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Physical Review A

Relaxation of coherent states in a two-qubit NMR quadrupole system

Roberto S. Sarthour, Eduardo Ribeiro DeAzevedo, Fábio Aurélio Bonk, Édson Luiz Gea Vidoto, Tito José Bonagamba, Alberto Passos Guimarães, Jair C. C. Freitas, Ivan S. Oliveira

Published Aug 22, 2003• 24 citations
Publisher

Abstract

We report a detailed study of the longitudinal relaxation of several coherent states on the nuclear-magnetic-resonance (NMR) two-qubit quadrupole system, ${}^{23}\mathrm{Na}$ (spin 3/2) in a lyotropic liquid-crystal system at room temperature. Relaxation of pseudopure states, simulated pseudo-Bell states and Hadamard states were investigated. The coherence of superposition states was verified by applying the respective quantum ``reading'' operators and comparing the recovered state with the original one. The degree of recovery varies between $\ensuremath{\approx}70%$ and $\ensuremath{\approx}100%,$ depending on the time length of the gate, as compared to relaxation times. Spin-lattice relaxation results follow a recently proposed multiexponential model that includes mixed magnetic dipolar and electric quadrupolar interactions. Relaxation curves are governed by initial conditions, and from the experimental curves individual transition rates are derived. The transverse relaxation time constant ${T}_{2}$ is found not to depend on the initial distribution of populations. This is a systematic study of relaxation in the context of NMR quantum computing.

DOI
10.1103/physreva.68.022311

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We have produced and characterized spin-squeezed states at a temperature of 26 °C in a nuclear magnetic resonance quadrupolar system. The experiment was carried out on 133Cs nuclei of spin I=7/2 in a sample of lyotropic liquid crystal. The source of spin squeezing was identified as the interaction between the quadrupole moment of the nuclei and the electric field gradients present within the molecules. We use the spin angular momentum representation to describe formally the nonlinear operators that produce the spin squeezing on a Hilbert space of dimension 2I+1=8. The quantitative and qualitative characterization of this spin-squeezing phenomenon is expressed by a squeezing parameter and squeezing angle developed for the two-mode Bose-Einstein condensate system, as well as by the Wigner quasiprobability distribution function. The generality of the present experimental scheme points to potential applications in solid-state physics.