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arXiv:2007.07160 · Physical Review Letters

Interferometric Unruh Detectors for Bose-Einstein Condensates

Cisco Gooding, Steffen Biermann, Sebastian Erne, Jorma Louko, William George Unruh, Jörg Schmiedmayer, Silke Weinfurtner

Published Nov 20, 2020• 92 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.125.213603

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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 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.
Quantum simulators based on Bose-Einstein condensates (BECs) provide a powerful platform to study relativistic quantum-field phenomena in the lab and in particular emulate relativistic analog particle detectors. However, such detectors typically couple to excitations beyond the acoustic phonon regime, so that the nonlinear Bogoliubov dispersion introduces corrections that cause the effective relativistic description to break down. We propose to overcome this limitation using an intrinsically momentum-selective Unruh-DeWitt detector model in which a tweezer-trapped atom couples to the condensate through a multimode optical cavity. Although the atom is effectively pointlike, the cavity-mediated interaction kernel causes it to sample density fluctuations over a controllable finite region of the BEC equivalent to a finite-size detector. The effective detector size is tunable via the cavity mode structure determining a controllable momentum cutoff that filters out nonphononic excitations. We analytically calculate the response of such a detector for uniform linear acceleration and uniform circular motion and show that this momentum selectivity can enhance the signal at experimentally accessible accelerations. Compatible with existing cavity-QED platforms our scheme thus provides a versatile setting for analog quantum-field measurements or relativistic quantum-information protocols.
The Unruh effect predicts that an accelerating observer perceives the Minkowski vacuum as a thermal bath, yet direct detection remains experimentally inaccessible. Its timelike counterpart, arising from the entanglement of massless fields between the future and past light cones, offers a more feasible route but requires a detector whose transition frequency follows a specific conformal-time scaling. We propose and analyze a practical implementation of such a detector using superconducting fluxonium circuits, which naturally provide two quasi-degenerate ground states and a tunable excited state, forming an effective ΛΛΛ-system. By modulating the excited-state transition frequency in Minkowski time, the detector accumulates a geometric phase associated with the timelike Unruh effect. Open-system simulations predict ∼10%\sim 10\%∼10% shift in the ground-state population within 530530530 ns, representing a three-order-of-magnitude sensitivity enhancement over two-level Unruh-DeWitt detectors. These results establish a realistic quantum-circuit platform for experimentally probing the timelike Unruh effect and, more broadly, for testing fundamental nature of quantum fields using engineered quantum systems.
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 ofquantum 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\textrm{nK}nK 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.
We propose and study methods for detecting Unruh-like acceleration radiation effects in a Bose-Einstein condensate in a (1+1)-dimensional setup. The Bogoliubov vacuum of a Bose-Einstein condensate is used to simulate a scalar field theory, and accelerated atom dots or optical lattices serve as detectors of phonon radiation due to acceleration effects. In particular, we study the dispersive effects of the Bogoliubov spectrum on the ideal case of exact thermalization. Our results suggest that acceleration radiation effects can be observed using currently accessible experimental methods.
We show that a bound impurity in a Bose-Einstein condensate can be directly mapped to an Unruh-DeWitt detector interacting with a relativistic quantum field. We provide explicit experimental parameters for an implementation using 41K{}^{41}\text{K}41K impurities coupled to a 87Rb{}^{87}\text{Rb}87Rb condensate via finite-time Feshbach tuning. As an application, we study the extraction of vacuum entanglement from distant regions of the condensate and find viable parameters for the implementation of entanglement harvesting.