Spin systems as quantum field theories in inflationary universe: A study with Unruh-DeWitt detectors

TL;DR

This paper demonstrates how spin systems can simulate quantum field theories in an inflationary universe, allowing experimental probing of thermal properties like the Gibbons-Hawking temperature using quantum detectors.

Contribution

It introduces a method to map QFT in an inflationary universe onto spin systems and shows how a spin-based Unruh-DeWitt detector can measure thermal effects.

Findings

Detector response approaches QFT predictions with increasing spin sites

Thermal distribution with temperature H/(2π) observed in detector response

Quantum simulation platforms can emulate quantum field theory in curved spacetime

Abstract

We propose a method to probe the thermal properties of quantum field theory (QFT) in an inflationary universe simulated by spin systems. Our previous work (arXiv:2410.07587) has demonstrated that QFT of Majorana fermions in an arbitrary two-dimensional spacetime can be mapped onto a spin system. In this study, we apply this mapping to investigate the thermal properties of an inflationary universe. An interaction between a quantum field and a detector allows one to extract information about the quantum field from the excitation probability of the detector, known as the Unruh-DeWitt detector. In an inflationary universe with Hubble constant $H$, the excitation probability of an Unruh-DeWitt detector follows a thermal distribution with temperature $H/(2\pi)$, indicating that a static observer in the inflationary universe perceives a thermal field. We consider a spin system corresponding to QFT in an inflationary universe and introduce a single spin interacting with this system as an Unruh-DeWitt detector. We demonstrate that the detector response asymptotically approaches the result of QFT with an appropriate power of the number of spin sites. Since the dynamics of spin systems can be implemented on programmable quantum simulation platforms, our study offers a concrete route toward experimentally probing the thermal properties of an inflationary universe in controlled quantum settings. This highlights the potential of quantum technologies to emulate and investigate aspects of quantum field theory in curved spacetimes.