Gaussian to Exponential Crossover in the Attenuation of Polarization Echoes in NMR

An ingenious pulse sequence devised by S. Zhang, B. H. Meier, and R. R. Ernst (Phys. Rev. Lett. {\bf 69}, 2149 (1992)) reverses the time evolution (``spin diffusion'') of the local polarization in a dipolar coupled $^{1}$H spin system. This refocusing originates a Polarization Echo whose amplitude attenuates by increasing the time $t_R$ elapsed until the dynamics is reversed. Different functional attenuations are found for a set of dipolar coupled systems: ferrocene, (C$_5$H$_5$)$_2$Fe, cymantrene, (C$_5$H$_5$)Mn(CO)$_3$, and cobaltocene, (C$_5$H$_5$)$_2$Co. To control a relevant variable involved in this attenuation a pulse sequence has been devised to progressively reduce the dipolar dynamics. Since it reduces the evolution of the polarization echo it is referred as REPE sequence. Two extreme behaviors were found while characterizing the materials: In systems with a strong source of relaxation and slow dynamics, the attenuation follows an exponential law (cymantrene). In systems with a strong dipolar dynamics the attenuation is mainly Gaussian. By the application of the REPE sequence the characteristic time of the Gaussian decay is increased until the presence of an underlying dissipative mechanism is revealed (cobaltocene). For ferrocene, however, the attenuation remains Gaussian within the experimental time scale. These two behaviors suggest that the many body quantum dynamics presents an extreme intrinsic instability which, in the presence of small perturbations, leads to the onset of irreversibility. This experimental conclusion is consistent with the tendencies displayed by the numerical solutions of model systems.Comment: 7 pages + 7 Postscript figure

Spin projection chromatography

We formulate the many-body spin dynamics at high temperature within the non-equilibrium Keldysh formalism. For the simplest XY interaction, analytical expressions in terms of the one particle solutions are obtained for linear and ring configurations. For small rings of even spin number, the group velocities of excitations depend on the parity of the total spin projection. This should enable a dynamical filtering of spin projections with a given parity i.e. a Spin projection chromatography.Comment: 13 pages, 3 figure

Attenuation of polarization echoes in NMR: A study of the emergence of dynamical irreversibility in many-body quantum systems

The reversal of the time evolution of the local polarization in an interacting spin system involves a sign change of the effective dipolar Hamiltonian which refocuses the 'spin diffusion' process generating a polarization echo. Here, the attenuation of these echo amplitudes as a function of evolution time is presented for cymantrene and ferrocene polycrystalline samples, involving one and two five spin rings per molecule respectively. We calculate the fraction of polarization which is not refocused because only the secular part of the dipolar Hamiltonian is inverted. The results indicate that, as long as the spin dynamics is restricted to a single ring, the non-inverted part of the Hamiltonian is notable by itself to explain the whole decay of the polarization echoes. A cross over from exponential (cymantrene) to Gaussian (ferrocene) attenuation is experimentally observed. This is attributed to an increase of the relative importance of the spin dynamics, as compared with irreversible interactions, which favors dynamical irreversibility.Comment: 6 pages in Revtex, 11 Postscript figures. Final versio

Decoherence as attenuation of mesoscopic echoes in a spin-chain channel

An initial local excitation in a confined quantum system evolves exploring the whole system, returning to the initial position as a mesoscopic echo at the Heisenberg time. We consider a two weakly coupled spin chains, a spin ladder, where one is a quantum channel while the other represents an environment. We quantify decoherence in the quantum channel through the attenuation of the mesoscopic echoes. We evaluate decoherence rates for different ratios between sources of amplitude fluctuation and dephasing in the inter-chain interaction Hamiltonian. The many-body dynamics is seen as a one-body evolution with a decoherence rate given by the Fermi golden rule.Comment: 12 pages, 7 figure

Quantum parallelism as a tool for ensemble spin dynamics calculations

Efficient simulations of quantum evolutions of spin-1/2 systems are relevant for ensemble quantum computation as well as in typical NMR experiments. We propose an efficient method to calculate the dynamics of an observable provided that the initial excitation is "local". It resorts a single entangled pure initial state built as a superposition, with random phases, of the pure elements that compose the mixture. This ensures self-averaging of any observable, drastically reducing the calculation time. The procedure is tested for two representative systems: a spin star (cluster with random long range interactions) and a spin ladder.Comment: 5 pages, 3 figures, improved version of the manuscrip

Perfect state transfers by selective quantum interferences within complex spin networks

We present a method that implement directional, perfect state transfers within a branched spin network by exploiting quantum interferences in the time-domain. That provides a tool to isolate subsystems from a large and complex one. Directionality is achieved by interrupting the spin-spin coupled evolution with periods of free Zeeman evolutions, whose timing is tuned to be commensurate with the relative phases accrued by specific spin pairs. This leads to a resonant transfer between the chosen qubits, and to a detuning of all remaining pathways in the network, using only global manipulations. As the transfer is perfect when the selected pathway is mediated by 2 or 3 spins, distant state transfers over complex networks can be achieved by successive recouplings among specific pairs/triads of spins. These effects are illustrated with a quantum simulator involving 13C NMR on Leucine's backbone; a six-spin network.Comment: 5 pages, 3 figure