Testing wave-function-collapse models using parametric heating of a trapped nanosphere

Goldwater, Daniel; Paternostro, Mauro; Barker, P. F.

doi:10.1103/physreva.94.010104

Cited by 77 publications

(96 citation statements)

References 41 publications

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“…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].…”

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confidence: 99%

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

et al. 2016

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

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“…Therefore, estimating Λ is equivalent, from this viewpoint, to the estimation of the equilibrium temperature of the mechanical system [12,13]. While the optimal estimation strategy for the inference of temperature of an equilibrium harmonic oscillator has been found to be provided by measurements of its energy (the QFI being proportional to the variance of the energy of the oscillator) [32], here we would like to exploit the coupling between the mechanical system and the cavity field to devise implementable strategies for the inference of Λ.…”

Section: The Model and The Core Resultsmentioning

confidence: 99%

“…Most remarkably, at variance with standardly pursued approaches [11], they bypass the need for the construction and quantum-limited management of large interferometers [12,13]. notwithstanding such promising features, the investigation of CMs still poses considerable experimental challenges, and a winning strategy to their inference has not yet been singled out [16].…”

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confidence: 99%

“…In order to fix the ideas and illustrate the pillars of our proposal in a concrete and relevant case, we focus on the continuous spontaneous localisation (CSL) model [22,23], which is one of the simplest and most studied CMs [7]. By applying the tools of quantum estimation theory to a paradigmatic cavity optomechanics system, we derive the ultimate bounds on the estimation precision of the core parameter entering the CSL model, thus going significantly beyond the achievements of any previous proposal in this context [12,13]. Moreover, we identify a feasible, nondisruptive all-optical measurement strategy able to provide significant information on a CSL-affected nano-mechanical oscillator.…”

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Quantum-limited estimation of continuous spontaneous localization

et al. 2017

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We apply the formalism of quantum estimation theory to extract information about potential collapse mechanisms of the continuous spontaneous localisation (CSL) form. In order to estimate the strength with which the field responsible for the CSL mechanism couples to massive systems, we consider the optomechanical interaction between a mechanical resonator and a cavity field. Our estimation strategy passes through the probing of either the state of the oscillator or that of the electromagnetic field that drives its motion. In particular, we concentrate on all-optical measurements, such as homodyne and heterodyne measurements. We also compare the performances of such strategies with those of a spin-assisted optomechanical system, where the estimation of the CSL parameter is performed through time-gated spin-like measurements.Understanding the nature of the quantum-to-classical (QtC) transition is a long-sought problem that attracts an evergrowing attention [1][2][3][4][5][6]. While quantum mechanics has undergone exhaustive and extremely successful testings in the microscopic realm, the apparent absence of quantum manifestations at the macroscopic scale cries for a deeper understanding. In particular, this lack of evidence reinforces the need of assessing the causes for the emergence of classical mechanics from fundamental quantum evolution. The most widely accepted theory behind such process is quantum decoherence [6]: The environment surrounding any quantum system monitors its state continuously, practically collapsing the system's wavefunction and curtailing any quantum behaviour. Such process is conjectured to occur more quickly with the growing size of the system at hand. Under this regime, macroscopic superpositions would be possible in macroscopic systems perfectly isolated from their environment, a condition that is, for all practical purposes, not realisable.However, a set of theories, usually referred to as collapse models (CMs), suggests an alternative route to the explanation of the QtC transition by putting forward fundamental underlying mechanisms responsible for the collapse of the wavefunction [7]. The strength of this effect should increase with the size (mass) of the system, leaving microscopic (macroscopic) systems fully within the quantum (classical) realm. The key difference between CMs and standard quantum mechanics is that in the framework entailed by the former, perfectly isolated macroscopic objects would continue to act classically.Among the proposals put forward so far to test (or rule out) some of the currently formulated CMs [8][9][10], those based on the experimental platform of cavity optomechanics offer features of undemanding scalability of the mass of the system to be probed and high-sensitivity of measurement. Most remarkably, at variance with standardly pursued approaches [11], they bypass the need for the construction and quantum-limited management of large interferometers [12,13]. notwithstanding such promising features, the investigation of CMs still poses considerable experim...

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“…10 Probing nonclassical behaviors using these systems allows us to explore quantum decoherence and potentially wave-function collapse models. 7,11 Lastly, levitated optomechanics has potential applications in measuring very small forces which is relevant for gravitational-wave detections 12 as well as Casimir forces or non-Newtonian gravity. 13 …”

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Millikelvin cooling of the center-of-mass motion of a levitated nanoparticle

Bullier¹,

Pontin²,

Barker³

2017

Optical Trapping and Optical Micromanipulation XIV

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Cavity optomechanics has been used to cool the center-of-mass motion of levitated nanospheres to millikelvin temperatures.1 Trapping the particle in the cavity field enables high mechanical frequencies 1-3 bringing the system close to the resolved-sideband regime. Here we describe a Paul trap constructed from a printed circuit board that is small enough to fit inside the optical cavity and which should enable an accurate positioning of the particle inside the cavity field. This will increase the optical damping and therefore reduce the final temperature by at least one order of magnitude. Simulations of the potential inside the trap enable us to estimate the chargeto-mass ratio of trapped particles by measuring the secular frequencies as a function of the trap parameters. Lastly, we show the importance of reducing laser noise to reach lower temperatures and higher sensitivity in the phase-sensitive readout.

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Testing wave-function-collapse models using parametric heating of a trapped nanosphere

Cited by 77 publications

References 41 publications

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

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

Quantum-limited estimation of continuous spontaneous localization

Millikelvin cooling of the center-of-mass motion of a levitated nanoparticle

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