Decomposition Methods and the Computation of Spatial Equilibria: An Application to Coal Supply and Demand Models

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Suppression of electron spin decoherence in a quantum dot

The dominant source of decoherence for an electron spin in a quantum dot is the hyperfine interaction with the surrounding bath of nuclear spins. The decoherence process may be slowed down by subjecting the electron spin to suitable sequences of external control pulses. We investigate the performance of a variety of dynamical decoupling protocols using exact numerical simulation. Emphasis is given to realistic pulse delays and the long-time limit, beyond the domain where available analytical approaches are guaranteed to work. Our results show that both deterministic and randomized protocols are capable to significantly prolong the electron coherence time, even when using control pulse separations substantially larger than what expected from the {\em upper cutoff} frequency of the coupling spectrum between the electron and the nuclear spins. In a realistic parameter range, the {\em total width} of such a coupling spectrum appears to be the physically relevant frequency scale affecting the overall quality of the decoupling.Comment: 8 pages, 3 figures. Invited talk at the XXXVII Winter Colloquium on the Physics of Quantum Electronics, Snowbird, Jan 2007. Submitted to J. Mod. Op

Selective coherence transfers in homonuclear dipolar coupled spin systems

Mapping the physical dipolar Hamiltonian of a solid-state network of nuclear spins onto a system of nearest-neighbor couplings would be extremely useful for a variety of quantum information processing applications, as well as NMR structural studies. We demonstrate such a mapping for a system consisting of an ensemble of spin pairs, where the coupling between spins in the same pair is significantly stronger than the coupling between spins on different pairs. An amplitude modulated RF field is applied on resonance with the Larmor frequency of the spins, with the frequency of the modulation matched to the frequency of the dipolar coupling of interest. The spin pairs appear isolated from each other in the regime where the RF power (omega_1) is such that omega_weak << omega_1 << omega_strong. Coherence lifetimes within the two-spin system are increased from 19 us to 11.1 ms, a factor of 572.Comment: 4 pages. Paper re-submitted with minor changes to clarify that the scheme demonstrated is not an exact mapping onto a nearest neighbor system. However, this is the first demonstration of a controlled evolution in a subspace of an extended spin system, on a timescale that is much larger than the dipolar dephasing tim

Entanglement in a Solid State Spin Ensemble

Entanglement is the quintessential quantum phenomenon and a necessary ingredient in most emerging quantum technologies, including quantum repeaters, quantum information processing (QIP) and the strongest forms of quantum cryptography. Spin ensembles, such as those in liquid state nuclear magnetic resonance, have been powerful in the development of quantum control methods, however, these demonstrations contained no entanglement and ultimately constitute classical simulations of quantum algorithms. Here we report the on-demand generation of entanglement between an ensemble of electron and nuclear spins in isotopically engineered phosphorus-doped silicon. We combined high field/low temperature electron spin resonance (3.4 T, 2.9 K) with hyperpolarisation of the 31P nuclear spin to obtain an initial state of sufficient purity to create a non-classical, inseparable state. The state was verified using density matrix tomography based on geometric phase gates, and had a fidelity of 98% compared with the ideal state at this field and temperature. The entanglement operation was performed simultaneously, with high fidelity, to 10^10 spin pairs, and represents an essential requirement of a silicon-based quantum information processor.Comment: 4 pages, 3 figures plus supporting information of 4 pages, 1 figure v2: Updated reference

The Intrinsic Origin of Spin Echoes in Dipolar Solids Generated by Strong Pi Pulses

In spectroscopy, it is conventional to treat pulses much stronger than the linewidth as delta-functions. In NMR, this assumption leads to the prediction that pi pulses do not refocus the dipolar coupling. However, NMR spin echo measurements in dipolar solids defy these conventional expectations when more than one pi pulse is used. Observed effects include a long tail in the CPMG echo train for short delays between pi pulses, an even-odd asymmetry in the echo amplitudes for long delays, an unusual fingerprint pattern for intermediate delays, and a strong sensitivity to pi-pulse phase. Experiments that set limits on possible extrinsic causes for the phenomena are reported. We find that the action of the system's internal Hamiltonian during any real pulse is sufficient to cause the effects. Exact numerical calculations, combined with average Hamiltonian theory, identify novel terms that are sensitive to parameters such as pulse phase, dipolar coupling, and system size. Visualization of the entire density matrix shows a unique flow of quantum coherence from non-observable to observable channels when applying repeated pi pulses.Comment: 24 pages, 27 figures. Revised from helpful referee comments. Added new Table IV, new paragraphs on pages 3 and 1

Efficient implementation of selective recoupling in heteronuclear spin systems using Hadamard matrices

We present an efficient scheme which couples any designated pair of spins in heteronuclear spin systems. The scheme is based on the existence of Hadamard matrices. For a system of $n$ spins with pairwise coupling, the scheme concatenates $cn$ intervals of system evolution and uses at most $c n^2$ pulses where $c \approx 1$. Our results demonstrate that, in many systems, selective recoupling is possible with linear overhead, contrary to common speculation that exponential effort is always required.Comment: 7 pages, 4 figures, mypsfig2, revtex, submitted April 27, 199

Planar 17O NMR study of Pr_yY_{1-y}Ba_2Cu_3O_{6+x}

We report the planar ^{17}O NMR shift in Pr substituted YBa_{2}Cu_{3}O_{6+x}, which at x=1 exhibits a characteristic pseudogap temperature dependence, confirming that Pr reduces the concentration of mobile holes in the CuO_{2} planes. Our estimate of the rate of this counterdoping effect, obtained by comparison with the shift in pure samples with reduced oxygen content, is found insufficient to explain the observed reduction of T_c. From the temperature dependent magnetic broadening of the ^{17}O NMR we conclude that the Pr moment and the local magnetic defect induced in the CuO_2 planes produce a long range spin polarization in the planes, which is likely associated with the extra reduction of T_c. We find a qualitatively different behaviour in the oxygen depleted Pr_yY_{1-y}Ba_2Cu_3O_{6.6}, i.e. the suppression of T$_c$ is nearly the same, but the magnetic broadening of the ^{17}O NMR appears weaker. This difference may signal a weaker coupling of the Pr to the planes in the underdoped compound, which might be linked with the larger Pr to CuO_2 plane distance, and correspondingly weaker hybridization.Comment: 8 pages, 9 figures, accepted in Phys Rev

An all silicon quantum computer

A solid-state implementation of a quantum computer composed entirely of silicon is proposed. Qubits are Si-29 nuclear spins arranged as chains in a Si-28 (spin-0) matrix with Larmor frequencies separated by a large magnetic field gradient. No impurity dopants or electrical contacts are needed. Initialization is accomplished by optical pumping, algorithmic cooling, and pseudo-pure state techniques. Magnetic resonance force microscopy is used for readout. This proposal takes advantage of many of the successful aspects of solution NMR quantum computation, including ensemble measurement, RF control, and long decoherence times, but it allows for more qubits and improved initialization.Comment: ReVTeX 4, 5 pages, 2 figure

Vortex State of Tl2_2Ba2_2CuO6+δ_{6+\delta} via 205^{205}Tl NMR at 2 Tesla

We report a $^{205}$Tl NMR study of vortex state for an aligned polycrystalline sample of an overdoped high-$T_c$ superconductor Tl$_2$Ba$_2$CuO$_{6+\delta}$ ($T_{c}\sim$85 K) with magnetic field 2 T along the c axis. We observed an imperfect vortex lattice, so-called Bragg glass at $T$=5 K, coexistence of vortex solid with liquid between 10 and 60 K, and vortex melting between 65 and 85 K. No evidence for local antiferromagnetic ordering at vortex cores was found for our sample.Comment: 4 pages with 5 figure

Gaps and excitations in fullerides with partially filled bands : NMR study of Na2C60 and K4C60

We present an NMR study of Na2C60 and K4C60, two compounds that are related by electron-hole symmetry in the C60 triply degenerate conduction band. In both systems, it is known that NMR spin-lattice relaxation rate (1/T1) measurements detect a gap in the electronic structure, most likely related to singlet-triplet excitations of the Jahn-Teller distorted (JTD) C60^{2-} or C60^{4-}. However, the extended temperature range of the measurements presented here (10 K to 700 K) allows to reveal deviations with respect to this general trend, both at high and low temperatures. Above room temperature, 1/T1 deviates from the activated law that one would expect from the presence of the gap and saturates. In the same temperature range, a lowering of symmetry is detected in Na2C60 by the appearance of quadrupole effects on the 23Na spectra. In K4C60, modifications of the 13C spectra lineshapes also indicate a structural modification. We discuss this high temperature deviation in terms of a coupling between JTD and local symmetry. At low temperatures, 1/T$_1$T tends to a constant value for Na2C60, both for 13C and 23Na NMR. This indicates a residual metallic character, which emphasizes the proximity of metallic and insulting behaviors in alkali fullerides.Comment: 12 pages, 13 figure