Improved Noninterferometric Test of Collapse Models Using Ultracold Cantilevers

Spontaneous collapse models predict that a weak force noise acts on any mechanical system, as a consequence of the collapse of the wave function. Significant upper limits on the collapse rate have been recently inferred from precision mechanical experiments, such as ultracold cantilevers and the space mission LISA Pathfinder. Here, we report new results from an experiment based on a high-$Q$ cantilever cooled to millikelvin temperatures, which is potentially able to improve the current bounds on the continuous spontaneous localization (CSL) model by 1 order of magnitude. High accuracy measurements of the cantilever thermal fluctuations reveal a nonthermal force noise of unknown origin. This excess noise is compatible with the CSL heating predicted by Adler. Several physical mechanisms able to explain the observed noise have been ruled out.

Figure 1

Simplified measurement scheme. The fundamental bending mode of a cantilever loaded with a ferromagnetic microsphere with magnetic moment $\mu$ is continuously monitored by a SQUID susceptometer. The SQUID measures the magnetic flux $\mathrm{\Phi }={\mathrm{\Phi }}_{x}x$ coupled by the displacement $x$ of the magnetic particle and is operated in a flux-locked loop (feedback electronics are not shown, for simplicity). The flux-dependent circulating current $J$, combined with finite feedback gain, causes a dynamical magnetic spring effect that modifies the apparent quality factor of the cantilever.

Figure 2

Examples of averaged spectra at three representative temperatures, with the respective best fit with Eq. (2).

Figure 3

Symmetric amplitude of the Lorentzian noise $B$, as measured by the SQUID, as function of the ratio $T/Q$, together with the best linear fit. In the inset, the data at the lowest $T/Q$ are zoomed in order to highlight the nonzero intercept of the fit.

Figure 4

Exclusion plot in the $\lambda -r_C$ plane based on our experimental data, compared with the best experimental upper bounds reported so far and with theoretical predictions. Continuous thick (red) curve: CSL collapse rate $\lambda$, as function of the characteristic length $r_C$, assuming that the observed noise is entirely due to CSL. The shaded region would be excluded by our experiment if the physical origin of the excess noise were identified. The other thin lines represent upper limits from labeled experiments: previous cantilever experiment (orange) [17], LISA Pathfinder (black) [21], cold atoms (green) [19], and x-ray spontaneous emission (dashed blue) [25]. The (dark green) bars represent the CSL collapse rate suggested by Adler [5].