Experimental Blueprint for Distinguishing Decoherence from Objective Collapse

TL;DR

This work tackles whether macroscopic quantum superpositions decay solely via environmental decoherence or also due to an intrinsic collapse mechanism. It develops a unified theoretical framework for generating tunable Schrödinger-cat states in a levitated nanosphere, embedding both calibrated environmental diffusion and a CSL term within a single master equation, and analyzes data with Bayesian model discrimination. The key contributions include a concrete, experimentally feasible protocol to detect CSL signatures—specifically saturation of the decoherence rate with separation and a quadratic mass scaling—alongside a rigorous procedure to distinguish such signals from calibrated noise. The approach aims to convert the quantum–classical boundary problem into a falsifiable test that could either reveal new physics beyond standard quantum mechanics or establish the strongest bounds on CSL to date, with clear metrological targets for pressure, temperature, and mass.

Abstract

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.

Figures (9)

• Figure 1: Experimental concept and protocol.(A) System schematic: A dielectric nanosphere of mass $m$ is levitated at the waist of an optical dipole trap (Gaussian profile). An internal two-level system (TLS, defect center) enables conditional control of the center-of-mass (COM) motion along $x$. The superposition separation is $\Delta x = 2|\alpha|x_{\mathrm{zpf}}$; insets show the ground state $\lvert 0\rangle$ and a cat state $\lvert \alpha\rangle + \lvert -\alpha\rangle$. (B) Cat-state generation: A spin–motion circuit implements $H \rightarrow U_{\text{gate}} \rightarrow H \rightarrow M$, where $H$ is a Hadamard on the TLS, $U_{\text{gate}}$ is a conditional displacement that entangles the TLS with the COM, and $M$ is a projective measurement (post-selection) preparing $\lvert \text{cat}\rangle \propto \lvert \alpha\rangle + \lvert -\alpha\rangle$. (C) Decoherence channels: Environmental noise sources acting on the spatial superposition: residual-gas collisions, blackbody emission/absorption/scattering, and a phenomenological CSL noise field. (D) Coherence readout: Time-resolved interference visibility showing fringe contrast fading from $t=0$ to $t=\tau$ and $t=2\tau$; the coherence $C(t)$ decays with the total rate set by calibrated environmental diffusion and any additional collapse contribution.
• Figure 2: Total decoherence rate $\Gamma(\Delta x)$ as a function of superposition size for nanoparticles of different masses. Environmental decoherence (dashed lines) rises quadratically with $\Delta x$, while the CSL contribution (solid lines) saturates for separations beyond the CSL correlation length of $r_C = 100~\mathrm{nm}$, forming a characteristic plateau. This plateau serves as a key signature of the collapse model. The simulation uses a particle mass of $m = 1.0\times10^{-17}~\mathrm{kg}$, a CSL rate of $\lambda_{\text{CSL}} = 10^{-21}~\mathrm{s^{-1}}$, a trap frequency of $\Omega = 2\pi \times 10^5~\mathrm{rad/s}$, and a reference mass of $m_0 = 1.66\times10^{-27}~\mathrm{kg}$ (atomic mass unit).
• Figure 3: Mass scaling of the maximum CSL decoherence rate, $\Gamma_{\text{CSL,max}}$. The predicted quadratic dependence on mass $m$ (solid line) differs qualitatively from typical environmental decoherence trends (dashed line), defining a critical mass region between $10^7$ and $10^8$ atomic mass units where CSL effects may become dominant. The simulation assumes a CSL rate of $\lambda_{\text{CSL}} = 10^{-16}~\mathrm{s^{-1}}$, a mass range of $m/m_0 = 10^{3}$--$10^{6}$, and a correlation length of $r_C = 100~\mathrm{nm}$.
• Figure 4: Time evolution of coherence $C(t)$ for a nanoparticle of mass $10^{-17}~\mathrm{kg}$. The CSL-induced decoherence (red curve) produces a subtle but cumulative excess decay relative to the environmental prediction (black curve, shown with a $\pm 20\%$ uncertainty band). The simulation parameters are an environmental decoherence rate of $\Gamma_{\text{env}} = 0.10~\mathrm{s^{-1}}$, a CSL-induced rate of $\Gamma_{\text{CSL}} = 0.03~\mathrm{s^{-1}}$ (for $\lambda_{\text{CSL}} = 10^{-21}~\mathrm{s^{-1}}$ and $r_C = 100~\mathrm{nm}$), and a total evolution time of $t_{\max} = 14~\mathrm{s}$.
• Figure 5: Joint posterior over collapse rate and environmental diffusion. Filled contours show the normalized posterior density $P\!\left(\log_{10}\lambda_{\mathrm{CSL}},\,D_{pp}\mid\mathrm{data}\right)$. The solid (dashed) line encloses the $68\%$ ($95\%$) highest-posterior-density region. The marker denotes the maximum a posteriori (MAP) point. This figure highlights the correlation between the collapse parameter and the calibrated environmental diffusion, demonstrating how independent calibration of $D_{pp}$ sharpens inference on $\lambda_{\mathrm{CSL}}$.