Angular and radial density-density correlation function in a (2+1)-dimensional sonic black hole in ultra cold Bose-Einstein condensates and entanglement measure between the Hawking pairs : Inderpreet Kaur and Sankalpa Ghosh*

A quasi two-dimensional sonic black-hole scenario where an ultra cold atomic Bose-Einstein condensate (BEC) flows through an annular ring-shaped supersonic-subsonic interface is considered [1]. We verify the existence of entanglement between the analogue Hawking pairs that emerges from the quantum character of the spontaneous Hawking radiation emitted from such configurations [2].We considered number of quasi-two dimensional cases that include spin-orbit coupled (SOC) BEC [1] as well as quasi two-dimensional BEC without any internal degrees of freedom and compare our results with the typical quasi one-dimensional sonic black hole configurations.We studied in detail the radial and angular density-density correlations in such quasi two diemsnional systems. We also assess the participation of the phonon and the non-phononic part of the collective excitation spectrum [3] in the entanglement measure.

References:

[1] Inderpreet Kaur and Sankalpa Ghosh,  Physical Review A 102, 023314 (2020).

[2] Inderpreet Kaur and Sankalpa Ghosh ( To be submitted).

[3] Inderpreet Kaur and Sankalpa Ghosh: Bogoliubov spectrum and dynamic structure factor in a quasi two-dimensional spin-orbit coupled BEC. ( Submitted, under peer review process).