Nuclear Spins as Quantum Memory in Semiconductor Nanostructures

We theoretically consider solid state nuclear spins in a semiconductor nanostructure environment as long-lived, high-fidelity quantum memory. In particular, we calculate, in the limit of a strong applied magnetic field, the fidelity versus time of P donor nuclear spins in random bath environments of Si and GaAs, and the lifetime of excited intrinsic spins in polarized Si and GaAs environments. In the former situation, the nuclear spin dephases due to spectral diffusion induced by the dipolar interaction among nuclei in the bath. We calculate the decay of nuclear spin quantum memory in the context of Hahn and Carr-Purcell-Meiboom-Gill (CPMG) refocused spin echoes using a formally exact cluster expansion technique which has previously been successful in dealing with electron spin dephasing in a solid state nuclear spin bath. With decoherence dominated by transverse dephasing (T2), we find it feasible to maintain high fidelity (losses of less than 10^{-6}) quantum memory on nuclear spins for times of the order of 100 microseconds (GaAs:P) and 1 to 2 milliseconds (natural Si:P) using CPMG pulse sequences of just a few (~2-4) applied pulses. We also consider the complementary situation of a central flipped intrinsic nuclear spin in a bath of completely polarized nuclear spins where decoherence is caused by the direct flip-flop of the central spin with spins in the bath. Exact numerical calculations that include a sufficiently large neighborhood of surrounding nuclei show lifetimes on the order of 1-5 ms for both GaAs and natural Si. Our calculated nuclear spin coherence times may have significance for solid state quantum computer architectures using localized electron spins in semiconductors where nuclear spins have been proposed for quantum memory storage

Transverse NMR relaxation as a probe of mesoscopic structure

Transverse NMR relaxation in a macroscopic sample is shown to be extremely sensitive to the structure of mesoscopic magnetic susceptibility variations. Such a sensitivity is proposed as a novel kind of contrast in the NMR measurements. For suspensions of arbitrary shaped paramagnetic objects, the transverse relaxation is found in the case of a small dephasing effect of an individual object. Strong relaxation rate dependence on the objects' shape agrees with experiments on whole blood. Demonstrated structure sensitivity is a generic effect that arises in NMR relaxation in porous media, biological systems, as well as in kinetics of diffusion limited reactions.Comment: 4 pages, 3 figure

Quantum theory for electron spin decoherence induced by nuclear spin dynamics in semiconductor quantum computer architectures: Spectral diffusion of localized electron spins in the nuclear solid-state environment

We consider the decoherence of a single localized electron spin due to its coupling to the lattice nuclear spin bath in a semiconductor quantum computer architecture. In the presence of an external magnetic field and at low temperatures, the dominant decoherence mechanism is the spectral diffusion of the electron spin resonance frequency due to the temporally fluctuating random magnetic field associated with the dipolar interaction induced flip-flops of nuclear spin pairs. The electron spin dephasing due to this random magnetic field depends intricately on the quantum dynamics of the nuclear spin bath, making the coupled decoherence problem difficult to solve. We provide a formally exact solution of this non-Markovian quantum decoherence problem which numerically calculates accurate spin decoherence at short times, which is of particular relevance in solid-state spin quantum computer architectures. A quantum cluster expansion method is developed, motivated, and tested for the problem of localized electron spin decoherence due to dipolar fluctuations of lattice nuclear spins. The method is presented with enough generality for possible application to other types of spin decoherence problems. We present numerical results which are in quantitative agreement with electron spin echo measurements in phosphorus doped silicon. We also present spin echo decay results for quantum dots in GaAs which differ qualitatively from that of the phosphorus doped silicon system. Our theoretical results provide the ultimate limit on the spin coherence (at least, as characterized by Hahn spin echo measurements) of localized electrons in semiconductors in the low temperature and the moderate to high magnetic field regime of interest in scalable semiconductor quantum computer architectures.Comment: 23 pages, 15 figure

Analysis of clogging in constructed wetlands using magnetic resonance

In this work we demonstrate the potential of permanent magnet based magnetic resonance sensors to monitor and assess the extent of pore clogging in water filtration systems. The performance of the sensor was tested on artificially clogged gravel substrates and on gravel bed samples from constructed wetlands used to treat wastewater. Data indicate that the spin lattice relaxation time is linearly related to the hydraulic conductivity in such systems. In addition, within biologically active filters we demonstrate the ability to determine the relative ratio of biomass to abiotic solids, a measurement which is not possible using alternative techniques

Composite-pulse magnetometry with a solid-state quantum sensor

The sensitivity of quantum magnetometers is challenged by control errors and, especially in the solid-state, by their short coherence times. Refocusing techniques can overcome these limitations and improve the sensitivity to periodic fields, but they come at the cost of reduced bandwidth and cannot be applied to sense static (DC) or aperiodic fields. Here we experimentally demonstrate that continuous driving of the sensor spin by a composite pulse known as rotary-echo (RE) yields a flexible magnetometry scheme, mitigating both driving power imperfections and decoherence. A suitable choice of RE parameters compensates for different scenarios of noise strength and origin. The method can be applied to nanoscale sensing in variable environments or to realize noise spectroscopy. In a room-temperature implementation based on a single electronic spin in diamond, composite-pulse magnetometry provides a tunable trade-off between sensitivities in the microT/sqrt(Hz) range, comparable to those obtained with Ramsey spectroscopy, and coherence times approaching T1

The Cone Phase of Liquid Crystals: Triangular Lattice of Double-Tilt Cylinders

We predict the existence of a new defect-lattice phase near the nematic - smectic-C (NC) transition. This tilt- analogue of the blue phase is a lattice of double-tilt cylinders. We discuss the structure and stability of the cone phase. We suggest that many `nematics' exhibiting short range layering and tilt order may in fact be in the molten cone phase, which is a line liquid.Comment: 4 Pages, 3 Figure

Towards T1-limited magnetic resonance imaging using Rabi beats

Two proof-of-principle experiments towards T1-limited magnetic resonance imaging with NV centers in diamond are demonstrated. First, a large number of Rabi oscillations is measured and it is demonstrated that the hyperfine interaction due to the NV's 14N can be extracted from the beating oscillations. Second, the Rabi beats under V-type microwave excitation of the three hyperfine manifolds is studied experimentally and described theoretically.Comment: 6 pages, 8 figure

Smectic blue phases: layered systems with high intrinsic curvature

We report on a construction for smectic blue phases, which have quasi-long range smectic translational order as well as three dimensional crystalline order. Our proposed structures fill space by adding layers on top of a minimal surface, introducing either curvature or edge defects as necessary. We find that for the right range of material parameters, the favorable saddle-splay energy of these structures can stabilize them against uniform layered structures. We also consider the nature of curvature frustration between mean curvature and saddle-splay.Comment: 15 pages, 11 figure

High-sensitivity diamond magnetometer with nanoscale resolution

We present a novel approach to the detection of weak magnetic fields that takes advantage of recently developed techniques for the coherent control of solid-state electron spin quantum bits. Specifically, we investigate a magnetic sensor based on Nitrogen-Vacancy centers in room-temperature diamond. We discuss two important applications of this technique: a nanoscale magnetometer that could potentially detect precession of single nuclear spins and an optical magnetic field imager combining spatial resolution ranging from micrometers to millimeters with a sensitivity approaching few femtotesla/Hz$^{1/2}$.Comment: 29 pages, 4 figure