Continuing from last week, for Thursday 29 November 2018 we will discuss:

- Inderpreet Kaur and Sankalpa Ghosh: Rotating sonic black hole from Spin-orbit coupled Bose-Einstein condensate

We show that a sonic analogue of rotating BTZ type of black hole can be realised in a quasi-two-dimensional spin-orbit coupled BEC without any external rotation. The corresponding equation for phase fluctuations in total density mode that describes phonon field in hydrodynamic approximation, is described by a scalar field equation in 2+1 dimension whose space-time metric can be identified with the space-time metric of rotating black hole of BTZ type. By time evolving the condensate in a suitably created laser induced potential, we show that the the moving condensate forms such rotating black hole in an annular region bounded by inner and outer event horizon as well as elliptical ergo surfaces. We discuss the self amplifying density modulations as well as the distribution of supersonic and subsonic zones in such rotating black hole that strongly depends on the spin-orbit coupled anisotropy that can be tested in experiments. We also calculate the density-density correlation in such analogue rotating black hole and the distribution of the analogue Hawking temperature on the event horizon.

Related to last week’s discussion is the following paper where they discuss some of the subtitles of measuring entanglement in the photons emitted by the dumb hole:

- Scott Robertson, Florent Michel, and Renaud Parentani: Assessing degrees of entanglement of phonon states in atomic Bose gases through the measurement of commuting observables [Phys. Rev. D 96, 045012, (2017)].

We show that measuring commuting observables can be sufficient to assess that a bipartite state is entangled according to either nonseparability or the stronger criterion of “steerability.” Indeed, the measurement of a single observable might reveal the strength of the interferences between the two subsystems, as if an interferometer were used. For definiteness, we focus on the two-point correlation function of density fluctuations obtained by in situ measurements in homogeneous one-dimensional cold atomic Bose gases. We then compare this situation to that found in transonic stationary flows mimicking a black hole geometry where correlated phonon pairs are emitted on either side of the sonic horizon by the analogue Hawking effect. We briefly apply our considerations to two recent experiments.