Experimental study of the relation between many-body thermalization and localization by directly measuring out-of-time-ordered commutators

ANALIA ZWICK; M. C. RODRIGUEZ; GONZALO A. ALVAREZ; F. DOMINGUEZ

Congreso; Quantum foundation and quantum information; 2019

The dynamics of many-body quantum systems present very interesting features. We study the feasibility to control large quantum systems when control is notperfect. We study a quantum many-body system using 1H spins from a polycrystalline sample of adamantane. We construct a Hamiltonian H 0 that createsclusters of correlated spins and we add a tuneable transversal field as a perturbation. We measure the temporal evolution of the cluster size of correlated spinsafter the perturbed Hamiltonian evolved in time, using multiple-quantum coherence techniques based on a time-reversed evolution. We observe that thecluster-size increases indefinitely as a function of time but its rate reduces with the perturbation strength. We then evolve the system forward in time with thetotal Hamiltonian and then we revert in time only H 0 . This procedure allows us to define a generalized fidelity that compares the density matrix of the perturbedevolution with the unperturbed one. We observe localization effects on the dynamics of the second moment of the generalized fidelity as a function of thecoherence order. These results sheeds new light about the possibility to control large quantum systems under realistic conditions like imperfect control.