# Loschmidt echo in many-spin systems: a quest for intrinsic decoherence and emergent irreversibility

## TL;DR

This paper explores the Loschmidt echo in many-spin systems, linking experimental spin dynamics with theoretical concepts of irreversibility and decoherence, and introduces a new approach using complex initial states to study system fragility.

## Contribution

It introduces a new framework for analyzing Loschmidt echo with complex initial states, connecting experimental protocols to theoretical models of irreversibility and decoherence.

## Key findings

- Increased initial state complexity leads to greater fragility against perturbations.
- The proposed global LE formalism relates many-body wave function overlaps to experimental observables.
- The study offers new insights for designing experiments to probe quantum irreversibility.

## Abstract

If a magnetic polarization excess is locally injected in a crystal of interacting spins, this "excitation" would spread as consequence of spin-spin interactions. Such an apparently irreversible process is known as spin diffusion and it can lead the system back to "equilibrium". Even so, a unitary quantum dynamics would ensure a precise memory of the non-equilibrium initial condition. Then, if at certain time, say $t/2$, an experimental protocol reverses the many-body dynamics, it would drive the system back to the initial non-equilibrium state at time $t$. As a matter of fact, the reversal is always perturbed by small experimental imperfections and/or uncontrolled internal or environmental degrees of freedom. This limits the amount of signal $M(t)$ recovered locally at time $t$. The degradation of $M(t)$ accounts for these perturbations, which can also be seen as the sources of decoherence. This idea defines the Loschmidt echo (LE), which embodies the various time-reversal procedures implemented in nuclear magnetic resonance. Here, we present an invitation to the study of the LE following the pathway induced by the experiments. With such a purpose, we provide a historical and conceptual overview that briefly revisits selected phenomena that underlie the LE dynamics, ultimately leading to the discussion of irreversibility as an emergent phenomenon. In addition, we introduce the LE formalism by means of spin-spin correlation functions and we present new results that could trigger new experiments and theoretical ideas. In particular, we propose to transform an initially localized excitation into a more complex initial state, enabling a dynamically prepared LE. This induces a global definition of the LE in terms of the raw overlap between many-body wave functions. Our results show that as the complexity of the prepared state increases, it becomes more fragile towards small perturbations.