Long-lived selective spin echoes in dipolar solids under periodic and aperiodic pi-pulse trains

The application of Carr-Purcell-Meiboom-Gill (CPMG) $\pi-$trains for dynamically decoupling a system from its environment has been extensively studied in a variety of physical systems. When applied to dipolar solids, recent experiments have demonstrated that CPMG pulse trains can generate long-lived spin echoes. While there still remains some controversy as to the origins of these long-lived spin echoes under the CPMG sequence, there is a general agreement that pulse errors during the $\pi-$pulses are a necessary requirement. In this work, we develop a theory to describe the spin dynamics in dipolar coupled spin-1/2 system under a CPMG($\phi_{1},\phi_{2}$) pulse train, where $\phi_{1}$ and $\phi_{2}$ are the phases of the $\pi-$pulses. From our theoretical framework, the propagator for the CPMG($\phi_{1},\phi_{2}$) pulse train is equivalent to an effective ``pulsed'' spin-locking of single-quantum coherences with phase $\pm\frac{\phi_{2}-3\phi_{1}}{2}$, which generates a periodic quasiequilibrium that corresponds to the long-lived echoes. Numerical simulations, along with experiments on both magnetically dilute, random spin networks found in C$_{60}$ and C$_{70}$ and in non-dilute spin systems found in adamantane and ferrocene, were performed and confirm the predictions from the proposed theory.Comment: 25 pages, 12 figures, submitted to Physical Review

Multiple Scattering Theory for Two-dimensional Electron Gases in the Presence of Spin-Orbit Coupling

In order to model the phase-coherent scattering of electrons in two-dimensional electron gases in the presence of Rashba spin-orbit coupling, a general partial-wave expansion is developed for scattering from a cylindrically symmetric potential. The theory is applied to possible electron flow imaging experiments using a moveable scanning probe microscope tip. In such experiments, it is demonstrated theoretically that the Rashba spin-orbit coupling can give rise to spin interference effects, even for unpolarized electrons at nonzero temperature and no magnetic field.Comment: 34 pages, 7 figure

Intravalley Multiple Scattering of Quasiparticles in Graphene

We develop a theoretical description of intravalley scattering of quasiparticles in graphene from multiple short-range scatterers of size much greater than the carbon-carbon bond length. Our theory provides a method to rapidly calculate the Green's function in graphene for arbitrary configurations of scatterers. We demonstrate that non-collinear multiple scattering trajectories generate pseudospin rotations that alter quasiparticle interference, resulting in significant modifications to the shape, intensity, and pattern of the interference fringes in the local density of states (LDOS). We illustrate these effects via theoretical calculations of the LDOS for a variety of scattering configurations in single layer graphene. A clear understanding of impurity scattering in graphene is a step towards exploiting graphene's unique properties to build future devices

Imaging a Single-Electron Quantum Dot

Images of a single-electron quantum dot were obtained in the Coulomb blockade regime at liquid He temperatures using a cooled scanning probe microscope (SPM). The charged SPM tip shifts the lowest energy level in the dot and creates a ring in the image corresponding to a peak in the Coulomb-blockade conductance. Fits to the lineshape of the ring determine the tip-induced shift of the electron energy state in the dot. SPM manipulation of electrons in quantum dots promises to be useful in understanding, building and manipulating circuits for quantum information processing.Comment: 14 pages including 3 figure

Pseudorandom Selective Excitation in NMR

In this work, average Hamiltonian theory is used to study selective excitation in a spin-1/2 system evolving under a series of small flip-angle $\theta-$pulses $(\theta\ll 1)$ that are applied either periodically [which corresponds to the DANTE pulse sequence] or aperiodically. First, an average Hamiltonian description of the DANTE pulse sequence is developed; such a description is determined to be valid either at or very far from the DANTE resonance frequencies, which are simply integer multiples of the inverse of the interpulse delay. For aperiodic excitation schemes where the interpulse delays are chosen pseudorandomly, a single resonance can be selectively excited if the $\theta$-pulses' phases are modulated in concert with the time delays. Such a selective pulse is termed a pseudorandom-DANTE or p-DANTE sequence, and the conditions in which an average Hamiltonian description of p-DANTE is found to be similar to that found for the DANTE sequence. It is also shown that averaging over different p-DANTE sequences that are selective for the same resonance can help reduce excitations at frequencies away from the resonance frequency, thereby improving the apparent selectivity of the p-DANTE sequences. Finally, experimental demonstrations of p-DANTE sequences and comparisons with theory are presented.Comment: 23 pages, 8 figure

Parametric spin excitations in lateral quantum dots

In this work, the spin dynamics of a single electron under parametric modulation of a lateral quantum dot's electrostatic potential in the presence of spin-orbit coupling is investigated. Numerical and theoretical calculations demonstrate that, by squeezing and/or moving the electron's wave function, spin rotations with Rabi frequencies on the order of tens of megahertz can be achieved with experimentally accessible parameters in both parabolic and square lateral quantum dots. Applications of parametric excitations for determining spin-orbit coupling parameters and for increasing the spin polarization in the electronic ground are demonstrated

Breakdown of linear response theory under low-power excitation in NMR. I. The case of long-lived signals in inhomogeneously broadened spin systems

In this work, we examine the application of linear response theory to the problem of low-power excitation in inhomogeneously broadened spin systems when the strength of the radiofrequency (RF) pulse, ν , is smaller than the inhomogeneous linewidth. Even for small overall excitations [Θ = 2πν T ≪ 1 where T is the RF pulse length], linear response theory is shown to break down for spins with resonance frequencies that are on the order of ν , which is due to the fact that the RF interaction cannot be treated as a small perturbation in this case. This breakdown in linear response theory can be partially corrected for by enforcing unitarity in the linear response. Furthermore, the nature of the spin echo generated by a π -pulse applied immediately after a low-power pulse is investigated. Numerical calculations and experiments performed in an inhomogeneously broadened H O/D O solution confirm the theoretical predictions presented in this work

Breakdown of linear response theory under low-power excitation in NMR. II. The case of "long-lived" signals in homogeneously broadened dipolar spin systems

In this work, the previous linear response theory developed to describe low-power, radiofrequency (RF) excitation in inhomogeneously broadened spin systems [Z. Gong and J. D. Walls, J. Chem. Phys. , 164201 (2016)] is applied to the problem of low-power excitation in homogeneously broadened dipolar spin systems when the strength of the RF pulse, , is much less than the homogeneous linewidth, . Application of a low-power pulse for a time with a nominal flip-angle of Θ generates a broad signal with a "dip" at the RF transmitter frequency that deepens with increasing Θ. When a delay is placed before signal acquisition, only a negative, "long-lived" signal from the narrow "dip" remains. If a -pulse is applied after low-power excitation, a "long-lived" signal lasting a time ≈ after the -pulse is generated where dephasing due to inhomogeneity, anisotropic bulk magnetic susceptibility, and chemical shift anisotropy is refocused while dephasing due to nonzero chemical shift differences is only partially refocused. Contrary to previous observations, experiments in powdered hexamethylbenzene demonstrate that these "long-lived" signals can exist even in the absence of nonzero chemical shift differences. Additional experimental demonstrations in powdered and single-crystalline adamantane and ferrocene samples are also presented

Diffusion Selective Pulses

The self-diffusion coefficient, , provides important chemical and physical information about a molecular species and its environment, and can be routinely measured under equilibrium conditions using nuclear magnetic resonance (NMR). Differences in diffusion coefficients can also be exploited in NMR to suppress signals from fast diffusing species relative to slow diffusing species. To date, no method for selectively suppressing signals only from species with a particular diffusion coefficient has been presented. In this work, diffusion selective pulses are developed that selectively suppress the magnetization only from species for which = . This is accomplished by interleaving NMR relaxation selective pulses between pulsed field gradients, where the effective transverse relaxation of the magnetization is related to . Experimental demonstrations of diffusion selective pulses on water and water/acetone/dimethyl sulfoxide samples and on a magnetic resonance imaging phantom are presented