Zehua Tian

The Unruh effect predicts that an accelerated observer perceives the Minkowski vacuum as a thermal bath, but its direct observation requires extreme accelerations beyond current experimental reach. Foundational theory [Olson & Ralph, Phys. Rev. Lett. 106, 110404 (2011)] shows that an equivalent thermal response, known as the timelike Unruh effect, can occur for detectors following specific timelike trajectories without acceleration, enabling laboratory tests with stationary yet time-dependent detectors. Here, we report a proof-of-principle demonstration of the timelike Unruh effect in a quantum system of trapped ion, where a two-level spin serves as the detector and is temporally coupled to the ambient field encoded in the ion's vibrational motion. Specifically, we study both excitation and emission dynamics of the detector moving along a spacetime trajectory in the future/past light cone, and demonstrate the thermal response of the detector to the Minkowski vacuum that resembles the Unruh effect. This work establishes a controllable tabletop platform for exploring relativistic quantum physics under accessible laboratory conditions.

The Unruh effect predicts an astonishing phenomenon that an accelerated detector would detect counts despite being in a quantum field vacuum in the rest frame. Since the required detector acceleration for its direct observation is prohibitively large, recent analog studies on quantum simulation platforms help to reveal various properties of the Unruh effect and explore the not-yet-understood physics of quantum gravity. To further reveal the quantum aspect of the Unruh effect, analogous experimental exploration of the correlation between the detector and the field, and the consequences for coherent quantum trajectories of the detector without classical counterparts, are essential steps but are currently missing. Here, we utilize a laser-controlled trapped ion to experimentally simulate an oscillating detector coupled with a cavity field. We observe joint excitation of both the detector and the field in the detector's frame, coincide with the coordinated dynamics predicted by the Unruh effect. Particularly, we simulate the detector moving in single and superposed quantum trajectories, where the latter case shows coherent interference of excitation. Our demonstration reveals properties of quantum coherent superposition of accelerating trajectories associated with quantum gravity theories that have no classical counterparts, and may offer a new avenue to investigate phenomena in quantum field theory and quantum gravity. We also show how a generalization of the method and results in this work may be beneficial for direct observation of the Unruh effect.

A general bound on the Lyapunov exponent of a quantum system is given by $λ_L\leq2π\,T/\hbar$, where $T$ is the system temperature, as established by Maldacena, Shenker, and Stanford (MSS). This upper bound is saturated when the system under consideration is the exact holographic dual of a black hole. It has also been shown that an inverted harmonic oscillator (IHO) may exhibit the behavior of thermal energy emission, in close analogy to the Hawking radiation emitted by black holes. We demonstrate that the Lyapunov exponent of the IHO indeed saturates the MSS bound, with an effective temperature equal to the analogue black hole radiation temperature, and propose using a trapped ion as a physical implementation of the IHO. We derive the corresponding out-of-time-ordered correlation function (OTOC) diagnosing quantum chaos, and theoretically show, for an experimentally realizable setup, that the effective temperature of the trapped-ion-IHO matches the upper MSS bound for the speed of scrambling.