Gravitational waves decohere quantum superpositions

TL;DR

The paper investigates how a classical gravitational field can decohere a quantum spatial superposition, using a distant gravitational-wave burst as the perturbation. It develops a framework that combines a local Minkowski-space decoherence description with an external wave burst, separating decoherence into memory (soft gravitons) and oscillatory (hard gravitons) channels and showing memory-dominated behavior. The leading decoherence matches a quadrupole-based estimate, while a quantum (quantised gravity) treatment reveals a small next-order correction, and the oscillatory part is strongly phase-dependent and suppressed. An electromagnetic analogue is discussed, illustrating the universality of memory-driven decoherence across gauge theories.

Abstract

Understanding the interplay between quantum mechanical systems and gravity is a crucial step towards unifying these two fundamental ideas. Recent theoretical developments have explored how global properties of spacetime would cause a quantum spatial superposition to lose coherence. In particular, this loss of coherence is closely related to the memory effect, which is a prominent feature of gravitational radiation. In this work, we explore how a burst of gravitational radiation from a far-away source would decohere a quantum superposition. We identify the individual contributions to the decoherence from the memory and oscillatory components of the gravitational wave source, corresponding to soft and hard graviton emissions, respectively. In general, the memory contributions dominate, while the oscillatory component of the decoherence is strongly dependent on the phase of the burst when it is switched off. This work demonstrates how quantum systems can lose coherence from interactions with a classical gravitational field. We also comment on the electromagnetic analogue of this effect and discuss its correspondence to the gravitational case.

Figures (2)

• Figure 1: The setup of the modified gedankenexperiment we consider in this paper. (a) A gravitational wave source at distance $R \gg d(t)$ from Alice emits a burst of gravitational radiation incident on her state which generates a time-dependent gravitational quadrupole, causing her to emit gravitational radiation. (b) Displacement between the components of Alice's state for the duration of her experiment. Alice creates the superposition over time $T_1$, initially separating the components by $d_0$ using a Stern-Gerlach device. While she maintains her superposition, she is subject to a gravitational wave burst over time $T_{\text{GW}}<T$, causing her state to oscillate according to $d_{\text{osc}}(t)$ and acquire a permanent displacement $d_{\text{mem}}(t)$ due to memory. After time $T$, she recombines her superposition in time $T_2$ using a reverse Stern-Gerlach device and measures some property of her state.
• Figure 2: (a) $l=2$ mode of the integrand of $\langle N\rangle$. Integrating over positive frequency modes ($\omega>0$) gives the leading-order contribution to the number of gravitons radiated by Alice during her experiment. The 'order-of' integrand displays the same low-frequency behaviour as the full integrand without the approximation. Frequency modes with $\omega \ll 1$ dominate the integral in both cases. (b) Comparison of the full Fourier transform $|\hat{d^2}(\omega)|^2$ and the 'order-of' estimate taken by approximating $\sin(\omega T/2) \sim 0$ and $\sin^2(\omega T/2) \sim 1/2$. The 'order-of' estimate changes the infrared structure of the Fourier transform by introducing a pole at $\omega = 0$. This divergent behaviour is unproblematic with an appropriate low-frequency cutoff $\omega_{\text{IR}} > 0$. The values used here only serve to demonstrate the generic behaviour of the integrand of $\langle N\rangle$ and the Fourier transform $\hat{d^2}(\omega)$.