Probing Hawking Temperature Threshold via Quantum Depletion in Bose-Einstein Condensate

Abstract

We investigate the correlation between quantum depletion and Hawking temperature in a ringshaped Bose-Einstein condensate featuring an analog black hole-white hole horizon pair, using the Bogoliubov approach. The presence of horizons is found to enhance the quantum depletion compared to horizon-free configurations, indicating a correlation between depletion and horizon dynamics. Via tuning the Hawking temperature, we observe its effect on the depletion profile. Our results show that depletion increases with Hawking temperature, and beyond a certain threshold, backreaction effects emerge, challenging the validity of the Bogoliubov approximation. We identify a viable parameter regime where the system remains both theoretically controlled and experimentally accessible, offering insight into horizon-induced quantum fluctuations, with implications for future studies of backreaction.

Figures (7)

• Figure 1: Artist's impression of ring BEC featuring acoustic black hole (left) and white hole (right) horizons. The state at $t = 0$ corresponds to an initial configuration with no quantum depletion. As time progresses to $t = t_m$, quantum depletion begins to evolve, eventually reaching a maximal value at $t = t_f$, beyond which the background can no longer be considered a condensate, with the quantum component dominating over the coherent background that characterized the initial state.
• Figure 2: mach number (orange) and g(x) (blue) vs x for n=3. The black line represents $y=1$ and is used for reference. The red dot represents the points on the x-axis where the Mach number crosses one, hence implying the presence of acoustic black hole and white hole horizons.
• Figure 3: Background condensate for $n=2$ (blue) when there are no horizons, and for $n=3$ (Red) when horizons are present.
• Figure 4: Global quantum depletion $(\mathfrak D)$ as a function of time with (red) and without (blue) horizons.
• Figure 5: Evolution of the condensate density at different times for $T_H = 0.027mc_0^2$.