One dimensional many-body dynamics in spin chains detected through multiple quantum coherence NMR experiments

E. RUFEIL FIORI; F. Y. OLIVA; P. R. LEVSTEIN; H. M. PASTAWSKI

Trieste

Conferencia; Conference on Quantum Phenomena in Confined Dimensions; 2007

Abdus Salam International Centre for Theoretical Physics

In this work, we test the dimensionality of the quantum 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 are measured under a double-quantum Hamiltonian 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, 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.  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. 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.