(2+1)$-dimensional sonic black hole from spin-orbit coupled Bose-Einstein condensate and its analogue Hawking radiation

TL;DR

This paper explores a 2+1 dimensional sonic black hole in a spin-orbit coupled Bose-Einstein condensate, analyzing its formation, properties, and analogue Hawking radiation through numerical simulations and correlation measurements.

Contribution

It introduces a novel 2+1D sonic black hole model in spin-orbit coupled BECs and studies its dynamic formation and Hawking radiation characteristics.

Findings

Sonic black hole forms in an annular region with inner and outer horizons.

Density modulations amplify due to horizon formation.

Hawking radiation exhibits thermal properties in the system.

Abstract

We study the properties of a $2+1$ dimensional Sonic black hole (SBH) that can be realised, in a quasi-two-dimensional two-component spin-orbit coupled Bose-Einstein condensate (BEC). The corresponding equation for phase fluctuations in the total density mode that describes phonon field in the hydrodynamic approximation is described by a scalar field equation in $2+1$ dimension whose space-time metric is significantly different from that of the SBH realised from a single component BEC that was studied experimentally, and, theoretically meticulously in literature. Given the breakdown of the irrotationality constraint of the velocity field in such spin-orbit coupled BEC, we study in detail how the time evolution of such condensate impacts the various properties of the resulting SBH. By time evolving the condensate in a suitably created laser-induced potential, we show that such a sonic black hole is formed, in an annular region bounded by inner and outer event horizon as well as elliptical ergo-surfaces. We observe amplifying density modulation due to the formation of such sonic horizons and show how they change the nature of analogue Hawking radiation emitted from such sonic black hole by evaluating the density-density correlation at different times, using the truncated Wigner approximation (TWA) for different values of spin-orbit coupling parameters. We finally investigate the thermal nature of such analogue Hawking radiation.