Multiple quantum coherence as detector of one-body one-dimensional dynamics in NMR experiments

ELENA RUFEIL FIORI; FABIANA Y. OLIVA; PATRICIA R. LEVSTEIN; HORACIO M. PASTAWSKI

Paraty, Rio de Janeiro, Brazil

Workshop; International Workshop on Quantum Information Paraty 2007; 2007

Multiple quantum coherence as detector of one-body one-dimensional dynamics in NMR experiments. Elena Rufeil-Fiori, Fabiana Oliva, Patricia R. Levstein, Horacio M. Pastawski.     In this work, we test the one-body dynamics in a network of coupled spins using solid state nuclear magnetic resonance. In particular, one can generate an effective double quantum Hamiltonian (flip-flip + flop-flop) that mixes subspaces with different spin projection creating many-body superposition states: the multiple quantum coherences. These states can be probed through a bidimensional technique that allows one to follow the superposition weights as they are created. Multiple-quantum coherence intensities [1] are measured under a double-quantum Hamiltonian [2] in hydroxyapatite. This system is a quasi-one-dimensional spin chain, as the distance between hydrogen spin chains is about three times larger than the distance between adjacent protons within the chain. As a consequence of the distance dependence of the dipolar interaction and the quantum Zeno effect [3], this should lead to a separation in about three orders of magnitude between the intra and inter-chain time scales. Analytical and numerical methods give exact expressions for the intensities of the multiple-quantum coherences in homogeneous one-dimensional linear chains of nuclear spins 1/2 coupled by nearest neighbor interactions [4].  As occurs with the XY (flip-flop) dynamics [5], the double-quantum dynamics has a simple mapping to non-interacting fermions under a Tight-Binding Hamiltonian [4]. As a consequence, only zero and second order coherences are expected in the case of a homogeneous chain.  As predicted by theory, we find that all the coherences orders above two cancel out. In contrast, the dynamics of the same system under a different effective Hamiltonian shows higher orders of coherence, revealing that this is not a limitation of signal to noise ratio. Decoherence is tested through a form of Loschmidt echo experiment which reveals that in this quasi-1-d system, the double-quantum dynamics presents an exponential decay, in contrast with results in 3-d systems.       References [1] H. G. Krojanski, D Suter, Decoherence in large NMR quantum registers, Phys. Rev. A 74,    062319 (2006). [2] H. Cho, P. Cappellaro, D. G. Cory, C. Ramanathan, Decay of highly correlated spin states in a dipolar-coupled solid: NMR study of CaF2, Phys. Rev. B 74, 224434 (2006). [3] G. A. Álvarez, E. P. Danieli, P. R. Levstein, and H. M. Pastawski, Environmentally induced Quantum Dynamical Phase Transition in the spin swapping operation, Jour. of Chem. Phys. 124, 194507 (2006), cond-mat/0504347 (2005). [4] S. I. Doronin, I. I. Maksimov, E. B. Fel’dman, Multiple-Quantum dynamics of one-dimensional spin systems in solids, Journ. of Exp. and Theor. Phys. 91, 597-609 (2000). [5] E. Rufeil-Fiori, H. M. Pastawski, Non-Markovian decay beyond the Fermi Golden Rule: Survival collapse of the polarization in spin chains, Chem. Phys. Lett. 420, 35-41 (2006), quant-ph/0511176 (2005).