Using nanokelvin quantum thermometry to detect timelike Unruh effect in a Bose-Einstein condensate

TL;DR

This paper proposes a method to detect the timelike Unruh effect using a stationary impurity in a Bose-Einstein condensate, leveraging quantum thermometry and open quantum systems to measure Unruh temperature at nanokelvin scales.

Contribution

It introduces a novel approach to observe the timelike Unruh effect via impurity-based quantum thermometry in BECs, combining quantum estimation and open quantum system theories.

Findings

Timelike Unruh effect can be detected with stationary impurities in BECs.

Quantum thermometry enables nanokelvin temperature measurements.

The method is feasible with current experimental technologies.

Abstract

It is found that the Unruh effect can not only arise out of the entanglement between two sets of modes spanning the left and right Rindler wedges, but also between modes spanning the future and past light cones. Furthermore, an inertial Unruh-DeWitt detector along a spacetime trajectory in one of these cones may exhibit the same thermal response to the vacuum as that of an accelerated detector confined in the Rindler wedge. This feature thus could be an alternative candidate to verify the ``Unruh effect", termed as the timelike Unruh effect correspondingly. In this paper we propose to detect the timelike Unruh effect by using an impurity immersed in a Bose-Einstein condensate (BEC). The impurity acts as the detector which interacts with the density fluctuations in the condensate, working as an effective quantum field. Following the paradigm of the emerging field of quantum thermometry, we combine quantum parameter estimation theory with the theory of open quantum systems to realize a nondemolition Unruh temperature measurement in the nanokelvin (nK) regime. Our results demonstrate that the timelike Unruh effect can be probed using a stationary two-level impurity with time-dependent energy gap immersed in a BEC within current technologies.