E. B. Fel’dman

Multiple-quantum dynamics of one-dimensional nuclear spin systems in solids

Multiple-quantum spin dynamics is studied using analytic and numerical methods for one-dimensional finite linear chains and rings of nuclear spins 1/2 coupled by dipole-dipole interactions. An approximation of dipole-dipole interaction between nearest neighbors having the same constants is used to obtain exact expressions for the intensities of the multiple-quantum coherences in the spin systems studied, which are initially in thermal equilibrium and whose evolution is described by a two-spin two-quantum Hamiltonian. An approximation of nearest neighbors with arbitrary dipole-dipole interaction constants is used to establish a simple relationship between the multiple-quantum dynamics and the dynamics of spin systems with an XY Hamiltonian. Numerical methods are developed to calculate the intensities of multiple-quantum coherences in multiple-quantum NMR spectroscopy. The integral of motion is obtained to expand the matrix of the two-spin two-quantum Hamiltonian into two independent blocks. Using the nearest-neighbor approximation the Hamiltonian is factorized according to different values of the projection operator of the total spin momentum on the direction of the external magnetic field. Results of calculations of the multiple-quantum dynamics in linear chains of seven and eight nuclear spins and a six-spin ring are presented. It is shown that the evolution of the intensities of the lowest-order multiple-quantum coherences in linear chains is accurately described allowing for dipole-dipole interaction of nearest and next-nearest neighbors only. Numerical calculations are used to compare the contributions of nearest and remote spins to the intensities of the multiple-quantum coherences.

Nonergodic nuclear depolarization in nanocavities

AbstractRecently, it has been observed that the effective dipolar interactions between nuclear spins of spin-carrying molecules of gas in closed nanocavities are independent of the spacing between all the spins. We derive an exact time-dependent polarization for all spins in the spin-1/2 ensemble with spatially independent effective dipolar interactions. If the initial polarization is on a single (first) spin, P1(0)=1, then the exact spin dynamics of the model exhibits periodic short pulses of the polarization of the first spin, typical of systems having a large number N of spins. If N≫1, then within the period 4π/g(2π/g) for odd (even) N-spin clusters, with g standing for spin coupling, the polarization of spin 1 switches quickly from unity to the time-independent value of 1/3 over a time interval of about

Evolution of spin entanglement and an entanglement witness in multiple-quantum NMR experiments

(g\sqrt N )^{ - 1}

Asymmetry of bipartite quantum discord

. Thus, spin 1 spends almost the entire time in the time-independent condition P1(t)=1/3. The period and the width of the pulses determine the volume and the form factor of the ellipsoidal cavity. The formalism is adapted to the case of time-varying nanofluctuations of the volume V(t) of cavitating nanobubbles. If the coupling g(V(t)) is varied by the Gaussian-in-time random noise due to the variation of the volume V(t), then the envelope of the polarization peaks passes irreversibly to 1/3. The polarization dynamics of a single spin exhibit a Gaussian (exponential) time dependence when the correlation time of fluctuations of the nanovolume is larger (smaller) than, 〈(δ g)2〉−1/2 where 〈(δg)2〉 is the variance of the g(V(t)) coupling. Finally, we report exact calculations of the NMR line shape for the N-spin gaseous aggregate.

Dipolar temperature and multiple-quantum NMR dynamics in dipolar ordered-spin systems

We consider the multiple quantum (MQ) NMR dynamics of a gas of spin carrying molecules in nanocavities. MQ NMR dynamics is determined by the residual dipole-dipole interactions which are not averaged completely due to the molecular diffusion in nanopores. Since the averaged nonsecular Hamiltonian describing MQ NMR dynamics depends on only one coupling constant, this Hamiltonian commutes with the square of the total spin angular momentum Î. We use the basis of common eigenstates of Î and the projection of I on the external magnetic field for investigation of MQ NMR dynamics. This approach allows us to study MQ NMR dynamics in systems consisting of several hundreds of spins. The analytical approximation of the stationary profile of MQ coherences is obtained. The analytical expressions for MQ NMR coherence intensities of the five-spin system in a nanopore are found. Numerical investigations allow us to find the dependencies of intensities of MQ coherences on their orders (the profiles of MQ coherences) in systems consisting of 600 spins and even more. It is shown that the stationary MQ coherence profile in the considered system is an exponential one.We consider the multiple quantum (MQ) NMR dynamics of a gas of spin carrying molecules in nanocavities. MQ NMR dynamics is determined by the residual dipole-dipole interactions, which are not averaged completely due to the molecular diffusion in nanopores. Since the averaged nonsecular Hamiltonian describing MQ NMR dynamics depends on only one coupling constant, this Hamiltonian commutes with the square of the total spin angular momentum I2. We use the basis of common eigenstates of I2 and the projection of I on the external magnetic field for investigation of MQ NMR dynamics. This approach allows us to study MQ NMR dynamics in systems consisting of several hundreds of spins. The analytical approximation of the stationary profile of MQ coherences is obtained. The analytical expressions for MQ NMR coherence intensities of the five-spin system in a nanopore are found. Numerical investigations allow us to find the dependencies of intensities of MQ coherences on their orders (the profiles of MQ coherences) ...

Exact solutions in the dynamics of alternating open chains of spins s = 1/2 with the XY Hamiltonian and their application to problems of multiple-quantum dynamics and quantum information theory

We investigate the evolution of entanglement in multiple-quantum (MQ) NMR experiments in crystals with pairs of close nuclear 1/2-spins. The initial thermodynamic equilibrium state of the system in a strong external magnetic field evolves under the nonsecular part of the dipolar Hamiltonian. As a result, MQ coherences of the zeroth and plus/minus second orders appear. A simple condition for the emergence of entanglement is obtained. We show that the measure of the spin-pair entanglement—concurrence—coincides qualitatively with the intensity of MQ coherences of the plus/minus second order and, hence, the entanglement can be studied with MQ NMR methods. We introduce an entanglement witness using MQ NMR coherences of the plus/minus second order.

NMR line shapes of a gas of nuclear spin-12 molecules in fluctuating nano-containers

Entanglement is studied in an open alternating chain of nuclear spins s = 1/2 with spin-spin couplings in an external magnetic field under the thermodynamic equilibrium conditions. A reduced density matrix has been calculated for an arbitrarily chosen spin pair. The entanglement of the spin pair has been estimated according to the Wootters criterion. The temperature at which an entangled state appears in a chosen pair has been determined. It has been shown that the numerical characteristics of the entanglement are oscillating functions of the position of the spin pair in the chain.

Exact results on spin dynamics and multiple quantum NMR dynamics in alternating spin-1/2 chains with XY Hamiltonian at high temperatures

It is known from the analysis of the density matrix for bipartite systems that the quantum discord (as a measure of quantum correlations) depends on the particular subsystem chosen for the projective measurements. We study asymmetry of the discord in a simple physical model of two spin-1/2 particles with the dipole-dipole interaction governed by the XY Hamiltonian in the inhomogeneous magnetic field. The dependence of the above discord asymmetry on the Larmour frequencies at both T = 0 (the ground state) and T > 0 has been investigated. It is demonstrated, in particular, that the asymmetry is negligible for high temperatures but it may become significant with the decrease in temperature.It is known from the analysis of the density matrix for bipartite systems that the quantum discord (as a measure of quantum correlations) depends on the particular subsystem chosen for the projective measurements. We study asymmetry of the discord in a simple physical model of two spin-1/2 particles with the dipole-dipole interaction governed by the XY Hamiltonian in the inhomogeneous magnetic field. The dependence of the above discord asymmetry on the Larmor frequencies at both T = 0 (the ground state) and T > 0 has been investigated. It is demonstrated, in particular, that the asymmetry is negligible for high temperatures but it may become significant with a decrease in the temperature.