Self-driven oscillation in Coulomb blockaded suspended carbon nanotubes

Suspended carbon nanotubes are known to support self-driven oscillations due to electromechanical feedback under certain conditions, including low temperatures and high mechanical quality factors. Prior reports identified signatures of such oscillations in Kondo or high-bias transport regimes. Here, we observe self-driven oscillations that give rise to significant conduction in normally Coulomb-blockaded low-bias transport. Using a master equation model, the self-driving is shown to result from strongly energy-dependent electron tunneling, and the dependencies of transport features on bias, gate voltage, and temperature are well reproduced.Comment: Main text + Appendices (8 pages, 10 figures

Sensitive Magnetic Force Detection with a Carbon Nanotube Resonator

We propose a technique for sensitive magnetic point force detection using a suspended carbon nanotube (CNT) mechanical resonator combined with a magnetic field gradient generated by a ferromagnetic gate electrode. Numerical calculations of the mechanical resonance frequency show that single Bohr magneton changes in the magnetic state of an individual magnetic molecule grafted to the CNT can translate to detectable frequency shifts, on the order of a few kHz. The dependences of the resonator response to device parameters such as length, tension, CNT diameter, and gate voltage are explored and optimal operating conditions are identified. A signal-to-noise analysis shows that in principle, magnetic switching at the level of a single Bohr magneton can be read out in a single shot on timescales as short as 10 microseconds. This force sensor should enable new studies of spin dynamics in isolated single molecule magnets, free from the crystalline or ensemble settings typically studied.Comment: Pages 1-6 are the main paper, pages 7-11 are supplementary materia

Simulated coherent electron shuttling in silicon quantum dots

Shuttling of single electrons in gate-defined silicon quantum dots is numerically simulated. A minimal gate geometry without explicit tunnel barrier gates is introduced, and used to define a chain of accumulation mode quantum dots, each controlled by a single gate voltage. One-dimensional potentials are derived from a three-dimensional electrostatic model, and used to construct an effective Hamiltonian for efficient simulation. Control pulse sequences are designed by maintaining a fixed adiabaticity, so that different shuttling conditions can be systematically compared. We first use these tools to optimize the device geometry for maximum transport velocity, considering only orbital states and neglecting valley and spin degrees of freedom. Taking realistic geometrical constraints into account, charge shuttling speeds up to $\sim$300 m/s preserve adiabaticity. Coherent spin transport is simulated by including spin-orbit and valley terms in an effective Hamiltonian, shuttling one member of a singlet pair and tracking the entanglement fidelity. With realistic device and material parameters, shuttle speeds in the range 10-100 m/s with high spin entanglement fidelities are obtained when the tunneling energy exceeds the Zeeman energy. High fidelity also requires the inter-dot valley phase difference to be below a threshold determined by the ratio of tunneling and Zeeman energies, so that spin-valley-orbit mixing is weak. In this regime, we find that the primary source of infidelity is a coherent spin rotation that is correctable, in principle. The results pertain to proposals for large-scale spin qubit processors in isotopically purified silicon that rely on coherent shuttling of spins to rapidly distribute quantum information between computational nodes.Comment: 31 pages, 15 figures including Appendi

Fast measurement of carbon nanotube resonator amplitude with a heterojunction bipolar transistor

Carbon nanotube (CNT) electromechanical resonators have demonstrated unprecedented sensitivities for detecting small masses and forces. The detection speed in a cryogenic setup is usually limited by the CNT contact resistance and parasitic capacitance. We report the use of a heterojunction bipolar transistor (HBT) amplifying circuit near the device to measure the mechanical amplitude at microsecond timescales. A Coulomb rectification scheme, in which the probe signal is at much lower frequency than the mechanical drive signal, allows investigation of the strongly non-linear regime. The behaviour of transients in both the linear and non-linear regimes is observed and modeled by including Duffing and non-linear damping terms in a harmonic oscillator equation. We show that the non-linear regime can result in faster mechanical response times, on the order of 10 microseconds for the device and circuit presented, potentially enabling the magnetic moments of single molecules to be measured within their spin relaxation and dephasing timescales.Comment: Pages 1-5 are the main paper, pages 6-8 are supplementary materia

Readout of Majorana parity states using a quantum dot

We theoretically examine a scheme for projectively reading out the parity state of a pair of Majorana bound states (MBS) using a tunnel coupled quantum dot. The dot is coupled to one end of the topological wire but isolated from any reservoir, and is capacitively coupled to a charge sensor for measurement. The combined parity of the MBS-dot system is conserved and charge transfer between the MBS and dot only occurs through resonant tunnelling. Resonance is controlled by the dot potential through a local gate and by the MBS energy splitting due to the overlap of the MBS pair wavefunctions. The latter splitting can be tuned from zero (topologically protected regime) to a finite value by gate-driven shortening of the topological wire. Simulations show that the oscillatory nature of the MBS splitting is not a fundamental obstacle to readout, but requires precise gate control of the MBS spatial position and dot potential. With experimentally realistic parameters, we find that high-fidelity parity readout is achievable given nanometer-scale spatial control of the MBS, and that there is a tradeoff between required precisions of temporal and spatial control. Use of the scheme to measure the MBS splitting versus separation would present a clear signature of topological order, and could be used to test the robustness of this order to spatial motion, a key requirement in certain schemes for scalable topological qubits. We show how the scheme can be extended to distinguish valid parity measurements from invalid ones due to gate calibration errors.Comment: 3 figures; added two tables in updated versio

Efficient continuous wave noise spectroscopy beyond weak coupling

The optimization of quantum control for physical qubits relies on accurate noise characterization. Probing the spectral density $S(\omega)$ of semi-classical phase noise using a spin interacting with a continuous-wave (CW) resonant excitation field has recently gained attention. CW noise spectroscopy protocols have been based on the generalized Bloch equations (GBE) or the filter function formalism, assuming weak coupling to a Markovian bath. However, this standard protocol can substantially underestimate $S(\omega)$ at low frequencies when the CW pulse amplitude becomes comparable to $S(\omega)$. Here, we derive the coherence decay function more generally by extending it to higher orders in the noise strength and discarding the Markov approximation. Numerical simulations show that this provides a more accurate description of the spin dynamics compared to a simple exponential decay, especially on short timescales. Exploiting these results, we devise a protocol that uses an experiment at a single CW pulse amplitude to extend the spectral range over which $S(\omega)$ can be reliably determined to $\omega=0$.Comment: 10 pages, 6 figure

Few-Qubit Magnetic Resonance Quantum Information Processors: Simulating Chemistry and Physics

We review recent progress made in quantum information processing (QIP) which can be applied in the simulation of quantum systems and chemical phenomena. The review is focused on quantum algorithms which are useful for quantum simulation of chemistry and advances in nuclear magnetic resonance (NMR) and electron spin resonance (ESR) QIP. Discussions also include a number of recent experiments demonstrating the current capabilities of the NMR QIP for quantum simulation and prospects for spin-based implementations of QIP.Comment: 47 pages, 9 figures. To appear in Adv. Chem. Phys., special issue on Quantum Information and Computation for Chemistr

Non-equilibrium Green's function study of magneto-conductance features and oscillations in clean and disordered nanowires

We explore various aspects of magneto-conductance oscillations in semiconductor nanowires, developing quantum transport models based on the non-equilibrium Green's function formalism. In the clean case, Aharonov-Bohm (AB - h/e) oscillations are found to be dominant, contingent upon the surface confinement of electrons in the nanowire. We also numerically study disordered nanowires of finite length, bridging a gap in the existing literature. By varying the nanowire length and disorder strength, we identify the transition where Al'tshuler-Aronov-Spivak (AAS - h/2e) oscillations start dominating, noting the effects of considering an open system. Moreover, we demonstrate how the relative magnitudes of the scattering length and the device dimensions govern the relative dominance of these harmonics with energy, revealing that the AAS oscillations emerge and start dominating from the center of the band, much higher in energy than the conduction band-edge. We also show the ways of suppressing the oscillatory components (AB and AAS) to observe the non-oscillatory weak localization corrections, noting the interplay of scattering, incoherence/dephasing, the geometry of electronic distribution, and orientation of magnetic field. This is followed by a study of surface roughness which shows contrasting effects depending on its strength and type, ranging from magnetic depopulation to strong AAS oscillations. Subsequently, we show that dephasing causes a progressive degradation of the higher harmonics, explaining the re-emergence of the AB component even in long and disordered nanowires. Lastly, we show that our model qualitatively reproduces the experimental magneto-conductance spectrum in [Holloway et al, PRB 91, 045422 (2015)] reasonably well while demonstrating the necessity of spatial-correlations in the disorder potential, and dephasing.Comment: 15 pages, 18 figure

Demonstration of sufficient control for two rounds of quantum error correction in a solid state ensemble quantum information processor

We report the implementation of a 3-qubit quantum error correction code (QECC) on a quantum information processor realized by the magnetic resonance of Carbon nuclei in a single crystal of Malonic Acid. The code corrects for phase errors induced on the qubits due to imperfect decoupling of the magnetic environment represented by nearby spins, as well as unwanted evolution under the internal Hamiltonian. We also experimentally demonstrate sufficiently high fidelity control to implement two rounds of quantum error correction. This is a demonstration of state-of-the-art control in solid state nuclear magnetic resonance, a leading test-bed for the implementation of quantum algorithms

Orbital Josephson Interference in a Nanowire Proximity Effect Junction

A semiconductor nanowire based superconductor-normal-superconductor (SNS) junction is modeled theoretically. A magnetic field is applied along the nanowire axis, parallel to the current. The Bogoliubov-de Gennes equations for Andreev bound states are solved while considering the electronic subbands due to radial confinement in the N-section. The energy-versus-phase curves of the Andreev bound states shift in phase as the N-section quasiparticles with orbital angular momentum couple to the axial field. A similar phase shift is observed in the continuum current of the junction. The quantum mechanical result is shown to reduce to an intuitive, semi-classical model when the Andreev approximation holds. Numerical calculations of the critical current versus axial field reveal flux-aperiodic oscillations that we identify as a novel form of Josephson interference due to this orbital subband effect. This behavior is studied as a function of junction length and chemical potential. Finally, we discuss extensions to the model that may be useful for describing realistic devices.Comment: New version contains 7 figures. Appendix on continuum current calculation