Proposal for a Noninterferometric Test of Collapse Models in Optomechanical Systems

The test of modifications to quantum mechanics aimed at identifying the fundamental reasons behind the unobservability of quantum mechanical superpositions at the macroscale is a crucial goal of modern quantum mechanics. Within the context of collapse models, current proposals based on interferometric techniques for their falsification are far from the experimental state of the art. Here we discuss an alternative approach to the testing of quantum collapse models that, by bypassing the need for the preparation of quantum superposition states might help us addressing nonlinear stochastic mechanisms such as the one at the basis of the continuous spontaneous localization model.

Figure 1

Scheme of the principle of the experimental setup proposed to test the CSL model. A Fabry-Perot optomechanical cavity is pumped by a laser at frequency ${\omega }_0$ and strength $\mathcal{E}$. The pump populates a mode of the cavity field that is coupled to a vibrating mirror (frequency ${\omega }_m$). A quarter-wave plate (QWP) and a polarizing beam splitter (PBS) are used to redirect the light leaking from the cavity after the interaction with mechanical mirror, which is affected by both radiation-pressure and the nonlinear mechanism responsible for CSL, to a spectrum analyzer. The rightmost pumping field is used to cool the mechanical oscillator to low temperatures. Zigzag arrows are used to represent the CSL mechanism ($\lambda$) and the Brownian noise ($\xi$) affecting the mechanical oscillator.

Figure 2

(a) Main panel: DNS $S(\omega )$ against the frequency $\omega$ for ${\omega }_m/2\pi =2.75\times 10^5\mathrm{Hz}$, ${\gamma }_m/2\pi ={\omega }_m/10^5$, $L=25\mathrm{mm}$, $\mathcal{P}=4\mathrm{mW}$, $\kappa =5\times 10^7\mathrm{Hz}$, $T=1\mathrm{mK}$, and for a cantilever of $1\mu \mathrm{m}$ of linear dimension. We have compared the DNS without any CSL effect (black dashed curve) to the one corresponding to $\lambda ={\lambda }_A$ (red solid line), for $m=15\mathrm{ng}$. Inset: Same as the main panel but for $m=150\mathrm{ng}$. All curves are evaluated at $\mathrm{\Delta }=4\kappa$, which results in a lower effective temperature of the mechanical mirror. (b) We plot the area underneath the DNS $S(\omega )$ against $m$ for two choices of the detuning and $\lambda ={\lambda }_A$. Other parameters are as in (a). The case of no CSL mechanism corresponds to a horizontal line at $\mathcal{I}=1$.