Quantum Simulation of the Unruh Temperature via the Thermal Properties of Virtually Evolving Bose-Einstein Condensates

This paper presents a novel theoretical model motivate a new experimental scheme to simulate the Unruh temperature by relating it to the critical temperature of multiple Bose-Einstein thermal baths. These thermal baths are conceptualized as snapshots of a Bose-Firework originating from an evolving driven Bose-Einstein condensate (BEC). The critical temperature of each snapshot is determined from the heat capacity, which is numerically estimated by calculating the partition function derived from the system's Hamiltonian. By analyzing the relationship between the average number of the phononic excitations at the critical temperature, acceleration, and the critical temperature itself, our model demonstrates a significant agreement with the Unruh temperature formula, thereby validating our hypothesis. This theoretical approach offers a cost-effective alternative experimental setup compared to other resources-intensive experimental simulations. Furthermore, it provides a unique perspective on quantum simulation by utilizing the critical phenomena of condensed matter systems to probe fundamental quantum relativistic effects.