Perturbation Independent Decay of the Loschmidt Echo in a Many-Body System

Abstract

When a qubit or spin interacts with others under a many-body Hamiltonian, the information it containsprogressively scrambles. Here, nuclear spins of an adamantane crystal are used as a quantum simulator tomonitor such dynamics through out-of-time-order correlators, while a Loschmidt echo (LE) asses howweak perturbations degrade the information encoded in these increasingly complex states. Bothobservables involve the implementation of a time-reversal procedure which, in practice, involves invertingthe sign of the effective Hamiltonian. Our protocols use periodic radio frequency pulses to modulate thenatural dipolar interaction implementing a Hamiltonian that can be scaled down at will. Meanwhile,experimental errors and strength of perturbative terms remain constant and can be quantified through theLE. For each scaling factor, information spreading occurs with a timescale,T₂, inversely proportional to thelocal second moment of the Hamiltonian. We find that, when the reversible interactions dominate over theperturbations, the information scrambled among up to10² spins can still be recovered. However, we findthat the LE decay rate cannot become smaller than a critical value 1/T₃~(0.15±0.02)=T₂, which onlydepends on the interactions themselves, and not on the perturbations. This result shows the emergence of aregime of intrinsic irreversibility in accordance to a central hypothesis of irreversibility, hinted fromprevious experiments.