Large Quantum Superpositions and Interference of Massive Nanometer-Sized Objects

We propose a method to prepare and verify spatial quantum superpositions of a nanometer-sized object separated by distances of the order of its size. This method provides unprecedented bounds for objective collapse models of the wave function by merging techniques and insights from cavity quantum optomechanics and matter-wave interferometry. An analysis and simulation of the experiment is performed taking into account standard sources of decoherence. We provide an operational parameter regime using present-day and planned technology.

Figure 1

Schematic representation of the proposal. (a) The optically trapped object is laser cooled using a high-finesse optical cavity. (b) The trap is switched off and the wave function expands during some time $t_1$. (c) The object enters into a second small cavity where a pulsed (of time $\tau$) interaction is performed using the quadratic optomechanical coupling. The homodyne measurement of the output phase measures ${\widehat{x}}^2$ and prepares a quantum superposition state conditional of the outcome result $p_L$. (d) The particle falls during a time $t_2$ until its center of mass position is measured, which after repetition unveils an interference pattern for each $p_L$.

Figure 2

(a) The operational parameter regime for the optomechanical double slit distance $d$ and the diameter of the sphere $D$ is plotted (see legend for the lower and upper bounds). The simulation of the interference pattern is computed for a sphere of 40 nm and (b) $d=D$ (triangle), (c) $d=1.3D$ (square), and (d) $d=0.7D$ (circle) in units of $D$. The solid blue (dashed grey) line is the simulated interference pattern with (without) standard decoherence. The dotted red line is the interference pattern in the presence of the CSL model with $\lambda ={10}^4{\lambda }_0{\mathrm{s}}^{-1}$ (the upper bound $d_{\max }^{\mathrm{CSL}}$ in the operational parameter plot provided by the CSL model is also shown—see legend). Experimental parameters for the environmental conditions are $P={10}^{-16}\mathrm{Torr}$, $T_e=4.5\mathrm{K}$, $\mathrm{Im}[({ϵ}_{\mathrm{bb}}-1)({ϵ}_{\mathrm{bb}}+2)]=0.1$, $\mathrm{Re}[{ϵ}_{\mathrm{bb}}]=2.3$, $\overline{n}=0.1$; for the cavity, they are $\mathcal{F}=1.3\times {10}^5$, length $2\mu \mathrm{m}$, $\mathrm{\text{waist}}=1.5\mu \mathrm{m}$, ${\lambda }_c=1064\mathrm{nm}$; and for a silica sphere, ${ϵ}_r=2.1+i2.5\times {10}^{-10}$, $\mathrm{\text{density}}=2201\mathrm{kg}/{\mathrm{m}}^3$, ${\omega }_t/2\pi =135\mathrm{kHz}$, and $\delta x=10\mathrm{nm}$. Using this, for a sphere of 40 nm and $d=D$, one obtains $\kappa /2\pi ={\tau }^{-1}=2.8\times {10}^8\mathrm{Hz}$, ${\mathcal{C}}_l=1500$, $n_{\mathrm{ph}}=272$, $T_i=206\mathrm{K}$, $t_1=3.3\mathrm{ms}$, $t_2=125\mathrm{ms}$, and $\sigma /x_0=2928$.