# Emergent perturbation independent decay of the Loschmidt echo in a many-spin system studied through scaled dipolar dynamics

## TL;DR

This study demonstrates that in many-spin quantum systems, the Loschmidt Echo decay rate becomes independent of perturbations and is governed solely by intrinsic interactions, revealing a fundamental aspect of quantum thermalization.

## Contribution

The paper introduces a protocol to scale coupling strength in a nuclear spin system, showing perturbation-independent decay of Loschmidt Echoes governed by intrinsic interactions.

## Key findings

- Loschmidt Echo decay rate depends only on interactions, not perturbations.
- Scaling coupling strength extends coherence time T2.
- Quantum information scrambling observed via OTOCs and LE metrics.

## Abstract

Evaluating the role of perturbations versus the intrinsic coherent dynamics in driving to equilibrium is of fundamental interest to understand quantum many-body thermalization, in the quest to build ever complex quantum devices. Here we introduce a protocol that scales down the coupling strength in a quantum simulator based on a solid-state nuclear spin system, leading to a longer decay time T2, while keeping perturbations associated to control error constant. We can monitor quantum information scrambling by measuring two powerful metrics, out-of-time-ordered correlators (OTOCs) and Loschmidt Echoes (LEs). While OTOCs reveal quantum information scrambling involving hundreds of spins, the LE decay quantifies, via the time scale T3, how well the scrambled information can be recovered through time reversal. We find that when the interactions dominate the perturbation, the LE decay rate only depends on the interactions themselves, T3 ~ T2, and not on the perturbation. Then, in an unbounded many-spin system, decoherence can achieve a perturbation-independent regime, with a rate only related to the local second moment of the Hamiltonian.