Lamb shift for the detection of the Unruh effect

The Unruh effect states that a uniformly accelerated observer perceives the inertial vacuum as a thermal state at a temperature proportional to the observer's acceleration. At the accelerations achievable in laboratory settings, the thermal signature in the atom’s response is so feeble that the Unruh effect has eluded experimental detection till now. Numerous physical observables, including atomic transition rates, particle decay rates, and geometric phase, have been studied under varied settings as possible candidates for capturing a measurable and unambiguous signature of the Unruh effect.



Here, we propose the Lamb shift in a uniformly accelerated atom, coupled to a quantum scalar field inside a long cylindrical cavity, to detect the Unruh effect. The Lamb shift, one of the most precisely measured observables in quantum electrodynamics, is a tiny shift in the energy levels of an atom arising from the atomic electron’s coupling to the field vacuum fluctuations. The field vacuum fluctuations are perceived differently by a noninertial atom than by an inertial atom, leading to a distinct noninertial contribution to the Lamb shift.



For an observable energy shift in a uniformly accelerated atom in free space, an acceleration of the order of 10²⁰ m/s² is required. We show that the noninertial contribution to the energy shift can be isolated and enhanced relative to the inertial contribution by suitably modifying the density of field modes, for example by employing an electromagnetic cavity. Specifically, a purely noninertial energy shift, orders of magnitude larger than the inertial energy shift, can be obtained at small, experimentally achievable accelerations. We argue that the Lamb shift is a promising observable for the detection of the Unruh effect with current technology.