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arXiv:2401.04665 · New Journal of Physics

Experimental bounds on linear-friction dissipative collapse models from levitated optomechanics

Giovanni Di Bartolomeo, Matteo Carlesso

Published Mar 27, 2024• 3 citations
arXivHTMLPDF

Abstract

Abstract Collapse models constitute an alternative to quantum mechanics that solve the well-know quantum measurement problem. In this framework, a novel approach to include dissipation in collapse models has been recently proposed, and awaits experimental scrutiny. Our work establishes experimental bounds on the so-constructed linear-friction dissipative Diósi-Penrose (dDP) and Continuous Spontaneous localisation (dCSL) models by exploiting experiments in the field of levitated optomechanics. Our results in the dDP case exclude collapse temperatures below 10−13 K and 6 × 10 − 12 K respectively for values of the localisation length smaller than 10−6 m and 10−8 m. In the dCSL case the entire parameter space is excluded for values of the temperature lower than 6 × 10 − 9 K.

DOI
10.1088/1367-2630/ad3842

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Abstract Collapse models constitute an alternative to quantum mechanics that solve the well-know quantum measurement problem. In this framework, a novel approach to include dissipation in collapse models has been recently proposed, and awaits experimental scrutiny. Our work establishes experimental bounds on the so-constructed linear-friction dissipative Diósi-Penrose (dDP) and Continuous Spontaneous localisation (dCSL) models by exploiting experiments in the field of levitated optomechanics. Our results in the dDP case exclude collapse temperatures below 10−13 K and 6 × 10 − 12 K respectively for values of the localisation length smaller than 10−6 m and 10−8 m. In the dCSL case the entire parameter space is excluded for values of the temperature lower than 6 × 10 − 9 K.
We present experimental tests of dissipative extensions of spontaneous wave function collapse models based on a levitated micromagnet with ultralow dissipation. The spherical micromagnet, with radius R = 27 µm, is levitated by Meissner effect in a lead trap at 4.2 K and its motion is detected by a SQUID. We perform accurate ringdown measurements on the vertical translational mode with frequency 57 Hz, and infer the residual damping at vanishing pressure γ/2π < 9 µHz. From this upper limit we derive improved bounds on the dissipative versions of the CSL (continuous spontaneous localization) and the DP (Di´osi-Penrose) models. In particular, dissipative models give rise to an intrinsic damping of an isolated system with the effect parameterized by a temperature constant – the dissipative CSL model with temperatures below 1 nK is ruled out, while the dissipative DP model is excluded for temperatures below 10−13 K. Furthermore, we present the first bounds on dissipative effects in a more recent model, which relates the wave function collapse to fluctuations of a generalized complex-valued spacetime metric.
Abstract We present a simple derivation of the interference pattern in matter-wave interferometry predicted by a class of quantum master equations. We apply the obtained formulae to the following collapse models: the Ghirardi–Rimini–Weber (GRW) model, the continuous spontaneous localization (CSL) model together with its dissipative (dCSL) and non-Markovian generalizations (cCSL), the quantum mechanics with universal position localization (QMUPL), and the Diósi–Penrose (DP) model. We discuss the separability of the dynamics of the collapse models along the three spatial directions, the validity of the paraxial approximation, and the amplification mechanism. We obtain analytical expressions both in the far field and near field limits. These results agree with those already derived in the Wigner function formalism. We compare the theoretical predictions with the experimental data from two recent matter-wave experiments: the 2012 far-field experiment of Juffmann T et al (2012 Nat. Nanotechnol . 7 297–300) and the 2013 Kapitza–Dirac–Talbot–Lau (KDTL) near-field experiment of Eibenberger et al (2013 Phys. Chem. Chem. Phys . 15 14696–700). We show the region of the parameter space for each collapse model that is excluded by these experiments. We show that matter-wave experiments provide model-insensitive bounds that are valid for a wide family of dissipative and non-Markovian generalizations.
Standard objective collapse models offer a unified approach to the quantum measurement problem but predict an unphysical, indefinite increase in the energy of the system. The dissipative Diósi-Penrose (dDP) model resolves this heating issue by introducing a linear friction mechanism. However, this modification induces complex, non-Gaussian phase-space dynamics. We rigorously establish the thermodynamic consistency of this friction mechanism -- extended to the CSL model -- across both weakly and strongly non-Gaussian regimes. Using the Wigner phase-space formalism, we go significantly beyond the quadratic approximation and, to bypass the failure of perturbative methods under strong dissipation, introduce a novel exact pseudo-spectral simulation approach. Our analysis reveals that the system subjected to the dDP mechanism does not thermalize, but rather settles into a non-equilibrium steady-state (NESS) where the asymptotic non-Gaussianity scales as the third power of the dissipation parameter βββ. By evaluating the Wigner entropy production, we confirm the thermodynamic validity of the model and demonstrate that highly sensitive information-theoretic quantities require exact numerical methods to accurately capture the key non-Gaussian tails of the distribution.
We construct and study the simplest universal dissipative Lindblad master equation for many-body systems with the purpose of a new dissipative extension of existing nonrelativistic theories of fundamental spontaneous decoherence and spontaneous wave function collapse in nature. It is universal as it is written in terms of second-quantized mass density $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\varrho}}$ and current $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbf{J}}$, thus making it independent of the material structure and its parameters. Assuming linear friction in the current, we find that the dissipative structure is strictly constrained. Following the general structure of our dissipative Lindblad equation, we derive and analyze the dissipative extensions of the two most known spontaneous wave function collapse models, the Di\'osi-Penrose and the continuous spontaneous localization models.
The possibility that the collapse of the wave function in quantum mechanics is real and ultimately connected to (classical) gravity has been debated for decades with main contributions by Diósi and Penrose (DP). In particular, Diósi proposed a noise-based dynamical reduction model, which captures the same order of magnitudes for the collapse time suggested by Penrose based on heuristic arguments. This is known in the literature as the DP model (Diósi–Penrose). A peculiarity of the DP model is the prediction of spontaneous heating of matter, which can be tested without the need for massive quantum superpositions. Notably, a very similar effect is predicted by recent theoretical approaches to gravity as a classical-only information channel. Here, we reconsider the current constraints on the DP model from spontaneous heating by analyzing experimental situations not properly considered before. We argue that the parameter-free version of the DP model is close to be ruled out by standard heat leak measurements at ultralow temperatures with a conclusive exclusion likely within reach with existing technology. This result would strengthen a recent claim of exclusion inferred by spontaneous x-ray emission experiments, which relies on the somewhat stronger assumption that the DP noise field is white up to x-ray frequencies.