Exchange coupling between silicon donors: the crucial role of the central cell and mass anisotropy

Donors in silicon are now demonstrated as one of the leading candidates for implementing qubits and quantum information processing. Single qubit operations, measurements and long coherence times are firmly established, but progress on controlling two qubit interactions has been slower. One reason for this is that the inter donor exchange coupling has been predicted to oscillate with separation, making it hard to estimate in device designs. We present a multivalley effective mass theory of a donor pair in silicon, including both a central cell potential and the effective mass anisotropy intrinsic in the Si conduction band. We are able to accurately describe the single donor properties of valley-orbit coupling and the spatial extent of donor wave functions, highlighting the importance of fitting measured values of hyperfine coupling and the orbital energy of the $1s$ levels. Ours is a simple framework that can be applied flexibly to a range of experimental scenarios, but it is nonetheless able to provide fast and reliable predictions. We use it to estimate the exchange coupling between two donor electrons and we find a smoothing of its expected oscillations, and predict a monotonic dependence on separation if two donors are spaced precisely along the [100] direction.Comment: Published version. Corrected b and B values from previous versio

Surface code architecture for donors and dots in silicon with imprecise and nonuniform qubit couplings

A scaled quantum computer with donor spins in silicon would benefit from a viable semiconductor framework and a strong inherent decoupling of the qubits from the noisy environment. Coupling neighbouring spins via the natural exchange interaction according to current designs requires gate control structures with extremely small length scales. We present a silicon architecture where bismuth donors with long coherence times are coupled to electrons that can shuttle between adjacent quantum dots, thus relaxing the pitch requirements and allowing space between donors for classical control devices. An adiabatic SWAP operation within each donor/dot pair solves the scalability issues intrinsic to exchange-based two-qubit gates, as it does not rely on sub-nanometer precision in donor placement and is robust against noise in the control fields. We use this SWAP together with well established global microwave Rabi pulses and parallel electron shuttling to construct a surface code that needs minimal, feasible local control.Comment: Published version - more detailed discussions, robustness to dephasing pointed out additionall

Hopping Conduction in Uniaxially Stressed Si:B near the Insulator-Metal Transition

Using uniaxial stress to tune the critical density near that of the sample, we have studied in detail the low-temperature conductivity of p-type Si:B in the insulating phase very near the metal-insulator transition. For all values of temperature and stress, the conductivity collapses onto a single universal scaling curve. For large values of the argument, the scaling function is well fit by the exponentially activated form associated with variable range hopping when electron-electron interactions cause a soft Coulomb gap in the density of states at the Fermi energy. The temperature dependence of the prefactor, corresponding to the T-dependence of the critical curve, has been determined reliably for this system, and is proportional to the square-root of T. We show explicitly that nevlecting the prefactor leads to substantial errors in the determination of the scaling parameters and the critical exponents derived from them. The conductivity is not consistent with Mott variable-range hopping in the critical region nor does it obey this form for any range of the parameters. Instead, for smaller argument of the scaling function, the conductivity of Si:B is well fit by an exponential form with exponent 0.31 related to the critical exponents of the system at the metal- insulator transition.Comment: 13 pages, 6 figure

Unsteady Flow Of A Viscous Incompressible Fluid Between Parallel Plates

In the present paper an exact solution of the Navier Stokes equations has been obtained, considering the flow of a viscous incompressible fluid between two infinitely extended parallel plates when upper plate is moving with uniform velocity and the lower plate is performing linear oscillations in its own plane. The technique of Laplace transform has been employed to obtain the velocity distribution, which has been shown graphically

Optical Photometry of the GRB 010222 Afterglow

The optical afterglow of GRB 010222 was observed using the recently installed 2-m telescope at the Indian Astronomical Observatory, Hanle, and the telescopes at the Vainu Bappu Observatory, Kavalur, beginning ~ 0.6 day after the detection of the event. The results based on these photometric observations combined with others reported in the literature are presented in this paper. The R band light curve shows an initial decline of intensities proportional to t^{-0.542} which steepens, after 10.3 hours, to t^{-1.263}. Following the model of collimated outflow, the early break in the light curve implies a very narrow beam angle (~ 2-3 deg). The two decay rates are consistent with the standard jet model in a uniform density ambient medium, but require a hard spectrum of electron power density with p ~ 1.5. The R band light between 14 and 17 hours since outburst departs from the power law fit by 0.1 mag and shows some evidence for fluctuations over timescales of an hour in the observer's frame. Such deviations are expected due to density inhomogeneities if the ambient medium is similar to the local interstellar medium. GRB 010222 is thus an example of a highly collimated outflow with a hard spectrum of electron energy distribution in normal interstellar environment.Comment: 15 pages, Latex, including 2 postscript figures, to appear in the Bull. astro. Soc. India, September 2001 issu

Exchange Monte Carlo Method and Application to Spin Glass Simulations

We propose an efficient Monte Carlo algorithm for simulating a ``hardly-relaxing" system, in which many replicas with different temperatures are simultaneously simulated and a virtual process exchanging configurations of these replica is introduced. This exchange process is expected to let the system at low temperatures escape from a local minimum. By using this algorithm the three-dimensional $\pm J$ Ising spin glass model is studied. The ergodicity time in this method is found much smaller than that of the multi-canonical method. In particular the time correlation function almost follows an exponential decay whose relaxation time is comparable to the ergodicity time at low temperatures. It suggests that the system relaxes very rapidly through the exchange process even in the low temperature phase.Comment: 10 pages + uuencoded 5 Postscript figures, REVTe

Spin Waves in Disordered III-V Diluted Magnetic Semiconductors

We propose a new scheme for numerically computing collective-mode spectra for large-size systems, using a reformulation of the Random Phase Approximation. In this study, we apply this method to investigate the spectrum and nature of the spin-waves of a (III,Mn)V Diluted Magnetic Semiconductor. We use an impurity band picture to describe the interaction of the charge carriers with the local Mn spins. The spin-wave spectrum is shown to depend sensitively on the positional disorder of the Mn atoms inside the host semiconductor. Both localized and extended spin-wave modes are found. Unusual spin and charge transport is implied.Comment: 14 pages, including 11 figure

Night sky at the Indian Astronomical Observatory during 2000-2008

We present an analysis of the optical night sky brightness and extinction coefficient measurements in UBVRI at the Indian Astronomical Observatory (IAO), Hanle, during the period 2003-2008. They are obtained from an analysis of CCD images acquired at the 2 m Himalayan Chandra Telescope at IAO. Night sky brightness was estimated using 210 HFOSC images obtained on 47 nights and covering the declining phase of solar activity cycle-23. The zenith corrected values of the moonless night sky brightness in mag/square arcsecs are 22.14(U), 22.42(B), 21.28(V), 20.54(R) and 18.86(I) band. This shows that IAO is a dark site for optical observations. No clear dependency of sky brightness with solar activity is found. Extinction values at IAO are derived from an analysis of 1325 images over 58 nights. They are found to be 0.36 in U-band, 0.21 in B-band, 0.12 in V-band, 0.09 in R-band and 0.05 in I-band. On average, extinction during the summer months is slightly larger than that during the winter months. No clear evidence for a correlation between extinction in all bands and the average night time wind speed is found. Also presented here is the low resolution moonless optical night sky spectrum for IAO covering the wavelength range 3000-9300 \AA. Hanle region thus has the required characteristics of a good astronomical site in terms of night sky brightness and extinction, and could be a natural candidate site for any future large aperture Indian optical-infrared telescope(s).Comment: 18 pages, 7 figures, uses basi.cls, accepted for publication in Bulletin of the Astronomical Society of Indi