Entanglement as a tool for ensemble spin dynamics: Application to mesoscopic echoes

ERNESTO P. DANIELI; GONZALO A. ÁLVAREZ; PATRICIA R. LEVSTEIN; HORACIO M. PASTAWSKI

Eilat, Israel

Simposio; The 2005 Minerva-Gentner Symposium - A Dive into Magnetic Resonance; 2005

Minerva-Gentner

The quantum evolution of a (1/2)-spin system of molecular dimensions is becoming interesting due to its potential applications to the field of Quantum Information Processing. The maximum profit would be obtained evolving quantum pure states, however the limitations in its experimental realization and dynamical control stimulate alternative procedures as the mixed state quantum computation [1]. This is the case of a spin ensemble at high temperature, typical in NMR experiments. The evolution of this mixed state is obtained averaging the individual dynamics of each components of the ensemble. Being the number of different realizations equivalent to the Hilbert space dimension, the required evolution demands long computational times. We propose a method that uses only one entangled pure initial state, composed by the superposition with random phases of the pure elements that conform the mixture. This reduces drastically the calculation time reproducing the ensemble evolution. With this tool we study the attenuation of the Mesoscopic Echoes [2] (recurrences associated with the system size) in a spin chain with XY interaction between nearest neighbors that is coupled to a second chain resembling the environment. Considering XY, dipolar, and Heisenberg coupling we obtain an exponential decay for the ME whose characteristic time agrees with the Fermi golden rule.