Virtual transitions in an atom-mirror system in the presence of two scalar photons

We examine the virtual transition of an atom-mirror system with the simultaneous emission of two scalar photons, where the atom and the mirror admit a relative acceleration between them. For the single photon emission, the literature [A. A. Svidzinsky et al., Phys. Rev. Lett. 121, 071301 (2018)] dictates that the transition probabilities of two individual systems, such as an atom accelerating with respect to the mirror and its reverse, turn out to be equivalent under the exchange of the frequencies of atom and the field. Addressing the observational merit of such excitation process, a detectable probability ($P\sim {10}^{-2}$) is also reported in the above literature. In the present manuscript our finding dictates that the simultaneous emission of dual photon instead of one, destroys the equivalence between the transition probabilities as reported in the above literature.

Figure 1

Plot of ${\mathcal{P}}_{\mathrm{exc}}$ vs $\omega$. Atom is accelerating with respect to the fixed mirror and two photons are simultaneously emitted.

Figure 2

Plot of ${\mathcal{P}}_{\mathrm{exc}}^{\prime }$ vs $\nu$. Mirror is accelerating with respect to a fixed atom and two photons are simultaneously emitted.

Figure 3

Plot of ${\mathcal{P}}_{\mathrm{exc}}^{\prime }$ vs $\nu$. for $\frac{\nu c}{a}\ll 1$.