Detecting the Circular Unruh Effect via Multi-Level Atoms

We propose a novel scheme for detecting the circular Unruh effect, which appears when the center of mass of an atom confined in a cylindrical cavity follows a planar circular trajectory and interacts with the electromagnetic vacuum field via magnetic dipole couplings. Naturally, the circular Unruh effect depends strongly on the ratio of the angular velocity α of the rotating atom and the transition frequency ω of its two relevant internal states. In order to find measurable excitation rates induced by the non-inertial motion of the atom, one has to maximize the ratio α/ω. To date, research has primarily considered either scalar fields [1] or electric dipole interactions [2]. However, typical magnetic dipole transition frequencies are in the GHz range, which is much lower than the THz-range frequencies characteristic of electric dipole transitions, leading to a more favorable α/ω ratio for magnetic dipole transitions. Due to technical limitations on the experimentally achievable angular velocity α of the atom, the main contribution to the circular Unruh effect comes from the low-frequency atomic transitions.

As is well known, the excitation rate induced by the (circular) Unruh effect has to exceed the spontaneous emission rate. While this requirement is generally possible [1] for angular velocities (much) larger than the transition frequencies, i.e., α»ω, in realistic experimental setups, however, the exact opposite of this condition is given [3], even when considering two internal states separated by hyperfine splitting. To overcome this limitation, we propose a new measurement scheme that takes advantage of the atom's internal multi-level structure to suppress the spontaneous emission rate, without relying on the condition α»ω.

[1] Hong-Tao Zheng, Xiang-Fa Zhou, Guang-Can Guo, and Zheng-Wei Zhou. Enhancing analog Unruh effect via superradiance in a cylindrical cavity. Phys. Rev. Res. 7:013027, Jan 2025.

[2] Yuebing Zhou, Jiawei Hu, and Hongwei Yu. Significant circular Unruh effect at small acceleration. Phys. Rev. D 111:L041702, Feb 2025.

[3] X. Fan, T. G. Myers, B. A. D. Sukra, and G. Gabrielse. Measurement of the electron magnetic moment. Phys. Rev. Lett. 130:071801, Feb 2023.