Interference phenomena in the dynamical Casimir effect for a single mirror with Robin conditions

In the literature, the interference phenomenon in the particle creation via the dynamical Casimir effect is investigated for cavities with two moving mirrors. Here, considering the Robin boundary condition (BC), we investigate the interference phenomenon produced by just a single moving mirror. Specifically, we consider a real massless scalar field in $1+1$ dimensions submitted to a Robin BC with a time-dependent Robin parameter at the instantaneous position of a moving mirror, and compute the expressions for the spectral distribution and the rate of created particles. These expressions, which include interference terms, generalize those found in the literature related to the isolated effects of a Robin BC with a time-dependent Robin parameter for a fixed mirror, or a Robin BC with a time-independent Robin parameter for a moving mirror. Differently from models where the problem of interference in the dynamical Casimir effect is considered for cavities with two Dirichlet moving mirrors, in the present model the spectrum is a continuum, and the interference pattern exhibits new features, in the sense that different regions of the spectrum can be affected in different manners by constructive or destructive effects. Furthermore, we also investigate interference in the context of superconducting circuits.

Figure 1

$N_{\mathrm{int}}(\omega )/(2{\epsilon }^2\tau {\tilde{\gamma }}_0\widetilde{q_0}{\pi }^{-1})$ as a function of $\omega$ for some values of ${\gamma }_0$, considering $\vartheta =0$ and ${\omega }_0=1$.

Figure 2

The rate of created particles (short-dashed line) and its individual parts as functions of ${\omega }_0$, considering ${\gamma }_0=1$, $\vartheta =0$, and ${\tilde{q}}_0={\tilde{\gamma }}_0=1$. The dot-dashed line corresponds to $[\pi /({\epsilon }^2\tau )]{\mathcal{N}}_q$. The long-dashed line corresponds to $[\pi /({\epsilon }^2\tau )]{\mathcal{N}}_{\gamma }$, whereas the solid line corresponds to $[\pi /({\epsilon }^2\tau )]{\mathcal{N}}_{\mathrm{int}}$. The value ${\gamma }_0{\omega }_0\approx 2.23$ is the border between constructive and destructive effects.

Figure 3

Spectral distribution for the case of one source of magnetic flux with frequency ${\omega }_1$ (dashed line), for the case of one source with frequency ${\omega }_1/2$ (dot-dashed line), and when both sources are considered simultaneously (solid line).

Figure 4

${|F(\omega )|}^2/\tau$ considering ${\omega }_1=0.5$ and some values for $\tau$ (${|G(\omega )|}^2/\tau$ behaves the same way).

Figure 5

Plot of $\mathrm{Re}[G(\omega )F^{*}(\omega )]/\tau$ considering ${\omega }_1\ne {\omega }_2$ with ${\omega }_1=0.5$ and ${\omega }_2=1.0$ and some values for $\tau$.