Harvesting entanglement from the Lorentz-violating quantum field vacuum in a dipolar Bose-Einstein condensate

TL;DR

The paper tackles entanglement harvesting from the vacuum of a Lorentz-violating quantum field by using two impurities embedded in a quasi-2D dipolar Bose-Einstein condensate as Unruh-DeWitt detectors. It models the LV field through density fluctuations in the dipolar BEC and derives the detector dynamics to second order via the Wightman function, analyzing how LV strength parameters $A$ and $R$ influence harvesting. The key findings show that, unlike the Lorentz-invariant case, smoother detector switching does not enhance harvesting in the LV vacuum, and increasing LV strength $A$ can shift the optimal detector energy gap $\Omega/M_*$ while leaving the optimal separation near zero; larger switching widths can even boost harvested entanglement in LV scenarios. The work provides a feasible experimental platform to test entanglement harvesting in LV quantum fields, with broader implications for probing Lorentz-violating physics in quantum field theory using controllable quantum fluids.

Abstract

We theoretically propose an experimentally viable scheme to explore the transfer of nonclassical correlations from a dipolar Bose-Einstein condensate (BEC) to a pair of impurities immersed in it. Operating at ultra-low temperature, density fluctuations of the dipolar BEC emulate a vacuum field with Lorentz-violating dispersion, while the two impurities function as Unruh-DeWitt detectors for the BEC quasiparticles. We study the harvesting of entanglement from the quantum vacuum of this analogue Lorentz-violating quantum field by spatially separated Unruh-DeWitt detectors. Our analysis reveals key parameter dependencies that optimize the harvesting of entanglement. In particular, unlike the Lorentz-invariant case, smoother detector switchings does not enhance the entanglement harvesting efficiency from the Lorentz-violating quantum field vacuum. Moreover, the strength of the Lorentz-invariant violation can shift the optimal energy structure of the detectors for harvesting entanglement from the Lorentz-violating quantum field vacuum-a clear deviation from the Lorentz-invariant scenario. As a fundamental quantum mechanical setup, our quantum fluid platform provides an experimentally realizable testbed for examining the entanglement harvesting protocol from an effective Lorentz-violating quantum field vacuum using a pair of impurity probers, which may also has potential implications for exploring the Lorentz-invariant violation in quantum field theory.

Figures (6)

• Figure 1: Schematic of two impurities with effective internal frequency $\Omega$ immersed in a quasi-two-dimensional dipolar condensate. $|e\rangle$ and $|g\rangle$ denote the effective excitation and ground state of the impurity, respectively. The two impurities act as two Unruh-DeWitt detectors, denoted as A and B, at separate locations, $(r, \theta_\text{A})$ and $(r, \theta_\text{B})$, respectively.
• Figure 2: The dimensionless function $f$ shown in \ref{['Dispersion']} as a function of $c_0|\mathbf{k}|/M_\ast$. LI denotes Lorentz invariant case with $f=1$, such that $\omega_\mathbf{k}=c_0|\mathbf{k}|$. $R=0$ denotes the contact interaction case, where $f$ is independent of $A$. For DDI dominance case, we take $R=\sqrt{\pi/2}$, in such case $f$ could dip below 1 for an interval of $c_0|\mathbf{k}|/M_\ast$. Note that $f$ becomes negative when $A>A_c=3.4454$, which means the spectrum of quasiparticle becomes unstable.
• Figure 3: Concurrence shown in Eq. \ref{['concurrence']} as a function of the energy-level spacing $\Omega/M_\ast$ and the interdetector distance $M_\ast L/c_0$ for the Lorentz-invariant vacuum case. The units of the concurrence is $\rho_0\lambda^2/c^2_0$, and the switching-function width $\sigma M_\ast=5$ and $8$ respectively corresponds to (a) and (b).
• Figure 4: Concurrence shown in Eq. \ref{['concurrence']} as a function of the energy-level spacing $\Omega/M_\ast$ and the interdetector distance $M_\ast L/c_0$ for the Lorentz-violating case. The units of the concurrence is $\rho_0\lambda^2/c^2_0$. The switching function width $\sigma M_\ast=1$ corresponds to (a), (b) and (c) cases, and $\sigma M_\ast=5$ corresponds to (d), (e) and (f) cases. We take $R=\sqrt{\pi/2}$ in the dispersion \ref{['Dispersion']} such that the strength of LI violation increases with the increase of $A$.
• Figure 5: Concurrence shown in Eq. \ref{['concurrence']} as a function of the strength of the LI violation, $A$. The units of the concurrence is $\rho_0\lambda^2/c^2_0$. Here the detector's energy-level spacing $\Omega/M_\ast$ is fixed, while the interdetector distance $M_\ast L/c_0$ varies. We take $R=\sqrt{\pi/2}$ in the dispersion \ref{['Dispersion']} such that the strength of LI violation increases with the increase of $A$. The switching function width $\sigma M_\ast=1$ corresponds to (a), (b) and (c) cases, and $\sigma M_\ast=5$ corresponds to (d), (e) and (f) cases.