Session S37: Semiconductor Qubits - Gated Dots and Impurities I

Dispersive measurement of electron spin states in Coulomb-confined silicon double quantum dots

We use radio frequency reflectometry with a resonant circuit to investigate a double quantum dot device patterned by the placement of phosphorus donors in silicon with scanning tunnelling microscope lithography. The circuit responds to electron tunnelling to and from the quantum dots, the complex admittance of which provides information about the tunnel coupling between the dots and the leads. With four electrons on two dots, the Pauli Exclusion Principle makes tunnelling of one electron between the two dots spin dependent, which we exploit to measure the electronic spin state. We map the ground state transition between singlet and triplet states as a function of electric and magnetic fields, which shows that the exchange energy can be tuned over an order of magnitude (about 10 to 100 $\mu$eV) or more in this device. We apply high frequency pulses to induce an excited spin state and observe that the dispersive measurement can detect the excited spin state in addition to the ground state.   

Bias Triangles Presented in Chemical Potential Space

Readout of spins in solid state electronic devices requires some form of spin-to-charge conversion. In several systems this is achieved by exploiting Pauli-spin blockade (PSB). A prerequisite to studies of PSB is a strong understanding of the measured bias triangles in the absence of blockade. To this end we present measurements of bias triangles in four different biasing configurations. Thorough analysis of the data allows us to present data from four different bias configurations on a single plot in chemical potential space. This presentation allows comparisons between different biasing directions to be made in a clean and straightforward manner. This ability will be useful for investigations into PSB where these comparisons are paramount.   

Single-electron regime and Pauli spin blockade in a silicon metal-oxide-semiconductor double quantum dot

Silicon quantum dots are promising candidates for quantum information processing as spin qubits with long coherence time. We present electrical transport measurements on a silicon metal-oxide-semiconductor (MOS) double quantum dot (DQD). First, Coulomb diamonds measurements demonstrate the one-electron regime at a relatively high temperature of 1.5 K. Then, the 8 mK stability diagram shows Pauli spin blockade with a large singlet-triplet separation of approximatively 0.40 meV, pointing towards a strong lifting of the valley degeneracy. Finally, numerical simulations indicate that by integrating a micro-magnet to those devices, we could achieve fast spin rotations of the order of 30 ns. Those results are part of the recent body of work demonstrating the potential of Si MOS DQD as reliable and long-lived spin qubits that could be ultimately integrated into modern electronic facilities.   

Tunable Radio-frequency Quantum Point Contact

Manipulating the spin of single electrons in quantum dots is a promising avenue for quantum information processing. As the readout of the spins is performed via spin-to-charge conversion, establishing a charge sensing technique[1] that is fast and highly sensitive is crucial. For this reason, radio-frequency quantum point contact charge sensors have become widespread[2]. Here we present a tunable quantum point contact charge sensor using a cryogenic variable capacitor[3], tunable from 2 to 12 pF. We obtain optimal impedance matching for different quantum dot devices over a frequency range from 125 to 210 MHz. The flexibility of our setup allows the integration of radio-frequency charge sensors to a variety of nanostructures.\\[4pt] [1]M. Field, C. Smith, M. Pepper et al. Phys. Rev. Lett. 70, 1311 (1993). \\[2pt] [2]R. J. Schoelkopf et al. Science 280, 1238 (1998).\\[2pt] [3]T. M\"{u}ller et al. Appl. Phys. Lett. 97, 202104 (2010).   

Measurement, modeling, and simulation of cryogenic SiGe HBT amplifier circuits for fast single spin readout

Fast, low-power quantum state readout is one of many challenges facing quantum information processing. Single electron transistors (SETs) are potentially fast, sensitive detectors for performing spin readout of electrons bound to Si:P donors. From a circuit perspective, however, their output impedance and nonlinear conductance are ill suited to drive the parasitic capacitance typical of coaxial conductors used in cryogenic environments, necessitating a cryogenic amplification stage. We will discuss calibration data, as well as modeling and simulation of cryogenic silicon-germanium (SiGe) heterojunction bipolar transistor (HBT) circuits connected to a silicon SET and operating at 4 K. We find a continuum of solutions from simple, single-HBT amplifiers to more complex, multi-HBT circuits suitable for integration, with varying noise levels and power vs. bandwidth tradeoffs. This work was performed, in part, at the Center for Integrated Nanotechnologies, a U.S. DOE Office of Basic Energy Sciences user facility. Sandia National Laboratories is a multi-program laboratory operated by Sandia Corporation, a Lockheed-Martin Company, for the U. S. Department of Energy under Contract No. DE-AC04-94AL85000.   

Giant valley splitting in Si/oxide: discriminating Fang-Howard or Tamm-Shockley interface states

The conduction band of silicon presents six inequivalent degenerate minima, or~valleys. The presence of an abrupt interface lifts this degeneracy by 0.1-1 meV, an energy scale that may directly affect spin qubits. Experiments reporting splittings over 20 meV [1] cannot be explained by this mechanism. Extended Si/oxide interface (Tamm-Shockley) states may account for this enhancement [2]. We present a renormalization solution for the 1D tight-binding (TB) model of this structure [2], so that the full range of TB parameters is readily accessible [3]. The renormalization language naturally reveals the role played by the chemical bond of atoms across the interface. Our approach eliminates the need for a supercell calculation [2], proving the formation of~intrinsic~interface states regardless of electric field. Moreover, the decimation rate of convergence provides quantitative estimates for the localization lengths of these states. We compare these interface states to the usual field-bound Fang-Howard states, suggesting capacitance measurements to differentiate them [3]. \\[4pt] [1] K. Takashina, et al, PRL 96, 236801 (2006)\\[0pt] [2] A. L. Saraiva et al, PRB 82, 245314 (2010)\\[0pt] [3] A. Dusko et al., Phys.~Rev. B 89, 205307 (2014)   

Interface roughness mediated phonon relaxation rates in Si quantum dots.

Si QDs are promising candidates for solid-state quantum computing due to long spin coherence times. However, the valley degeneracy in Si adds an additional degree of freedom to the electronic structure. Although the valley and orbital indices can be uniquely identified in an ideal Si QD, interface roughness mixes valley and orbital states in realistic dots. Such valley-orbit coupling can strongly influence $T_{1}$ times in Si QDs. Recent experimental measurements of various relaxation rates differ from previous predictions of phonon relaxation in ideal Si QDs. To understand how roughness affects different relaxation rates, for example spin relaxation due to spin-valley coupling, which is a byproduct of spin-orbit and valley-orbit coupling, we need to understand the effect of valley-orbit coupling on valley relaxation first. Using a full-band atomistic tight-binding description for both the system's electron and electron-phonon hamiltonian, we analyze the effect of atomic-scale interface disorder on phonon induced valley relaxation and spin relaxation in a Si QD. We find that, the valley splitting dependence of valley relaxation rate governs the magnetic field dependence of spin relaxation rate. Our results help understand experimentally measured relaxation times.   

Theory of 1- and 3-electron g-factors in Si quantum dots for spin-qubit manipulation

Although the spin-orbit interaction in silicon is very weak, it is possible to map out the electron spin resonance (ESR) frequency with high precision in MOS quantum dot (QD) qubits by using isotopically purified silicon [1]. Using this method, the g-factor with 1 and 3 electrons in the dot has been measured with an in-plane magnetic field and as a function of the applied electric field perpendicular to the interface (along the growth direction <001>) [2]. Here, we present a theoretical model of the electron g-factor in silicon QDs. We show that the results could be explained with the effect of an electron envelope function deformation in the confining interface region. Since the QD orbital splitting is much larger than the valley splitting at the interface, the system with 1 or 3 electrons probes the valley states at the interface, and the sign and size of the g-factor renormalization (order of tens of MHz in the chosen range of the electric field) could be explained via the spin-orbit 2D interaction induced at the interface. Electrical g-factor control opens the possibility of fast and all-electric manipulation of a few electron spin-qubit, without the need of a nanomagnet or a nuclear spin-background.\\[4pt] [1] Veldhorst et al, Nat.Nanotech(2014)\\[0pt] [2] Veldhorst et al, (Unpublished)   

Counted Sb donors in Si quantum dots

Deterministic control over the location and number of donors is critical for donor spin qubits in semiconductor based quantum computing. We have developed techniques using a focused ion beam and a diode detector integrated next to a silicon MOS single electron transistor to gain such control. With the diode detector operating in linear mode, the numbers of ions implanted have been counted and single ion implants have been detected. Poisson statistics in the number of ions implanted have been observed. Transport measurements performed on samples with counted number of implants have been performed and regular coulomb blockade and charge offsets observed. The capacitances to various gates are found to be in agreement with QCAD simulations for an electrostatically defined dot. This work was performed, in part, at the Center for Integrated Nanotechnologies, a U.S. DOE Office of Basic Energy Sciences user facility. The work was supported by Sandia National Laboratories Directed Research and Development Program. Sandia National Laboratories is a multi-program laboratory operated by Sandia Corporation, a Lockheed-Martin Company, for the U. S. Department of Energy under Contract No. DE-AC04-94AL85000.   

Development of Linear Mode Detection for Top-down Ion Implantation of Low Energy Sb Donors

Fabrication of donor spin qubits for quantum computing applications requires deterministic control over the number of implanted donors and the spatial accuracy to within which these can be placed. We present an ion implantation and detection technique that allows us to deterministically implant a single Sb ion (donor) with a resulting volumetric distribution of \textless 10 nm. This donor distribution is accomplished by implanting 30keV Sb into Si which yields a longitudinal straggle of \textless 10 nm and combined with a \textless 50 nm spot size using the Sandia NanoImplanter (nI). The ion beam induced charge signal is collected using a MOS detector that is integrated with a Si quantum dot for transport measurments. This work was performed, in part, at the Center for Integrated Nanotechnologies, a U.S. DOE Office of Basic Energy Sciences user facility. The work was supported by Sandia National Laboratories Directed Research and Development Program. Sandia National Laboratories is a multi-program laboratory operated by Sandia Corporation, a Lockheed-Martin Company, for the U. S. Department of Energy under Contract No. DE-AC04-94AL85000.   

Long-lived spin coherence and nuclear modulation effects of the silicon vacancy in 4H-SiC at room temperature

The silicon vacancy in silicon carbide is currently being considered for applications in quantum information and sensing, with several studies showing room temperature spin polarization and manipulation. We perform room temperature optically-detected magnetic resonance and spin echo measurements on an ensemble of silicon vacancies to better characterize the nature of this system and determine the spin coherence properties. The spin coherence time is shown to be dependent on magnetic field, varying from a few $\mu $s at low fields to longer than 30 $\mu $s at 50 mT. Strong spin echo modulation that varies with magnetic field is also observed. The modulation is attributed to the interaction with nearby nuclear spins and is well-described by a theoretical model.   

Oxygen-Boron Vacancy Defect in Cubic Boron Nitride: A Diamond NV$^-$ Isoelectronic Center

The promises of NV$^?$ center in diamond for quantum information application have inspired unprecedented research interests in optical manipulations of defect states, and have stimulated the search for alternative isoelectronic defect systems. In this talk, we present a diamond NV$^-$ like color center in $c$-BN based on first-principles electronic structure calculations using the Heyd-Scuseria-Ernzerhof hybrid functional. The defect consists of an substitutional oxygen and an adjacent boron vacancy (O$_{\mathrm{N}}$$-$V$_{\mathrm{B}}$). We discuss the electronic and optical properties of this center in comparison with the NV- center GC-2 defect center in c-BN. We acknowledge the computational support provided by the Center for Computational Research at the University at Buffalo, SUNY. This work is supported by the US Department of Energy under Grant No. DE-SC0002623 and by the National Science Foundation under Grant No. DMR-0946404. Work at Beijing CSRC is supported by the National Natural Science Foundation of China (Grant No. 11328401).   

Observation of a single rare-earth ion in a crystal by electric-field modulation spectroscopy for a readout of a nuclear-spin qubit

Nuclear spin states of rare-earth-metal ions in a crystal are known as good candidates for qubits in solids because of their long coherence time and their good controllability by lights. In the frequency-domain quantum computer (FDQC), nuclear spin states of the ions are employed as qubits defined in a frequency domain, and interaction between the qubits is mediated by a single cavity mode. In FDQC we can use adiabatic passage with dark states to perform single-qubit gates and two-qubit gates [1], and a single-qubit gate using adiabatic passage has been demonstrated [2]. For two-qubit gates, quantum states of qubit ions need to be read out and operated individually. In order to observe a single ion in a crystal, we studied modulated signals due to ions in a cavity-mode spectrum of a monolithic optical cavity made of Pr$^{3+}$:Y$_2$SiO$_5$. Owing to the cavity enhancement and the electric-field modulation spectroscopy, signals which are likely due to individual ions (statistical fine structure in an inhomogeneously broadened optical trandition) were observed.\\[4pt] [1] K. Ichimura, Opt. Commun., 196, 119 (2001).\\[0pt] [2] H. Goto and K. Ichimura, Phys. Rev. A, 75, 033404 (2007).   

Wavefunction dynamics in a quantum-dot electron pump under a high magnetic field

A quantum-dot electron pump, formed and operated by applying time-dependent potential barriers to a two dimensional electron gas system, provides a promising redefinition of ampere. The pump operation consists of capturing an electron from a reservoir into a quantum dot and ejecting it to another reservoir. The capturing process has been theoretically understood by a semi-classical treatment of the tunneling between the dot and reservoir.\footnote{V. Kashcheyevs, B. Kaestner, PRL \textbf{104}, 186805 (2010)} But the dynamics of the wavefunction of the captured electron in the ejection process has not been theoretically addressed, although it is useful for enhancing pump accuracy and for utilizing the pump as a single-electron source for mesoscopic quantum electron devices. We study the dynamics under a strong magnetic field that leads to magnetic confinement of the captured electron, which dominates over the electrostatic confinement of the dot. We find that the wave packet of the captured electron has the Gaussian form with the width determined by the strength of the magnetic field, and that the time evolution of the packet follows the classical drift motion, with maintaining the Gaussian form. We discuss the possible signatures of the wave packet dynamics in experiments.   

Semiconducting nanodimer as a photonic cavity: Large and well-defiined Rabi splitting

A metallic nanodimer acts as a photonic cavity because a strong light field appears at the gap region due to a surface plasmon resonance. In this talk, we propose a photonic cavity consisting of a semiconducting nanodimer with a small gap, and theoretically demonstrate large and well-defined vacuum Rabi splitting of a two-level emitter placed at the photonic cavity. A light field is strongly enhanced at the gap region of the semiconducting nanodimer due to an exciton resonance. The interaction between the enhanced light and the emitter is significantly larger than that in a conventional photonic cavity, because the semiconducting nanodimer has a small cavity-mode volume beyond the diffraction limit as well as the metallic nanodimer. In contrast to the metallic nanodimer, the exciton decay rate at low temperature is very small, and as a result, the quality factor reaches $Q \sim 10^4$ which is about 100 times larger than that of the metallic nanodimer. Consequently, the large Rabi splitting energy ($\sim 1.7$ meV) appears for the small dipole moment ($\sim 25$ Debye) of the emitter, and the splitting energy is two times larger than the spectral width. Such a well-defined Rabi splitting is highly suited for both fundamental researches and applications.