Loschmidt echo in many-spin systems: contrasting time scales of local and global measurements.

PABLO ZANGARA; DENISE BENDERSKY; PATRICIA R. LEVSTEIN; HORACIO M. PASTAWSKI

PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL AND PHYSICAL SCIENCES

ROYAL SOC

Lugar: Londres; Año: 2016 vol. 374 p. 20150163 - 20150163

0080-4614

Zangara PR, Bendersky D, Levstein PR, Pastawski HM. 2016 Phil. Trans. R. Soc. A 374: 20150163.http://dx.doi.org/10.1098/rsta.2015.0163local excitation in a quantum many-spin system evolves deterministically. A time-reversal procedure,involving the inversion of the signs of every energy and interaction, should produce the excitation revival. This idea, experimentally coined in nuclear magneticresonance, embodies the concept of the Loschmidt echo (LE). While such an  implementation involves a single spin autocorrelation M1,1, i.e. a local LE,theoretical efforts have focused on the study of the recovery probability of a complete many-body state, referred to here as global or many-body LE MMB. Here, we analyse the relation between these magnitudes, with regard to their characteristic time scales and their dependence on the number of spins N. We show that the global LE can be understood, to some extent, as the simultaneous occurrence of N independent local LEs, i.e. MMB ∼(M1,1)N/4. This extensive hypothesis is exact for very short times and confirmed numerically beyond such a regime. Furthermore, we discuss a general picture of the decay of M1,1 as a consequence of the interplay between thetime scale that characterizes the reversible interactions (T2) and that of the perturbation (τΣ). Our analysis suggests that the short-time decay, characterized by the time scale τΣ, is greatly enhanced by the complex processes that occur beyond T2. This would ultimatelylead to the experimentally observed T3, which was found to be roughly independent of τΣ but closely tied to T2.