Unruh effect of detectors with quantized center of mass

The Unruh effect is the prediction that particle detectors accelerated through the vacuum get excited by the apparent presence of radiation quanta—a fundamental quantum phenomenon in the presence of acceleration. Prior treatments of the Unruh effect, that presume a classically prescribed trajectory, do not account for the quantum dynamics of the center of mass. Here, we study more realistic detectors whose center of mass is a quantized degree of freedom being accelerated by an external classical field. We investigate the detector’s recoil due to the emission of Unruh quanta. Vice versa, we also study the recoil’s impact on the emission of Unruh quanta and the excitation of the detector. We find that the recoil due to the emission of Unruh quanta may be a relevant experimental signature of the Unruh effect.

Figure 1

Emission probability for an accelerated UDW detector. (a) The total (i.e., angle-integrated) probability $P_{\mathrm{U}}(k)$ for the emission of an Unruh quantum with momentum $k$, for various values of the energy gap $\mathrm{\Omega }$. (b) Angle-resolved emission probability $P_{\mathrm{U}}(k,\theta )$ (in units of ${10}^{-6}cT{q}^2$), for energy gap $\mathrm{\Omega }=0.2/T$. Both plots are for acceleration, $a=8\times {10}^{-3}(c/T)$. Note that the oscillations in (a) arise from accelerating the detector for a time interval that is compact.

Figure 2

Emission and recoil probability for a massive UDW detector. (a) Plot shows the difference of the emission probabilities between the cases where the detector center of mass is infinitely heavy [i.e., $P_{\mathrm{U}}(k)$] and the case where the detector center of mass has a finite mass [i.e., $P_{\mathrm{M}}(k)$]. (b) Recoil probability density $P_{\mathrm{M}}(r,\zeta )$ [in units of ${10}^{-6}(cT{q}^2{)}^{-1}$] as a function of recoil momentum angle $\zeta$, for a few values of the magnitude of the recoil momentum magnitude $r$. The detector mass is $M=10/(c^{2}T)$, while in both panels, its internal energy gap is $\mathrm{\Omega }=0.2/T$, acceleration $a=8\times {10}^{-3}(c/T)$, and the center-of-mass wavepacket has an initial width, $L=100(cT)$.