Concatenated dynamical decoupling in a solid-state spin bath

Concatenated dynamical decoupling (CDD) pulse sequences hold much promise as a strategy to mitigate decoherence in quantum information processing. It is important to investigate the actual performance of these dynamical decoupling strategies in real systems that are promising qubit candidates. In this Rapid Communication, we compute the echo decay of concatenations of the Hahn echo sequence for a solid-state electronic spin qubit in a nuclear spin bath using a cluster expansion technique. We find that each level of concatenation reverses the effect of successive levels of intrabath fluctuations. On the one hand, this advances CDD as a versatile and realistic decoupling strategy. On the other hand, this invalidates, as overly optimistic, results of the simple pair approximation used previously to study restoration, through CDD, of coherence lost to a mesoscopic spin bath

Numerical calculations of the phase diagram of cubic blue phases in cholesteric liquid crystals

We study the static properties of cubic blue phases by numerically minimising the three-dimensional, Landau-de Gennes free energy for a cholesteric liquid crystal close to the isotropic-cholesteric phase transition. Thus we are able to refine the powerful but approximate, semi-analytic frameworks that have been used previously. We obtain the equilibrium phase diagram and discuss it in relation to previous results. We find that the value of the chirality above which blue phases appear is shifted by 20% (towards experimentally more accessible regions) with respect to previous estimates. We also find that the region of stability of the O5 structure -- which has not been observed experimentally -- shrinks, while that of BP I (O8-) increases thus giving the correct order of appearance of blue phases at small chirality. We also study the approach to equilibrium starting from the infinite chirality solutions and we find that in some cases the disclination network has to assemble during the equilibration. In these situations disclinations are formed via the merging of isolated aligned defects.Comment: 16 pages, 5 figures. Accepted for publication in Phys. Rev.

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

Qubit coherence control in a nuclear spin bath

Coherent dynamics of localized spins in semiconductors is limited by spectral diffusion arising from dipolar fluctuation of lattice nuclear spins. Here we extend the semiclassical theory of spectral diffusion for nuclear spins I=1/2 to the high nuclear spins relevant to the III-V materials and show that applying successive qubit pi-rotations at a rate approximately proportional to the nuclear spin quantum number squared (I^2) provides an efficient method for coherence enhancement. Hence robust coherent manipulation in the large spin environments characteristic of the III-V compounds is possible without resorting to nuclear spin polarization, provided that the pi-pulses can be generated at intervals scaling as I^{-2}

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

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

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

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

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