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

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.