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arXiv:1506.08782 · Physical Review A

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

Daniel Goldwater, Mauro Paternostro, P. F. Barker

Published Jul 14, 2016• 96 citations
arXivHTMLPDF

Abstract

We propose a mechanism for testing the theory of collapse models such as continuous spontaneous localization (CSL) by examining the parametric heating rate of a trapped nanosphere. The random localizations of the center of mass for a given particle predicted by the CSL model can be understood as a stochastic force embodying a source of heating for the nanosphere. We show that by utilizing a Paul trap to levitate the particle and optical cooling, it is possible to reduce environmental decoherence to such a level that CSL dominates the dynamics and contributes the main source of heating. We show that this approach allows measurements to be made on the time scale of seconds and that the free parameter ${\ensuremath{\lambda}}_{\mathrm{csl}}$ which characterizes the model ought to be testable to values as low as ${10}^{\ensuremath{-}12}$ Hz.

DOI
10.1103/physreva.94.010104

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Scientific Reports•Aug 25, 2015•2 citations
We propose a mechanism for testing the theory of collapse models such as continuous spontaneous localization (CSL) by examining the parametric heating rate of a trapped nanosphere. The random localizations of the center of mass for a given particle predicted by the CSL model can be understood as a stochastic force embodying a source of heating for the nanosphere. We show that by utilizing a Paul trap to levitate the particle and optical cooling, it is possible to reduce environmental decoherence to such a level that CSL dominates the dynamics and contributes the main source of heating. We show that this approach allows measurements to be made on the time scale of seconds and that the free parameter \ensuremathλcsl{\ensuremath{\lambda}}_{\mathrm{csl}}\ensuremathλcsl​ which characterizes the model ought to be testable to values as low as 10\ensuremath−12{10}^{\ensuremath{-}12}10\ensuremath−12 Hz.
The continuous spontaneous localization (CSL) theory alters the Schr\"odinger equation. It describes wave-function collapse as a dynamical process instead of an ill-defined postulate, thereby providing macroscopic uniqueness and solving the so-called measurement problem of standard quantum theory. CSL contains a parameter $\ensuremath{\lambda}$ giving the collapse rate of an isolated nucleon in a superposition of two spatially separated states and, more generally, characterizing the collapse time for any physical situation. CSL is experimentally testable, since it predicts some behavior different from that predicted by standard quantum theory. One example is the narrowing of wave functions, which results in energy imparted to particles. Here we consider energy given to trapped ultracold atoms. Since these are the coldest samples under experimental investigation, it is worth inquiring how they are affected by the CSL heating mechanism. We examine the CSL heating of a Bose-Einstein condensate (BEC) in contact with its thermal cloud. Of course, other mechanisms also provide heat and also particle loss. From varied data on optically trapped cesium BECs, we present an energy audit for known heating and loss mechanisms. The result provides an upper limit on CSL heating and thereby an upper limit on the parameter $\ensuremath{\lambda}$. We obtain $\ensuremath{\lambda}\ensuremath{\lesssim}1(\ifmmode\pm\else\textpm\fi{}1)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$ ${\mathrm{s}}^{\ensuremath{-}1}$.
The transition from the quantum to the classical realm remains one of the most profound open questions in physics. While quantum theory predicts the existence of macroscopic superpositions, their apparent absence in the everyday world is attributed either to environmental decoherence or to an intrinsic mechanism for wave-function collapse. This work presents a quantitative and experimentally grounded framework for distinguishing these possibilities. We propose a levitated optomechanical platform capable of generating controllable Schrodinger-cat states in the center of mass motion of a dielectric nanosphere. A comprehensive master equation incorporates gas collisions, black-body radiation, and photon-recoil noise, establishing a calibrated environmental baseline. The Continuous Spontaneous Localization (CSL) model is embedded within the same framework, predicting a characteristic saturation of the decoherence rate with superposition size and a quadratic scaling with mass. A Bayesian inference protocol is outlined to discriminate collapse induced excess decoherence from environmental noise. Together these elements provide a concrete experimental blueprint for a decisive test of quantum linearity, either revealing new physics beyond standard quantum mechanics or setting the most stringent bounds to date on objective-collapse parameters.
{The Continuous Spontaneous Localization (CSL) theory alters the Schrodinger equation. It describes wave function collapse as a dynamical process instead of an ill-defined postulate, thereby providing macroscopic uniqueness and solving the so-called measurement problem of standard quantum theory. CSL contains a parameter λ\lambdaλ giving the collapse rate of an isolated nucleon in a superposition of two spatially separated states and, more generally, characterizing the collapse time for any physical situation. CSL is experimentally testable, since it predicts some behavior different from that predicted by standard quantum theory. One example is the narrowing of wave functions, which results in energy imparted to particles. Here we consider energy given to trapped ultra-cold atoms. Since these are the coldest samples under experimental investigation, it is worth inquiring how they are affected by the CSL heating mechanism. We examine the CSL heating of a BEC in contact with its thermal cloud. Of course, other mechanisms also provide heat and also particle loss. From varied data on optically trapped cesium BEC's, we present an energy audit for known heating and loss mechanisms. The result provides an upper limit on CSL heating and thereby an upper limit on the parameter λ\lambdaλ. We obtain λ≲1(±1)×10−7\lambda\lesssim 1(\pm1)\times 10^{-7}λ≲1(±1)×10−7sec−1^{-1}−1.}
Continuous spontaneous localization (CSL) is a model that captures the effects of a class of extensions to quantum theory which are expected to result from quantum gravity and is such that wave-function collapse is a physical process. The rate of such a process could be very much lower than the upper bounds set by searches to date and yet still modify greatly the interpretation of quantum mechanics and solve the quantum measurement problem. Consequently experiments are sought to explore this. We describe an experiment that has the potential to extend sensitivity to CSL by many orders of magnitude. The method is to detect heating of the motion of charged macroscopic objects confined in a Paul trap. We discuss the detection and the chief noise sources. We find that CSL with standard parameters could be observed using a vibration-isolated ion trap of size 1 cm at ultralow pressure with optical interferometric detection.
Wavefunction collapse models modify Schrödinger's equation so that it describes the collapse of a superposition of macroscopically distinguishable states as a dynamical process. This provides a basis for the resolution of the quantum measurement problem. An additional generic consequence of the collapse mechanism is that it causes particles to exhibit a tiny random diffusive motion. Here it is shown that for the continuous spontaneous localization (CSL) model---one of the most well developed collapse models---the diffusions of two sufficiently nearby particles are positively correlated. An experimental test of this effect is proposed in which random displacements of pairs of free nanoparticles are measured after they have been simultaneously released from nearby traps. The experiment must be carried out at sufficiently low temperature and pressure in order for the collapse effects to dominate over the ambient environmental noise. It is argued that these constraints can be satisfied by current technologies for a large region of the viable parameter space of the CSL model. The effect disappears as the separation between particles exceeds the CSL length scale. The test therefore provides a means of bounding this length scale.
Wavefunction collapse models modify Schrödinger's equation so that it describes the collapse of a superposition of macroscopically distinguishable states as a dynamical process. This provides a basis for the resolution of the quantum measurement problem. An additional generic consequence of the collapse mechanism is that it causes particles to exhibit a tiny random diffusive motion. Here it is shown that for the continuous spontaneous localization (CSL) model—one of the most well developed collapse models—the diffusions of two sufficiently nearby particles are positively correlated. An experimental test of this effect is proposed in which random displacements of pairs of free nanoparticles are measured after they have been simultaneously released from nearby traps. The experiment must be carried out at sufficiently low temperature and pressure in order for the collapse effects to dominate over the ambient environmental noise. It is argued that these constraints can be satisfied by current technologies for a large region of the viable parameter space of the CSL model. The effect disappears as the separation between particles exceeds the CSL length scale. The test therefore provides a means of bounding this length scale.