Amplified Optomechanical Transduction of Virtual Radiation Pressure

Here we describe how, utilizing a time-dependent optomechanical interaction, a mechanical probe can provide an amplified measurement of the virtual photons dressing the quantum ground state of an ultrastrongly coupled light-matter system. We calculate the thermal noise tolerated by this measurement scheme and discuss an experimental setup in which it could be realized.

Figure 1

Total displacement visibility $F$ in the presence (full blue curve, $\eta =0.1$) and absence (full black curve, $\eta =0$) of matter in the cavity as a function of the number of thermal light-matter excitations $\overline{n}$ (for an optomechanical coupling $g_0/{\mathrm{\Gamma }}_m=3{\overline{\eta }}_0^{\mathrm{SQL}}$, for ${\overline{\eta }}_0^{\mathrm{SQL}}=2/{\eta }^2$). For high values of $\overline{n}$, the two curves asymptotically converge to a parallel behavior ([66], Sec. III B). In the absence of matter, when $\overline{n}\to 0$ a zero photon population implies no displacement (black curve). However, in the presence of matter, virtual photons can displace the mechanical oscillator even for $\overline{n}\to 0$ (blue curve). The relative displacement contribution purely due to virtual radiation-pressure effects $F_{\mathrm{GS}}$ is represented by the blue dashed curve showing that, for $\overline{n}\to 0$, the displacement is mainly due to the dressed structure of the ground state. The gray vertical line represents the theoretical upper bound ${\overline{n}}_{\max }$. Below this critical value, it is possible to tune $g_0/{\mathrm{\Gamma }}_m$ to resolve the ground-state signal. This is shown in the inset, which magnifies the main plot around $\overline{n}={\overline{n}}_{\max }$. The blue curve corresponds to the same color-coded ones in the main figure. The dotted purple and dot-dashed red curves are plotted for different values of $g_0/{\mathrm{\Gamma }}_m$ ($16{\overline{\eta }}_0^{\mathrm{SQL}}$ and $2{\overline{\eta }}_0^{\mathrm{SQL}}$, respectively). For $\overline{n}<{\overline{n}}_{\max }$, it is always possible to find optomechanical couplings which, in principle, allow one to resolve the ground-state signal (i.e., $F_{\mathrm{GS}}>1$).