Gibbons-Hawking Effect in the Sonic de Sitter Space-Time of an Expanding Bose-Einstein-Condensed Gas

We propose an experimental scheme to observe the Gibbons-Hawking effect in the acoustic analog of a $(1+1)$-dimensional de Sitter universe, produced in an expanding, cigar-shaped Bose-Einstein condensate. It is shown that a two-level system created at the center of the trap, an atomic quantum dot interacting with phonons, observes a thermal Bose distribution at the de Sitter temperature.

Figure 1

Expansion of a cigar-shaped Bose-Einstein condensate. The stationary horizon surfaces are located at $\pm z_{\mathrm{H}}$, respectively. The thick dark lines represent lasers creating an optical potential well in the center.

Figure 2

Level scheme of the atomic quantum dot, which is embedded in the superfluid cigar, and created by an optical well for atoms of a hyperfine species different from that of the condensate. Double occupation of the dot is prevented by a collisional blockade mechanism.