Bose polarons as relativistic Unruh-DeWitt detectors: Entanglement harvesting from Bose-Einstein condensates

Abstract

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 ${}^{39}\text{K}$ impurities coupled to a ${}^{87}\text{Rb}$ 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.

Figures (5)

• Figure 1: A bound Bose polaron as an Unruh-DeWitt detector. An impurity trapped in a harmonic trap is coupled for a finite time with a Bose-Einstein condensate (BEC) by temporal Feshbach tuning to non-vanishing scattering length. The detector probes local degrees of freedom of the condensate in a causal diamond, determined by the speed of sound. After the interaction, the impurity is partially in a superposition of motional ground and excited state, revealing quantum information of the quantum state of the BEC.
• Figure 2: Spacetime density plot of the interaction regions $\Lambda_\textsc{i}(\mathsf x) = \chi(t) f_\textsc{i}(\bm x)$ for the probes. In the plot above we use $\sigma = 0.35 c_\textsc{s} T$ for illustration purposes, corresponding to $\Omega/2\pi = 6 \text{kHz}$ when using ${}^{39}$K.
• Figure 3: Negativity in the final state of the two impurities as a function of the trap frequency $\Omega$ for different values of interaction time parameter $T$.
• Figure 4: Plot of the signaling estimator as a function of $\Omega$ for the different setups considered in Fig. 2 of the main text when potassium probes coupled to a rubidium BEC are separated by distances $L = 5.25 c_\textsc{s} T$.
• Figure 5: Plot of the integrands $\mathcal{L}(|\bm k|)$, $\mathcal{M}^+(|\bm k|)$, and $\mathcal{M}^-(|\bm k|)$ as a function of $|\bm k|$ for two potassium impurities probing a rubidium BEC while separated by a distance $L = 5.25 c_\textsc{s} T$, where $T = 0.065 \,\text{ms}$ controls the time profile of the interaction, and the trap frequency of the impurities is $\Omega = 35 \, 2 \pi \text{kHz}$