# Quantum sensors for the generating functional of interacting quantum field theories

## TL;DR

This paper proposes a quantum-sensing protocol using trapped ions to measure the generating functional of interacting quantum field theories, enabling insights into complex in or out of equilibrium phenomena in condensed matter and high-energy physics.

## Contribution

It introduces a novel collective interferometric scheme that generalizes Schwinger sources for probing quantum field theories with trapped ion quantum simulators.

## Key findings

- Protocol can measure the generating functional of interacting quantum fields.
- Feasible implementation with trapped ion crystals as analog quantum simulators.
- Provides a new method to explore out-of-equilibrium quantum phenomena.

## Abstract

Difficult problems described in terms of interacting quantum fields evolving in real time or out of equilibrium are abound in condensed-matter and high-energy physics. Addressing such problems via controlled experiments in atomic, molecular, and optical physics would be a breakthrough in the field of quantum simulations. In this work, we present a quantum-sensing protocol to measure the generating functional of an interacting quantum field theory and, with it, all the relevant information about its in or out of equilibrium phenomena. Our protocol can be understood as a collective interferometric scheme based on a generalization of the notion of Schwinger sources in quantum field theories, which make it possible to probe the generating functional. We show that our scheme can be realized in crystals of trapped ions acting as analog quantum simulators of self-interacting scalar quantum field theories.