Interferometric Unruh Detectors for Bose-Einstein Condensates

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.

Figure 1

Simplified schematic of our proposed experimental arrangement. An initial beam sharply peaked at frequency ${\omega }_L$ is modulated to create sidebands peaked at a pair of frequencies ${\omega }_L\pm {\omega }_M$ that are oppositely detuned from an atomic resonance. The central band is then filtered out. The two remaining sideband beams traverse the same path, intersecting a 2D BEC along a circular trajectory in the BEC plane. Because of the opposite detuning, the side beams pick up opposite phase shifts when interacting with the BEC.

Figure 2

Signal-to-noise ratio $\mathrm{\Delta }SN$ as a function of dimensionless energy $\tilde{E}=\hslash \omega /\mu$ for ${}^{133}\mathrm{Cs}$ and $N={10}^6$ experimental realizations. The experimental parameters chosen are the scattering rate ${\mathrm{\Gamma }}_{\mathrm{sc}}\approx 0.1\mathrm{Hz}$, beam width $r_0=3\mu \mathrm{m}$, chemical potential $\mu \approx 2\pi \hslash 9.5\mathrm{Hz}$, healing length $\xi \approx 2\mu \mathrm{m}$, density ${\rho }_0={10}^3\mu {\mathrm{m}}^{-2}$, scattering length $a_s=25\mathrm{pm}$, transverse confinement $a_{\perp }=1\mu \mathrm{m}$ resulting in a peak 3D density $\max [{\rho }_{3\mathrm{D}}]\approx 5.6\times {10}^{14}{\mathrm{cm}}^{-3}$ and speed of sound $c_s\approx 1.7\times {10}^2\mu \mathrm{m}/\mathrm{s}$. The observer trajectory radius $R=10\mu \mathrm{m}\approx 5\xi$ and velocity $v=0.95c_s$ lead to $T_U\approx 60\mathrm{pK}$. Note that the signal vanishes for $\tilde{E}\to 0$, due to the suppression of density perturbations $\delta \rho$ at long wavelength. The signal to noise ratio within the whole phononic band (below the dashed black line) given by Eq. (17) for ${\mathcal{B}}_{\mathrm{m}}=1\mathrm{Hz}$ is $\overline{\mathrm{\Delta }SN}\approx 5.8$.