Upper Bounds on Spontaneous Wave-Function Collapse Models Using Millikelvin-Cooled Nanocantilevers

Abstract

Collapse models predict a tiny violation of energy conservation, as a consequence of the spontaneous collapse of the wave function. This property allows us to set experimental bounds on their parameters. We consider an ultrasoft magnetically tipped nanocantilever cooled to millikelvin temperature. The thermal noise of the cantilever fundamental mode has been accurately estimated in the range 0.03-1 K, and any other excess noise is found to be negligible within the experimental uncertainty. From the measured data and the cantilever geometry, we estimate the upper bound on the continuous spontaneous localization collapse rate in a wide range of the correlation length r C . Our upper bound improves significantly previous constraints for r C > 10 −6 m, and partially excludes the enhanced collapse rate suggested by Adler. We discuss future improvements. DOI: 10.1103/PhysRevLett.116.090402 Spontaneous wave function collapse models [1][2][3][4] have been proposed to reconcile the linear and deterministic evolution of quantum mechanics with the nonlinear and stochastic character of the measurement process. According to such phenomenological models, random collapses occur spontaneously in any material system, leading to a spatial localization of the wave function. The collapse rate scales with the size (number of constituents) of the system, leading to rapid localization of any macroscopic system, while giving no measurable effect at the microscopic level, where conventional quantum mechanics is recovered.Here we consider the mass-proportional version of the continuous spontaneous localization (CSL) model [2], the most widely studied one, originally introduced as a refinement of the Ghirardi-Rimini-Weber (GRW) model [1]. CSL is characterized by two phenomenological constants, a collapse rate λ, and a characteristic length r C , which characterize, respectively, the intensity and the spatial resolution of the spontaneous collapse. 11AE2 times larger at r C ¼ 10 −6 m. The direct effect of collapse models like CSL is to destroy quantum superpositions, resulting in a loss of coherence in interferometric tests with matter-wave [6][7][8] or mechanical resonators [9][10][11]. Recently, noninterferometric tests have been proposed, which promise to set stronger bounds on these models [12][13][14][15][16][17][18][19]. Among such tests, the measurement of heating effects in mechanical systems, a byproduct of the collapse process, seems particularly promising [15][16][17][18]. Here, we demonstrate for the first time this method, by accurately measuring the mean energy of a nanocantilever in thermal equilibrium at millikelvin temperatures. We infer an experimental upper bound on λ, which is 2 orders of magnitude stronger than that set by matter-wave interferometry [20][21][22] for r C ¼ 10 −7 m, and the strongest one to date for r C > 10 −6 m. Theoretical model.-The detection of CSL-induced heating in realistic optomechanical systems has been extensively discussed in the recent literature [15][16][17][18][19]. Here we summarize th...

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“…Both bounds, however, are weaker than those coming from non-interferometric tests: violation of the equipartition theorem with cantilevers [18], and X-ray measurements [17]. At present, non-interferometric tests proved the strongest upper bound for the CSL parameters; what is not clear is whether these bounds are robust against changes in the collapse mechanism, while those associated to interferometric tests are [19].…”

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“…In both cases, we have considered the value of the CSL parameter as λ GRW = 1. Mpc −1 , which corresponds to a value favored by experimental data [55,56,59,60]. The various plots in each figure correspond to different values of the characteristic energy of inflation V 1/4 , and the total e-foldings N that inflation is assumed to last, which also set the values of τ and η f .…”

“…However, Adler suggested a greater value λ Adler 10 −8 s −1 for r C 100 nm [58] (the parameter r C is called the correlation length of the noise and provides a measure for the spatial resolution of the collapse [41,43,57]). Recent experiments have been devised to set bounds on the parameter λ [59,60]. Furthermore, it is claimed that matter-wave interferometry provides the most generic way to experimentally test the collapse models [55,56].…”

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“…[38] bound other collapse models [48] in the spirit of what has been done in Refs. [49,50], for example.…”