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arXiv:1611.09989 · Physical Review A

Probing spontaneous wave-function collapse with entangled levitating nanospheres

Jing Zhang, Tiancai Zhang, Jie Li

Published Jan 30, 2017• 22 citations
arXivHTMLPDF

Abstract

Wave-function collapse models are considered to be the modified theories of standard quantum mechanics at the macroscopic level. By introducing nonlinear stochastic terms in the Schr\"odinger equation, these models (different from standard quantum mechanics) predict that it is fundamentally impossible to prepare macroscopic systems in macroscopic superpositions. The validity of these models can only be examined by experiments, and hence efficient protocols for these kinds of experiments are greatly needed. Here we provide a protocol that is able to probe the postulated collapse effect by means of the entanglement of the center-of-mass motion of two nanospheres optically trapped in a Fabry-P\'erot cavity. We show that the collapse noise results in a large reduction of the steady-state entanglement, and the entanglement, with and without the collapse effect, shows distinguishable scalings with certain system parameters, which can be used to determine unambiguously the effect of these models.

DOI
10.1103/physreva.95.012141

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Wave-function collapse models are considered to be the modified theories of standard quantum mechanics at the macroscopic level. By introducing nonlinear stochastic terms in the Schr"odinger equation, these models (different from standard quantum mechanics) predict that it is fundamentally impossible to prepare macroscopic systems in macroscopic superpositions. The validity of these models can only be examined by experiments, and hence efficient protocols for these kinds of experiments are greatly needed. Here we provide a protocol that is able to probe the postulated collapse effect by means of the entanglement of the center-of-mass motion of two nanospheres optically trapped in a Fabry-P'erot cavity. We show that the collapse noise results in a large reduction of the steady-state entanglement, and the entanglement, with and without the collapse effect, shows distinguishable scalings with certain system parameters, which can be used to determine unambiguously the effect of these models.
Collapse models postulate the existence of intrinsic noise which modifies quantum mechanics and is responsible for the emergence of macroscopic classicality. Assessing the validity of these models is extremely challenging because it is nontrivial to discriminate unambiguously their presence in experiments where other hardly controllable sources of noise compete to the overall decoherence. Here we provide a simple procedure that is able to probe the hypothetical presence of the collapse noise with a levitated nanosphere in a Fabry-P\'erot cavity. We show that the stationary state of the system is particularly sensitive, under specific experimental conditions, to the interplay between the trapping frequency, the cavity size, and the momentum diffusion induced by the collapse models, allowing one to detect them even in the presence of standard environmental noises.
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 basic strategy underlying models of spontaneous wave function collapse (collapse models) is to modify the Schrödinger equation by including nonlinear stochastic terms, which tend to localize wave functions in space in a dynamical manner. These terms have negligible effects on microscopic systems—therefore their quantum behaviour is practically preserved. On the other end, since the strength of these new terms scales with the mass of the system, they become dominant at the macroscopic level, making sure that wave functions of macro-objects are always well-localized in space. We will review these basic features. By changing the dynamics of quantum systems, collapse models make predictions, which are different from standard quantum mechanical predictions. Although they are difficult to detect, we discuss the most relevant scenarios, where such deviations can be observed.
There are few proposals, which explicitly allow for (experimentally testable) deviations from standard quantum theory. Collapse models are among the most-widely studied proposals of this kind. The Schrödinger equation is modified by including nonlinear and stochastic terms, which describe the collapse of the wave function in space. These spontaneous collapses are rare for microscopic systems, hence their quantum properties are left almost unaltered. On the other hand, collapses become more and more frequent, the larger the object, to the point that macroscopic superpositions are rapidly suppressed. The main features of collapse models will be reviewed. An update of the most promising experimental tests will be presented.
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.
An open problem in modern physics is why microscopic quantum objects can be at two places at once (i.e. a superposed quantum state) while macroscpoic classical object never show such a behaviour. Collapse models provides a quantitative answer for this problem and explain how macroscopic classical world emerges out of microscopic quantum world. A universal noise field is postulated in collapse models, inducing appropriate Brownian- motion corrections to standard quantum dynamics. The strength of collapse-driven Brownian fluctuations depend on: (i) the parameters characterizing the system (e.g., mass, size, density), and (ii) two phenomenological parameters defining the statistical properties of the collapse noise. The collapse-driven Brownian motion works such that microscopic systems behave quantum mechanically, while macroscopic objects are classical. At the intermediate mesocopic scale, collapse models predict deviations from standard quantum predictions. This issue has been subject of experimental tests. All experiments to date have been at the scales where collapse effects are negligible for all practical purposes. However, recent experimental progress in revealing quantum features of larger objects, increases the hope for testing at unprecedented scales where collapse models can be falsified. Current experiments are mainly focused on the preparation of macroscopic systems in a spatial quantum superposition state. The collapse effects would then manifest as loss of visibility in the observed inference pattern. However, one needs a quantum interference with single particles of mass ∼ 10 10 amu for a decisive test of collapse models. Creating such massive superpositionsis quite challenging, and beyond currectstate-of-the-art. Quite recently, an alternative approach has been proposed where the collapse manifests in the fluctuating properties of light interacting with the quantum system. The great advantage of this new approach is that here there is no need for the preparation of a quantum superposed state. It has been discussed that promising results can be revealed in the spectrum of light interacting with a radiation pressure-driven mechanical oscillator in a cavity optomechanics setting. Here, we review the theoretical modelling of the above optomechenical proposal. We discuss how collapse-driven Brownian motion modifies the spectrum. We quantify the collapse effect and explain how it depends on the parameters of the mechanical oscillator (e.g., mass, density, geometry).