Tracking Quantum State Collapse/Decoherence in Real Time via a Superposition Trap

TL;DR

This work tackles the long-standing measurement problem by proposing the superposition trap, a mechanism that exploits the quantum continuity equation to spatially confine coherent superpositions while permitting collapsed or decohered components to escape. The authors develop the theory around probability-density continuity, introducing the concept of a probability density bubble formed by boundaries where $|\psi|^2=0$, and show how coherent states can be noninvasively monitored through leakage dynamics. They present two concrete realizations: an optical analogue based on a Mach-Zehnder interferometer with a one-way boundary, and a practical atom-interferometry implementation using strontium with internal-state-selective transitions to separate collapsed components. The approach enables real-time probing of collapse mechanisms and decoherence rates, with potential to bound objective-collapse models such as CSL and to illuminate the quantum-to-classical transition, while offering generalization to other quantum platforms and control strategies.

Abstract

We propose a novel method for probing quantum state collapse and decoherence in real time using a mechanism we term the superposition trap. This approach exploits the continuity equation in quantum mechanics to engineer a configuration that spatially confines only coherent superpositions, while allowing decohered or collapsed states to escape. By monitoring this leakage, the dynamics of collapse processes-whether environmentally induced or intrinsic to objective collapse models-can be experimentally accessed without disturbing the coherent evolution itself. We outline a concrete implementation using an atom interferometer with strontium atoms, where internal-state-selective operations enable physical separation of collapsed components. This technique offers a new experimental avenue to test collapse models, measure decoherence rates, and investigate the quantum-to-classical transition.

Figures (7)

• Figure 1: This figure demonstrates the abstract goal of a superposition trap, physically separating the collapsed state from the superposition state.
• Figure 2: Top figure shows the radial wavefunction $R_{20}(r)$ and radial probability density $r^{2}\lvert R_{20}(r)\rvert^{2}$ of the hydrogen $2s$ state (atomic units). The vertical dashed line marks the radial node at $r = 2 a_{0}$. Bottom figure shows logarithmically scaled density plot of $\lvert \psi_{2s}(x,y,z\!=\!0) \rvert^{2}$ for the hydrogen $2s$ orbital in the plane $z=0$ (atomic units). Node can be clearly seen as a dark ring.
• Figure 3: Abstract figure represents the continuity constraint. If the surface is made of zero probability points then the probability density is contained by the closed surface
• Figure 4: The schematic represents the schematic of the optical trap. In the ideal case the light will be trapped between $M3$ and one way mirror, as long as it remains coherent. On the other hand, light can be detected at $D1$ and $D2$ when there is decoherence while traversing through the interferometer. Thus, $D1$ and $D2$ only detects the collapsed state.
• Figure 5: Schematic diagram illustrating the energy levels of the strontium atom relevant to our discussion boyd2007high.