Maintaining coherence in Quantum Computers

The effect of the inevitable coupling to external degrees of freedom of a quantum computer are examined. It is found that for quantum calculations (in which the maintenance of coherence over a large number of states is important), not only must the coupling be small but the time taken in the quantum calculation must be less than the thermal time scale, $\hbar/k_B T$. For longer times the condition on the strength of the coupling to the external world becomes much more stringent.Comment: 13 page

Dephasing of Electrons on Helium by Collisions with Gas Atoms

The damping of quantum effects in the transport properties of electrons deposited on a surface of liquid helium is studied. It is found that due to vertical motion of the helium vapour atoms the interference of paths of duration $t$ is damped by a factor $\exp - (t/\tau_v)^3$. An expression is derived for the weak-localization lineshape in the case that damping occurs by a combination of processes with this type of cubic exponential damping and processes with a simple exponential damping factor.Comment: 7 pages, 2 figures, Revte

Skyrmion Dynamics and NMR Line Shapes in QHE Ferromagnets

The low energy charged excitations in quantum Hall ferromagnets are topological defects in the spin orientation known as skyrmions. Recent experimental studies on nuclear magnetic resonance spectral line shapes in quantum well heterostructures show a transition from a motionally narrowed to a broader `frozen' line shape as the temperature is lowered at fixed filling factor. We present a skyrmion diffusion model that describes the experimental observations qualitatively and shows a time scale of $\sim 50 \mu{\rm sec}$ for the transport relaxation time of the skyrmions. The transition is characterized by an intermediate time regime that we demonstrate is weakly sensitive to the dynamics of the charged spin texture excitations and the sub-band electronic wave functions within our model. We also show that the spectral line shape is very sensitive to the nuclear polarization profile along the z-axis obtained through the optical pumping technique.Comment: 6 pages, 4 figure

NMR quantum computation with indirectly coupled gates

An NMR realization of a two-qubit quantum gate which processes quantum information indirectly via couplings to a spectator qubit is presented in the context of the Deutsch-Jozsa algorithm. This enables a successful comprehensive NMR implementation of the Deutsch-Jozsa algorithm for functions with three argument bits and demonstrates a technique essential for multi-qubit quantum computation.Comment: 9 pages, 2 figures. 10 additional figures illustrating output spectr

Distribution of local density of states in disordered metallic samples: logarithmically normal asymptotics

Asymptotical behavior of the distribution function of local density of states (LDOS) in disordered metallic samples is studied with making use of the supersymmetric $\sigma$--model approach, in combination with the saddle--point method. The LDOS distribution is found to have the logarithmically normal asymptotics for quasi--1D and 2D sample geometry. In the case of a quasi--1D sample, the result is confirmed by the exact solution. In 2D case a perfect agreement with an earlier renormalization group calculation is found. In 3D the found asymptotics is of somewhat different type: P(\rho)\sim \exp(-\mbox{const}\,|\ln^3\rho|).Comment: REVTEX, 14 pages, no figure

Anomalous NMR Magnetic Shifts in CeCoIn_5

We report ^{115}In and ^{59}Co Nuclear Magnetic Resonance (NMR) measurements in the heavy fermion superconductor CeCoIn_5 above and below T_c. The hyperfine couplings of the In and Co are anisotropic and exhibit dramatic changes below 50K due to changes in the crystal field level populations of the Ce ions. Below T_c the spin susceptibility is suppressed, indicating singlet pairing.Comment: 4 pages, 4 figure

In-Situ Nuclear Magnetic Resonance Investigation of Strain, Temperature, and Strain-Rate Variations of Deformation-Induced Vacancy Concentration in Aluminum

Critical strain to serrated flow in solid solution alloys exhibiting dynamic strain aging (DSA) or Portevin–LeChatelier effect is due to the strain-induced vacancy production. Nuclear magnetic resonance (NMR) techniques can be used to monitor in situ the dynamical behavior of point and line defects in materials during deformation, and these techniques are nondestructive and noninvasive. The new CUT-sequence pulse method allowed an accurate evaluation of the strain-enhanced vacancy diffusion and, thus, the excess vacancy concentration during deformation as a function of strain, strain rate, and temperature. Due to skin effect problems in metals at high frequencies, thin foils of Al were used and experimental results correlated with models based on vacancy production through mechanical work (vs thermal jogs), while in situ annealing of excess vacancies is noted at high temperatures. These correlations made it feasible to obtain explicit dependencies of the strain-induced vacancy concentration on test variables such as the strain, strain rate, and temperature. These studies clearly reveal the power and utility of these NMR techniques in the determination of deformation-induced vacancies in situ in a noninvasive fashion.

Single Spin Measurement using Single Electron Transistors to Probe Two Electron Systems

We present a method for measuring single spins embedded in a solid by probing two electron systems with a single electron transistor (SET). Restrictions imposed by the Pauli Principle on allowed two electron states mean that the spin state of such systems has a profound impact on the orbital states (positions) of the electrons, a parameter which SET's are extremely well suited to measure. We focus on a particular system capable of being fabricated with current technology: a Te double donor in Si adjacent to a Si/SiO2 interface and lying directly beneath the SET island electrode, and we outline a measurement strategy capable of resolving single electron and nuclear spins in this system. We discuss the limitations of the measurement imposed by spin scattering arising from fluctuations emanating from the SET and from lattice phonons. We conclude that measurement of single spins, a necessary requirement for several proposed quantum computer architectures, is feasible in Si using this strategy.Comment: 22 Pages, 8 Figures; revised version contains updated references and small textual changes. Submitted to Phys. Rev.

Real-Time-RG Analysis of the Dynamics of the Spin-Boson Model

Using a real-time renormalization group method we determine the complete dynamics of the spin-boson model with ohmic dissipation for coupling strengths $\alpha\lesssim 0.1-0.2$. We calculate the relaxation and dephasing time, the static susceptibility and correlation functions. Our results are consistent with quantum Monte Carlo simulations and the Shiba relation. We present for the first time reliable results for finite cutoff and finite bias in a regime where perturbation theory in $\alpha$ or in tunneling breaks down. Furthermore, an unambigious comparism to results from the Kondo model is achieved.Comment: 4 pages, 5 figures, 1 tabl

Density Matrix in Quantum Mechanics and Distinctness of Ensembles Having the Same Compressed Density Matrix

We clarify different definitions of the density matrix by proposing the use of different names, the full density matrix for a single-closed quantum system, the compressed density matrix for the averaged single molecule state from an ensemble of molecules, and the reduced density matrix for a part of an entangled quantum system, respectively. We show that ensembles with the same compressed density matrix can be physically distinguished by observing fluctuations of various observables. This is in contrast to a general belief that ensembles with the same compressed density matrix are identical. Explicit expression for the fluctuation of an observable in a specified ensemble is given. We have discussed the nature of nuclear magnetic resonance quantum computing. We show that the conclusion that there is no quantum entanglement in the current nuclear magnetic resonance quantum computing experiment is based on the unjustified belief that ensembles having the same compressed density matrix are identical physically. Related issues in quantum communication are also discussed.Comment: 26 pages. To appear in Foundations of Physics, 36 (8), 200