Methods for Detecting Acceleration Radiation in a Bose-Einstein Condensate

We propose and study methods for detecting Unruh-like acceleration radiation effects in a Bose-Einstein condensate in a ($1+1$)-dimensional setup. The Bogoliubov vacuum of a Bose-Einstein condensate is used to simulate a scalar field theory, and accelerated atom dots or optical lattices serve as detectors of phonon radiation due to acceleration effects. In particular, we study the dispersive effects of the Bogoliubov spectrum on the ideal case of exact thermalization. Our results suggest that acceleration radiation effects can be observed using currently accessible experimental methods.

Figure 1

Thermalization of an oscillator as a function of the smearing time $\gamma$. The field is modeled by 20 modes, $a=2$, ${\omega }_d=1$, and the coupling is ${\Omega }_a=1/50$. The green squares are numerical results described in the text, and the solid blue line is derived by integration of the transition amplitudes $A_{\pm }(\omega )$. The inset shows the thermalization curve for $\gamma =17$, where the red (medium gray) line shows the theoretical limiting temperature. The blue (light gray) and green (dark gray) graphs shows the cooling and the heating curves. The results are in units of ${\omega }_d$. The thermal nature of the result is checked by calculating the trace norm distance between the final density matrix and the closet thermal state.

Figure 2

The final temperature using the full Bogoliubov theory, as a function of the interaction time $t_0$ (with $\gamma =0$). The ratio of the energy gap and the cutoff energy was taken as $1:500$; hence deviations due to the effective energy gap are expected for $\omega \ge 120{\omega }_d$. This corresponds to acceleration times $t_0\approx 1/a\log 120\approx 2.4$. Indeed, the theoretically predicted temperature, $T\approx 0.67$, is obtained in this simulation for $t<t_0$.