arXiv subjects

Mark Friesen

Publications and source records attributed to Mark Friesen.

144 records · Page 8Linked to original sources

arXiv2005

Theory of the Stark Effect for P donors in Si

We develop a multi-valley effective mass theory for substitutional donors in silicon in an inhomogeneous environment. Valley-orbit coupling is treated perturbatively. We apply the theory to the Stark effect in Si:P. The method becomes more accurate at high fields, and it is designed to give correct experimental binding energies at zero field. Unexpectedly, the ground state energy for the donor electron is found to increase with electric field as a consequence of spectrum narrowing of the 1s manifold. Our results are of particular importance for the Kane quantum computer.

cond-mat.mtrl-sci↗

arXiv2005

Quantum Dots and Etch-Induced Depletion of a Silicon 2DEG

The controlled depletion of electrons in semiconductors is the basis for numerous devices. Reactive-ion etching provides an effective technique for fabricating both classical and quantum devices. However, Fermi level pinning can occur, and must be carefully considered in the development of small devices, such as quantum dots. Because of depletion, the electrical size of the device is reduced in comparison with its physical dimension. To investigate this issue, we fabricate several types of devices in silicon-germanium heterostructures using two different etches, CF$_4$ and SF$_6$. We estimate the depletion width associated with each etch by two methods: (i) conductance measurements in etched wires of decreasing thickness (to determine the onset of depletion), (ii) capacitance measurements of quantum dots (to estimate the size of the active region). We find that the SF$_6$ etch causes a much smaller depletion width, making it more suitable for device fabrication.

cond-mat.mes-hall↗

arXiv2004

One-spin quantum logic gates from exchange interactions and a global magnetic field

It has been widely assumed that one-qubit gates in spin-based quantum computers suffer from severe technical difficulties. We show that one-qubit gates can in fact be generated using only modest and presently feasible technological requirements. Our solution uses only global magnetic fields and controllable Heisenberg exchange interactions, thus circumventing the need for single-spin addressing.

quant-ph↗

arXiv2004

Coulomb Blockade in a Silicon/Silicon-Germanium Two-Dimensional Electron Gas Quantum Dot

We report the fabrication and electrical characterization of a single electron transistor in a modulation doped silicon/silicon-germanium heterostructure. The quantum dot is fabricated by electron beam lithography and subsequent reactive ion etching. The dot potential and electron density are modified by laterally defined side gates in the plane of the dot. Low temperature measurements show Coulomb blockade with a single electron charging energy of 3.2 meV.

cond-mat.mtrl-sci↗

arXiv2004

Spin Readout and Initialization in a Semiconductor Quantum Dot

Electron spin qubits in semiconductors are attractive from the viewpoint of long coherence times. However, single spin measurement is challenging. Several promising schemes incorporate ancillary tunnel couplings that may provide unwanted channels for decoherence. Here, we propose a novel spin-charge transduction scheme, converting spin information to orbital information within a single quantum dot by microwave excitation. The same quantum dot can be used for rapid initialization, gating, and readout. We present detailed modeling of such a device in silicon to confirm its feasibility.

cond-mat.mtrl-sci↗

arXiv2003

Valley splitting in strained silicon quantum wells

A theory based on localized-orbital approaches is developed to describe the valley splitting observed in silicon quantum wells. The theory is appropriate in the limit of low electron density and relevant for proposed quantum computing architectures. The valley splitting is computed for realistic devices using the quantitative nanoelectronic modeling tool NEMO. A simple, analytically solvable tight-binding model is developed, it yields much physical insight, and it reproduces the behavior of the splitting in the NEMO results. The splitting is in general nonzero even in the absence of electric field in contrast to previous works. The splitting in a square well oscillates as a function of S, the number of layers in the quantum well, with a period that is determined by the location of the valley minimum in the Brillouin zone. The envelope of the splitting decays as $S^3$. Finally the feasibility of observing such oscillations experimentally in modern Si/SiGe heterostructures is discussed.

cond-mat.mes-hall↗

arXiv2002

Pseudo-Digital Qubits: A General Approach

Pseudo-digital coupling has recently been proposed as a simple but robust technique for reducing gating errors in quantum dot quantum computers. Here, we discuss the technique in the context of simulations on silicon heterostructures. Additionally, we generalize and extend the pseudo-digital concept to other settings. In particular, we consider superconducting charge qubits and suggest a simple circuit for implementing dual, pseudo-digital working points.

cond-mat.mes-hall↗

arXiv2002

Experimental observation of high field diamagnetic fluctuations in Niobium

We have performed a magnetic study of a bulk metallic sample of Nb with critical temperature $T_{c}=8.5$ K. Magnetization versus temperature (M {\it vs} T) data obtained for fixed magnetic fields above 1 kOe show a superconducting transition which becomes broader as the field is increased. The data are interpreted in terms of the diamagnetic lowest Landau level (LLL) fluctuation theory. The scaling analysis gives values of the superconducting transition temperature $T_{c}(H)$ consistent with $H_{c2}(T)$% . We search for universal 3D LLL behavior by comparing scaling results for Nb and YBaCuO, but obtain no evidence for universality.

cond-mat.supr-con↗

arXiv2002

Pseudo-digital quantum bits

Quantum computers are analog devices; thus they are highly susceptible to accumulative errors arising from classical control electronics. Fast operation--as necessitated by decoherence--makes gating errors very likely. In most current designs for scalable quantum computers it is not possible to satisfy both the requirements of low decoherence errors and low gating errors. Here we introduce a hardware-based technique for pseudo-digital gate operation. We perform self-consistent simulations of semiconductor quantum dots, finding that pseudo-digital techniques reduce operational error rates by more than two orders of magnitude, thus facilitating fast operation.

quant-ph↗

arXiv2002

Decoherence of electron spin qubits in Si-based quantum computers

Direct phonon spin-lattice relaxation of an electron qubit bound by a donor impurity or quantum dot in SiGe heterostructures is investigated. The aim is to evaluate the importance of decoherence from this mechanism in several important solid-state quantum computer designs operating at low temperatures. We calculate the relaxation rate $1/T_1$ as a function of [100] uniaxial strain, temperature, magnetic field, and silicon/germanium content for Si:P bound electrons. The quantum dot potential is much smoother, leading to smaller splittings of the valley degeneracies. We have estimated these splittings in order to obtain upper bounds for the relaxation rate. In general, we find that the relaxation rate is strongly decreased by uniaxial compressive strain in a SiGe-Si-SiGe quantum well, making this strain an important positive design feature. Ge in high concentrations (particularly over 85%) increases the rate, making Si-rich materials preferable. We conclude that SiGe bound electron qubits must meet certain conditions to minimize decoherence but that spin-phonon relaxation does not rule out the solid-state implementation of error-tolerant quantum computing.

cond-mat.mtrl-sci↗

arXiv2002

Design and proof of concept for silicon-based quantum dot quantum bits

Spins based in silicon provide one of the most promising architectures for quantum computing. Quantum dots are an inherently scalable technology. Here, we combine these two concepts into a workable design for a silicon-germanium quantum bit. The novel structure incorporates vertical and lateral tunneling, provides controlled coupling between dots, and enables single electron occupation of each dot. Precise modeling of the design elucidates its potential for scalable quantum computing. For the first time it is possible to translate the requirements of fault-tolerant error correction into specific requirements for gate voltage control electronics in quantum dots. We demonstrate that these requirements are met by existing pulse generators in the kHz-MHz range, but GHz operation is not yet achievable. Our calculations further pinpoint device features that enhance operation speed and robustness against leakage errors. We find that the component technologies for silicon quantum dot quantum computers are already in hand.

cond-mat.mtrl-sci↗

arXiv2000

Dynamic scaling theory of the Kosterlitz-Thouless-Berezinskii transition: ubiquitous finite size effects

A numerical study of the neutral two-dimensional (2D) lattice Coulomb gas is performed to examine dynamic scaling, finite size effects, and the dynamic critical exponent $z$ of the Kosterlitz-Thouless-Berezinskii transition. By studying large system sizes ($L=100$), we show $z=2.0 \pm0.2$ using Fisher-Fisher-Huse (FFH) scaling. We also present evidence that the vortex correlation length is finite below the transition temperature, in contrast to conventional wisdom. Finally, we conclude that previous findings for a variety of experimental systems that $z\simeq 5.6$ using FFH scaling indicates that finite size effects are ubiquitous in 2D superconductors and Josephson Junction Arrays.

cond-mat.supr-con↗

arXiv1999

Dynamic scaling of I-V data for the neutral 2D Coulomb gas

The value of the dynamic critical exponent z has been studied for experimental two-dimensional superconducting and Josephson Junction array systems in zero magnetic field via the Fisher-Fisher-Huse dynamic scaling analysis. We found z~5.6, a relatively large value indicative of non-diffusive dynamics. We extend this work here to simulational I-V curves that are also found to be characterized by the same large value of z.

cond-mat.supr-con↗

arXiv1998

3D XY scaling theory of the superconducting phase transition

The intermediate 3D XY scaling theory of superconductivity at zero and nonzero magnetic fields is developed, based only upon the dimensional hypothesis $B\sim (Length)^{-2}$. Universal as well as nonuniversal aspects of the theory are identified, including background terms and demagnetization effects. Two scaling regions are predicted: an "inner" region (very near the zero field superconducting transition, $T_c$), where the fields $B$, $H$, and $H_{ex}$ differ substantially, due to the presence of diamagnetic fluctuations, and an "outer" region (away from $T_c$), where the fields can all be treated similarly. The characteristic field ($H_0$) and temperature ($t_1$) scales, separating the two regimes, are estimated. Scaling theories of the phase transition line, magnetization, specific heat, and conductivity are discussed. Multicritical behavior, involving critical glass fluctuations, is investigated along the transition line, $T_m(B)$, at nonzero fields.

cond-mat.supr-con↗

arXiv1997

Two-Phase Region of the Vortex-Solid Melting Transition: 3D XY Theory

In clean enough samples of the high-$T_c$ oxide materials, the phase transition into the superconducting state occurs along a first order line in the $H$-$T$ plane. This means that a two-phase region occurs in the B-$T$ plane, in which the liquid and solid vortex phases coexist. We discuss the thermodynamics of this two-phase region, developing formulae relating experimental quantities of interest. We then apply the 3D XY scaling theory to the problem, obtaining detailed predictions for the boundaries of the coexistence region. By using published data, we are able to predict the width of the two-phase region, and determine the physical parameters involved in the 3D XY description.

cond-mat.supr-con↗

arXiv1997

Dynamic Scaling at the Zero-field 2D Superconducting Transition

Zero-field current-voltage (I-V) characteristics of a thin ("two-dimensional") $Bi_2Sr_2CaCu_2O_{8+δ}$ crystal are reported and analyzed in two ways. The "conventional" approach yields ambiguous results while a dynamical scaling analysis offers new insights into the Kosterlitz-Thouless-Berezinskii transition. The scaling theory predicts that the universal jump of the $I$-$V$ exponent $α$ should be between $z+1$ and 1. A value of $z \simeq 5.6$ is obtained for the dynamical critical exponent, and is corroborated by data from other 2D superconductors. A simple dynamical model is presented to account for the results.

cond-mat.supr-con↗

arXiv1997

Universality of glass scaling in a YBa$_2$Cu$_3$O$_{7-δ}$ thin film

The universal behavior of the continuous superconducting (glass) phase transition is studied in a YBa$_2$Cu$_3$O$_{7-δ}$ thin film. A new analysis technique for extracting critical exponents is developed, using current-voltage ($J$-$E$) measurements. The method places narrow limits on the glass scaling exponents, $z_g$ and $ν_g$, as well as the glass transition temperature, $T_g(H)$. The universal values $z_g = 3.8\pm 0.2$ and $ν_g = 1.8\pm 0.1$ are obtained. Using these values, the data are scaled for fields in the range 1-9~T. Collapse of the scaling forms at different fields describes the universal scaling function. The field dependence of the universal collapse is interpreted in terms of the 3D~XY multicritical scaling theory.

cond-mat.supr-con↗

arXiv1997

Order Parameter and Magnetic Field of a Vortex Line Pinned at a Point Defect: Ginzburg-Landau Theory

Recent theoretical work has derived the correct form of the Ginzburg-Landau differential equations, for the superconducting order parameter and vector potential, in the presence of a small defect. Here, these equations are applied to the case of a single vortex line pinned on such a defect. We develop the coupled set of partial differential equations, and show how to derive analytic solutions for the order parameter and magnetic field perturbations in the region of space near the defect. Certain properties of the unperturbed vortex solution are needed to totally specify our result; these are evaluated numerically, and compared with those deduced from Clem's approximate solution.

cond-mat.supr-con↗