Discriminating the effects of collapse models from environmental diffusion with levitated nanospheres

Collapse models postulate the existence of intrinsic noise which modifies quantum mechanics and is responsible for the emergence of macroscopic classicality. Assessing the validity of these models is extremely challenging because it is nontrivial to discriminate unambiguously their presence in experiments where other hardly controllable sources of noise compete to the overall decoherence. Here we provide a simple procedure that is able to probe the hypothetical presence of the collapse noise with a levitated nanosphere in a Fabry-Pérot cavity. We show that the stationary state of the system is particularly sensitive, under specific experimental conditions, to the interplay between the trapping frequency, the cavity size, and the momentum diffusion induced by the collapse models, allowing one to detect them even in the presence of standard environmental noises.

Figure 1

(a), (b) Diffusion rates for the scattering of trapping light $D_t$ (blue), cavity light $D_c$ (red), air molecules $D_a$ (gray), and the collapse rate ${\lambda }_{\mathrm{sph}}$ (green) vs the mechanical frequency $\omega$ with (a) $R=0.5r_c$ and $G=0.05\kappa$, (b) $R=r_c$ and $G=0.01\kappa$. Note that the curves of $D_c$ and $D_a$ in (b) are very close to the $\omega$ axis and no longer visible. (c), (d) Steady-state variance of the optical phase quadrature $\langle Y^2\rangle$ vs the trapping frequency $\omega$. Blue (red) lines refer to the case with (without) the CSL effect. The parameters for (c) [(d)] correspond to those for (a) [(b)]. The other parameters are $L=R_c=1$ cm, $\mathcal{F}={10}^5$ (corresponding to $\kappa =0.47$ MHz), $\mathrm{\Delta }=0.01\kappa , {\lambda }_c=1064$ nm, $\mathcal{N}=0.6, T=1$ K, $P_a={10}^{-10}$ Torr, $\lambda ={10}^{-8} {\mathrm{s}}^{-1}, r_c=100$ nm, and we consider a diamond nanosphere with ${\rho }_0=3.5 \mathrm{g}/{\mathrm{cm}}^3$ and $\epsilon =5.76$.

Figure 2

Steady-state variance of the optical phase quadrature $\langle Y^2\rangle$ vs the trapping frequency $\omega$ for (a) $\lambda ={10}^{-9} {\mathrm{s}}^{-1}, T=200$ mK, $P_a={10}^{-10}$ Torr, (b) $\lambda ={10}^{-10} {\mathrm{s}}^{-1}, T=100$ mK, $P_a=3\times {10}^{-11}$ Torr, (c) $\lambda ={10}^{-11} {\mathrm{s}}^{-1}, T=60$ mK, $P_a={10}^{-11}$ Torr, and (d) $\lambda ={10}^{-12} {\mathrm{s}}^{-1}, T=10$ mK, $P_a={10}^{-12}$ Torr. Blue (red) lines represent the case with (without) the CSL effect. In all plots we take $G=0.001\kappa$. The other parameters are as in Fig. 1.

Figure 3

Steady-state variance of the optical phase quadrature $\langle Y^2\rangle$ vs the cavity length $L$ with (a) $\omega =\mathrm{\Delta }=0.02\kappa , G=0.15\kappa , P_a={10}^{-10}$ Torr, (b) $\omega =\mathrm{\Delta }=0.008\kappa , G=0.08\kappa , P_a={10}^{-10}$ Torr, (c) $\omega =\mathrm{\Delta }=0.008\kappa , G=0.025\kappa , P_a={10}^{-11}$ Torr, and (d) $\omega =\mathrm{\Delta }=0.008\kappa , G=0.009\kappa , P_a={10}^{-12}$ Torr. The values of $\lambda$ are reported in each plot. All the curves are evaluated for $T=100$ mK and $R_c=2$ cm, and the other parameters are as in Fig. 2. Blue (red) lines represent the case with (without) the CSL effect.