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Physical Review A

Quantum simulation of the Unruh effect with a Rydberg-dressed Bose-Einstein condensate

Tianze Sheng, Jun Qian, Xiaolin Li, Yueping Niu, Shangqing Gong

Published Jan 4, 2021• 10 citations
Publisher

Abstract

We propose a scheme for investigating the Unruh effect, i.e., the thermal radiation observed by uniformly accelerating observers or detectors, with ultracold atoms coupled by an off-resonant laser. We find that periodic modulation of the Rydberg-dressing interaction between atoms plays a significant role in the manipulation of a thermal bath in a uniformly accelerating reference frame. Our calculations show that the resulting Unruh temperature strongly depends on the driving frequency of the modulated Rydberg-dressing potential and the soft-core nature of the dressing interaction, i.e., the soft-core radius and height. These results reveal the potential applications of ultracold atoms with controllable long-range interaction in a wide variety of analog gravity phenomena.

DOI
10.1103/physreva.103.013301

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We propose a scheme for investigating the Unruh effect, i.e., the thermal radiation observed by uniformly accelerating observers or detectors, with ultracold atoms coupled by an off-resonant laser. We find that periodic modulation of the Rydberg-dressing interaction between atoms plays a significant role in the manipulation of a thermal bath in a uniformly accelerating reference frame. Our calculations show that the resulting Unruh temperature strongly depends on the driving frequency of the modulated Rydberg-dressing potential and the soft-core nature of the dressing interaction, i.e., the soft-core radius and height. These results reveal the potential applications of ultracold atoms with controllable long-range interaction in a wide variety of analog gravity phenomena.
We study the dynamics of an atomic Bose-Einstein condensate in an optical lattice in which the electronic ground state of each atom is weakly coupled to a highly excited Rydberg state by a far off-resonant laser. This dressing induces a switchable effective soft-core interaction between ground-state atoms which, in the lattice, gives rise to on-site as well as long-range interaction terms. Upon switching on the dressing laser the coherence properties of the atomic superfluid undergo a nontrivial collapse and revival dynamics which can be observed in the interference pattern that is created after a release of the atoms from the optical lattice. This interference signal strongly depends on the strength and the duration of the dressing laser pulse and can be used to probe and characterize the effective interaction between Rydberg-dressed atoms.
Abstract 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 in quantum simulation platforms help in revealing various properties of the Unruh effect and thus to 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 with respect to the detector and the field, and the consequences for coherent quantum trajectories of the detector that without classical counterparts, are essential steps but 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, matching 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.
The Unruh effect predicts a thermal response for an accelerated detector moving through the vacuum. Here we propose an interferometric scheme to observe an analogue of the circular Unruh effect using a localized laser coupled to a Bose-Einstein condensate (BEC). Quantum fluctuations in the condensate are governed by an effective relativistic field theory, and as demonstrated, the coupled laser field acts as an effective Unruh-DeWitt detector thereof. The effective speed of light is lowered by 12 orders of magnitude to the sound velocity in the BEC. For detectors traveling close to the sound speed, observation of the Unruh effect in the analogue system becomes experimentally feasible.
The Unruh effect is a quantum relativistic effect where the accelerated observer perceives the vacuum as a thermal state. Here we propose the experimental realization of the Unruh effect for interacting ultracold fermions in optical lattices by a sudden quench resulting in vacuum acceleration with varying interactions strengths in the real temperature background. We observe the inversion of statistics for the low lying excitations in the Wightman function as a result of competition between the spacetime and BCS Bogoliubov transformations. This paper opens up new perspectives for simulators of quantum gravity.
The Unruh effect states an accelerated particle detector registers a thermal response when moving through the Minkowski vacuum, and its thermal feature is believed to be inseparable from Lorentz symmetry: Without the latter, the former disappears. Here we propose to observe the analog circular Unruh effect using an impurity atom in a quasi-two-dimensional Bose-Einstein condensate (BEC) with dominant dipole-dipole interactions between atoms or molecules in the ultracold gas. Quantum fluctuations in the condensate possess a Bogoliubov spectrum ${\ensuremath{\omega}}_{\mathbf{k}}={c}_{0}|\mathbf{k}|f(\ensuremath{\hbar}{c}_{0}|\mathbf{k}|/{M}_{*})$, working as an analog Lorentz-violating quantum field with the Lorentz-breaking scale M∗{M}_{*}M∗​, and the impurity acts as an effective Unruh-DeWitt detector thereof. When the detector travels close to the sound speed, observation of the Unruh effect in our quantum fluid platform becomes experimentally feasible. In particular, the deviation of the Bogoliubov spectrum from the Lorentz-invariant case is highly engineerable through the relative strength of the dipolar and contact interactions, and thus a viable laboratory tool is furnished to experimentally investigate whether the thermal characteristic of the Unruh effect is robust to the breaking of Lorentz symmetry.
Rydberg-dressed ground state atoms are atoms with an electron off-resonantly excited to a very high energy state, i.e., a state of high principal quantum number n ≫ 1. This thesis investigates the quantum dynamics of interacting Rydberg-dressed ground state atoms trapped in several multi-well potential traps. Rydberg atoms are atoms with exaggerated properties. One of their most interesting properties is that they exhibit a strong and long-ranged interaction that can be tuned leading to a variety of different quantum behaviours. My work focuses on studying the effects of these interacting atoms when loaded in multi-well potential traps. Generally, multi-well systems are considered as the simplest example of a finite optical lattice structure. For this reason, this thesis covers three research topics that examine the effects of long-range interaction on Rydberg-dressed atoms trapped in several potential confinements. I begin, in the introduction, by discussing the theoretical background of relevance to this work. It starts with presenting the physics of Bose-Einstein condensate. Then, the fundamentals of the interaction between two-level atom and light are analytically studied. This study has the purpose of understanding both; the dressed interacting atoms and optical lattices. The definition, characteristics, and the nature of the interaction between Rydberg atoms are analysed afterwards. The second chapter examines the dynamics of an ensemble of interacting Rydberg- dressed atoms trapped in static, i.e., time-independent, multi-well potentials using a mean-field theoretical approach. I choose one-dimensional double- and triple-well in addition to a two-dimensional quadruple-well potentials. The time-dependent non-linear Gross-Pitaevskii equation is used to numerically explore the ensemble’s quantum dynamics. Solving the dynamical differential equations along with tuning the strength of the applied long-range interaction shows that the behaviour of non-interacting Rydberg-dressed atoms does not differ conceptually according to the geometry of the trapping potential. However, this changes when the interactions are switched on where the shape of the confinement leads to interesting outcomes especially in the non-linear interacting limit, such as macroscopic quantum self-trapping. After investigating an ensemble of interacting Rydberg-dressed atoms in static multi-well potential traps, the second research topic examines the dynamical evolution of these atoms when loaded in a finite optical lattice using the extended Bose-Hubbard model. In this chapter, the atoms ensemble is assumed to be in a superfluid state where I investigate both, the order parameter when the Rydberg excitation laser is applied and the interference pattern of the condensates in different dimensions. The study shows the emerging long-range interactions lead to a rapid collapse of the superfluid order parameter and in general allow only for partial revivals. In addition, the interference experiments can directly reveal the interaction between Rydberg-dressed atoms. In the fourth chapter, the dynamics of Rydberg-dressed atoms trapped in a dynamical, i.e., time-dependent, potential confinement is presented. The dynamical trap is constructed such that it begins as a harmonic oscillator and ends as a double- well potential. The analysis investigates an ensemble of contact-interacting atoms via the time-dependent non-linear GP equation.