Probing quantum many-body dynamics using subsystem Loschmidt echos

TL;DR

This paper introduces the subsystem Loschmidt echo as an experimentally accessible measure to study quantum many-body dynamics, revealing quantum phase transitions, Hilbert space structure, and ergodicity breaking.

Contribution

It demonstrates the experimental use of subsystem Loschmidt echo to probe non-equilibrium dynamics and ergodicity breaking in quantum many-body systems.

Findings

Observation of a dynamical quantum phase transition.

Quantitative determination of the effective Hilbert space dimension.

Experimental evidence of ergodicity breaking due to Hilbert space fragmentation.

Abstract

The Loschmidt echo - the probability of a quantum many-body system to return to its initial state following a dynamical evolution - generally contains key information about a quantum system, relevant across various scientific fields including quantum chaos, quantum many-body physics, or high-energy physics. However, it is typically exponentially small in system size, posing an outstanding challenge for experiments. Here, we experimentally investigate the subsystem Loschmidt echo, a quasi-local observable that captures key features of the Loschmidt echo while being readily accessible experimentally. Utilizing quantum gas microscopy, we study its short- and long-time dynamics. In the short-time regime, we observe a dynamical quantum phase transition arising from genuine higher-order correlations. In the long-time regime, the subsystem Loschmidt echo allows us to quantitatively determine the effective dimension and structure of the accessible Hilbert space in the thermodynamic limit. Performing these measurements in the ergodic regime and in the presence of emergent kinetic constraints, we provide direct experimental evidence for ergodicity breaking due to fragmentation of the Hilbert space. Our results establish the subsystem Loschmidt echo as a novel and powerful tool that allows paradigmatic studies of both non-equilibrium dynamics and equilibrium thermodynamics of quantum many-body systems, applicable to a broad range of quantum simulation and computing platforms.