experimental results of density modulations in the mean field, and thus without AHR, using only the mean field Gross-Pitaevskii equation (GPE) for the BEC. Furthermore, we include the quantum fluctuation to study the density-density correlation function that is in qualitative agreement with the experiment using the truncated Wigner approximation (TWA). Finally, we then calculate the One Body Density Matrix (OBDM) to distinguish condensed from non-condensed atoms using the Penrose Onsager criterion. We are able to contribute to a discussion in the literature regarding the quantum field or mean field origin of the mean density oscillations in the experiment.