We report electron counting experiments in a silicon metal-oxide-semiconductor quantum dot architecture which has been previously demonstrated to generate a quantized current in excess of 80 pA with uncertainty below 30 parts per million. Single-shot detection of electrons pumped into a reservoir dot is performed using a capacitively coupled single-electron transistor. We extract the full probability distribution of the transfer of n electrons per pumping cycle for n = 0, 1, 2, 3, and 4. We find that the probabilities extracted from the counting experiment are in agreement with direct current measurements in a broad range of dc electrochemical potentials of the pump. The electron counting technique is also used to confirm the improving robustness of the pumping mechanism with increasing electrostatic confinement of the quantum dot.
Non-adiabatic charge pumping through a single-level quantum dot with periodically modulated parameters is studied theoretically. By means of a quantum-master-equation approach the full counting statistics of the system is obtained. We find a trinomial-probability distribution of the charge transfer, which adequately describes the reversal of the pumping current by sweeping the driving frequency. Further, we derive equations of motion for current and noise, and solve those numerically for two different driving schemes. Both show interesting features which can be fully analyzed due to the simple…
Nanoscale single-electron pumps can be used to generate accurate currents, and can potentially serve to realize a new standard of electrical current based on elementary charge. Here, we use a silicon-based quantum dot with tunable tunnel barriers as an accurate source of quantized current. The charge transfer accuracy of our pump can be dramatically enhanced by controlling the electrostatic confinement of the dot using purposely engineered gate electrodes. Improvements in the operational robustness, as well as suppression of non-adiabatic transitions that reduce pumping accuracy, are achieved …
Statistics of charge transport in an adiabatic pump are determined by the dynamics of the scattering matrix S(t). We show that, up to an integer offset, the statistics depend only on the corresponding path N(t)=S^\daggerσ_3 S in the coset space (the sphere for a single channel). For a general loop S(t) we solve for the noise-minimizing pumping strategy. The average current is given by the area enclosed by N(t) in the coset space; its minimal noise by the area of a minimal surface (soap film) spanned by N(t) in the space of all matrices. We formulate conditions for quantization of the pumped ch…
We consider quantum statistics of charge transmitted through a mesoscopic device in the adiabatic pumping process. A general formula for the distribution function of the transmitted charge in terms of the time-dependent S-matrix is obtained. It is applied to a few simple examples of the pumping cycles. We identify coherent pumping strategies which lead to the binomial charge distribution and minimize the fluctuations of the pumped current. Conditions for the ideal noiseless quantized pump are discussed.
We calculate the charge transport in a flux biased dissipative Cooper pair pump using the method of full counting statistics (FCS). This is instead of a more traditional technique of integrating a very small expectation value of the instantaneous current over the pumping period. We show that the rotating wave approximation (RWA), which fails in the traditional technique, produces accurate results within the FCS method.
We study the full charge counting statistics of a charge pump based on a nearly open single electron transistor. The problem is mapped onto an exactly soluble problem of a g=1/2 non-equilibrium Luttinger liquid with an impurity. We obtain an analytic expression for the generating function of the transmitted charge for an arbitrary pumping strength. Even though this model contains fractionally charged excitations only integer transmitted charges can be observed during finite observation times.
Electron counting statistics of a current pump in an open system has universal form in the weak pumping current regime. In the time domain, charge transmission is described by two uncorrelated Poisson processes, corresponding to electron transmission in the right and left direction. Overall noise is super-poissonian, and can be reduced to poissonian by tuning the amplitude and phase of driving signal so that current to noise ratio is maximized. Measuring noise in this regime provides a new method for determining charge quantum in an open system without any fitting parameters.
The full counting statistics of a non adiabatic pure spin pump are calculated with particular emphasis on the second and third moments. We show that incoherence can change the sign of spin shot noise cross-correlations from negative to positive, implying entanglement for spin-singlet electronic sources, a truly counterintuitive result. The third moment on the other hand is shown to be much more resilient to incoherence.
We optimize the operation of single-electron charge pumps using full counting statistics techniques. To this end, we evaluate the statistics of pumped charge on a wide range of driving frequencies using Floquet theory, focusing here on the current and the noise. For charge pumps controlled by one or two gate voltages, we demonstrate that our theoretical framework may lead to enhanced device performance. Specifically, by optimizing the driving parameters, we predict a significant increase in the frequencies for which a quantized current can be produced. For adiabatic two-parameter pumps, we exp…
We perform in-situ detection of individual electrons pumped through a single-electron turnstile based on ultrasmall normal metal - insulator - superconductor tunnel junctions. In our setup, limited by the detector bandwidth, at low repetition rates we observe errorless sequential transfer of up to several hundred electrons through the system. At faster pumping speeds up to 100 kHz, we show relative error rates down to 10^-3, comparable to typical values obtained from measurements of average pumped current in non-optimized individual turnstiles. The work constitutes an initial step towards a se…
Semiconductor-based quantum dot single-electron pumps are currently the most promising candidates for the direct realization of the emerging quantum standard of the ampere in the International System of Units. Here, we discuss a silicon quantum dot single-electron pump with radio frequency control over the transparencies of entrance and exit barriers as well as the dot potential. We show that our driving protocol leads to robust bidirectional pumping: one can conveniently reverse the direction of the quantized current by changing only the phase shift of one driving waveform with respect to the…
For donor nuclear spins in silicon, we show how to deterministically prepare various symmetric and asymmetric Dicke states which span a complete basis of the many-body Hilbert space. The state preparation is realized by cooperative pumping of nuclear spins by coupled donor electrons, and the required controls are in situ to the prototype Kane proposal for quantum computation. This scheme only requires a sub-gigahertz donor exchange coupling which can be readily achieved without atomically precise donor placement, hence it offers a practical way to prepare multipartite entanglement of spins in …
The Electron Counting Capacitance Standard currently pursued at PTB aims to close the Quantum Metrological Triangle with a final precision of a few parts in 10^7. This paper reports the considerable progress recently achieved with a new generation of single-electron tunnelling devices. A five-junction R-pump was operated with a relative charge transfer error of five electrons in 10^7, and was used to successfully perform single-electron charging of a cryogenic capacitor. The preliminary result for the single-electron charge quantum has an uncertainty of less than two parts in 10^6 and is consi…
We discuss the problem of full counting statistics for periodic pumping. The probability generating function is usually defined on a circle of the "physical" values of the counting parameter, with its periodicity corresponding to charge quantization. The extensive part of the generating function can either be an analytic function on this circle or have singularities. These two cases may be interpreted as different thermodynamic phases in time domain. We discuss several examples of phase transitions between these phases for classical and quantum systems. Finally, we prove a criterion for the "a…
A capacitance standard based on the definition of capacitance C = Ne/U is realized when a capacitor is charged with a known number N of electrons (e is the elementary charge) and the voltage U across the capacitor is measured. If U is measured by means of a Josephson voltage standard, C is solely determined by quantum numbers and fundamental constants. Presently, PTB is setting up this experiment using a special type of single-electron pump, the so-called r-pump, for transferring electrons one by one onto a cryogenic vacuum capacitor with the decadic capacitance C = 1 pF. We report on the prog…
We demonstrate that the dynamic nuclear polarization (DNP) of phosphorus donors in silicon can be very effective in a magnetic field of 4.6 T and at temperatures below 1 K. The DNP occurs due to the Overhauser effect following a cross relaxation via the forbidden flip-flop or flip-flip transitions. Nuclear polarization values $P>0.98$ were reached after 20 min of pumping with 0.4 $μ$W of microwave power. We evaluated that the ratio of hyperfine state populations increased by three orders of magnitude after 2 hours of pumping, and an extremely pure nuclear spin system containing $<10^{-11}$ of …
Microscopic theory of counting statistics of electrical noise is reviewed. We discuss a model of passive charge detector based on current fluctuations coupled to a spin, and its relation with the theory of photon counting in quantum optics. The statistics of tunneling current and, in particular, the properties of the third moment are studied in detail. The third moment is shown to be temperature-independent for tunneling in a generic many-body system. Then the statistics of mesoscopic transport is discussed. We consider applications of the functional determinant formula for the generating func…
In-Memory AM Demodulation Using an All-Silicon Independent-Dual-Gate Gain-Cell Memory with $<10^{-22}$ A Leakage Determined by Single-Electron Counting
Institute for Multidisciplinary Sciences, Yokohama National University（横滨国立大学多学科科学研究所）；Basic Research Laboratories, NTT Inc.（日本电信电话株式会社基础实验室）；Research Center for Integrated Quantum Electronics, Hokkaido University（北海道大学综合量子电子学研究中心）
An inverse spin Hall effect (ISHE) in n-type silicon was observed experimentally when conduction electrons were scattered on the spin-orbit potential of bismuth. The spin current in the silicon layer was generated by excitation of the magnetization precession during ferromagnetic resonance in a thin permalloy (Py) layer deposited on a Si layer doped by phosphor and bismuth. From the angular dependences of the dc voltage for different Py/n-Si:Bi structures aligned along the [011] or [100] crystal axes, we were able to distinguish the planar Hall effect (PHE) and ISHE contributions. The ISHE dc …
We investigate a hybrid metallic island / single dopant electron pump based on fully-depleted silicon on insulator technology. Electron transfer between the central metallic island and the leads is controlled by resonant tunneling through single phosphorus dopants in the barriers. Top gates above the barriers are used control the resonance conditions. Applying radio frequency signals to the gates, non-adiabatic quantized electron pumping is achieved. A simple deterministic model is presented and confirmed by comparing measurements with simulations.
Presented in this paper is a proof-of-concept for a new approach to single electron pumping based on a Single Atom Transistor (SAT). By charge pumping electrons through an isolated dopant atom in silicon, precise currents of up to 160 pA at 1 GHz are generated, even if operating at 4.2 K, with no magnetic field applied, and only when one barrier is addressed by sinusoidal voltage cycles.
Due to the difficulty to grow high quality semiconductors on ferromagnetic metals, the study of spin diffusion transport in Si was only limited to lateral geometry devices. In this work, by using ultra-high vacuum wafer-bonding technique, we have successfully fabricated metal semiconductor metal CoFeB/MgO/Si/Pt vertical structures. We hereby demonstrate pure spin-current injection and transport in the perpendicular current flow geometry over a distance larger than 2μm in n-type Si at room temperature. In those experiments, a pure propagating spin-current is generated via ferromagnetic resonanc…
For an open quantum system, we investigate the pumped current induced by a slow modulation of control parameters on the basis of the quantum master equation and full counting statistics. We find that the average and the cumulant generating function of the pumped quantity are characterized by the geometrical Berry-phase-like quantities in the parameter space, which is associated with the generator of the master equation. From our formulation, we can discuss the geometrical pumping under the control of the chemical potentials and temperatures of reservoirs. We demonstrate the formulation by spin…
The fabrication of single atom transistors paved the way for electronics based on single dopants. Recently the spectrum of a single dopant was measured electrically by coupling two such devices. The next step towards promising functionalities for future nanoelectronics consists in manipulating a single electron over two dopants. Here we demonstrate electron pumping through two phosphorus donors in series implanted in a silicon nanowire. While quantized pumping is achieved in the low frequency adiabatic regime, we observe remarkable features at higher frequency when the charge transfer is limit…
Single donors in semiconductor nanostructures represent a key element to develop spin related quantum functionalities in atomic scale devices. Quantum transport through a single Arsenic donor in the channel of a Silicon nano-field effect transistor under microwave irradiation is investigated. The device is characterized at mK temperatures in the regime of Coulomb-blockade. Photon assisted tunneling and microwave induced electron pumping regimes are revealed respectively at low and high microwave power. At sufficiently high power, the microwave irradiation induces tunneling through the first ex…
We report on measurements of the spin relaxation time T1 of individual electron spins in the few electron regime of a Si/SiO2-based quantum dot (QD). Energy-spectroscopy of the QD has been performed using a charge sensing technique. The spin relaxation times are subsequently measured in the time-domain by a pump-and-probe method. For the QD that contains an unpaired spin, likely only a single electron, we find that T1 depends strongly on the applied magnetic field. Possible mechanisms leading to the observed spin relaxation are discussed.
Single-electron pumps based on semiconductor quantum dots are promising candidates for the emerging quantum standard of electrical current. They can transfer discrete charges with part-per-million (ppm) precision in nanosecond time scales. Here, we employ a metal-oxide-semiconductor silicon quantum dot to experimentally demonstrate high-accuracy gigahertz single-electron pumping in the regime where the number of electrons trapped in the dot is determined by the thermal distribution in the reservoir leads. In a measurement with traceability to primary voltage and resistance standards, the avera…
In quantum metrology, semiconductor single-electron pumps are used to generate accurate electric currents with the ultimate goal of implementing the emerging quantum standard of the ampere. Pumps based on electrostatically defined tunable quantum dots (QDs) have thus far shown the most promising performance in combining fast and accurate charge transfer. However, at frequencies exceeding approximately 1 GHz, the accuracy typically decreases. Recently, hybrid pumps based on QDs coupled to trap states have led to increased transfer rates due to tighter electrostatic confinement. Here, we operate…
Reliable detection of single electron tunneling in quantum dots (QD) is paramount to use this category of device for quantum information processing. Here, we report charge sensing in a degenerately phosphorus-doped silicon QD by means of a capacitively coupled single-electron tunneling device made of the same material. Besides accurate counting of tunneling events in the QD, we demonstrate that this architecture can be operated to reveal asymmetries in the transport characteristic of the QD. Indeed, the observation of gate voltage shifts in the detector's response as the QD bias is changed is …
We consider charge pumping in a system of parafermions, implemented at fractional quantum Hall edges. Our pumping protocol leads to a noisy behavior of the pumped current. As the adiabatic limit is approached, not only does the noisy behavior persist but the counting statistics of the pumped current becomes robust and universal. In particular, the resulting Fano factor is given in terms of the system's topological degeneracy and the pumped quasiparticle charge. Our results are also applicable to the more conventional Majorana fermions.
Hybrid spin-mechanical systems are a promising platform for future quantum technologies. Usually they require application of additional microwave fields to project integer spin to a readable state. We develop a theory of optically detected spin-mechanical resonance associated with half-integer spin defects in silicon carbide (SiC) membranes. It occurs when a spin resonance frequency matches a resonance frequency of a mechanical mode, resulting in a shortening of the spin relaxation time through resonantly enhanced spin-phonon coupling. The effect can be detected as an abrupt reduction of the p…
Electron counting experiments attempt to provide a current of a known number of electrons per unit time. We propose architectures utilizing a few readily available electron-pumps or turnstiles with the typical error rates of 100 ppm with common sensitive electrometers to achieve the desirable accuracy of 1 part in 10 ppb. This is achieved not by counting all transferred electrons but by counting only the errors of individual devices; these are less frequent and therefore readily recognized and accounted for. We thereby ease the route towards quantum based standards for current and capacitance.
Electron counting experiments attempt to provide a current of a known number of electrons per unit time. We propose architectures utilizing a few readily available electron-pumps or turnstiles with modest error rates of 1 part per $10^4$ with common sensitive electrometers to achieve the desirable accuracy of 1 part in $10^8$. This is achieved not by counting all transferred electrons but by counting only the errors of individual devices; these are less frequent and therefore readily recognized and accounted for. Our proposal thereby eases the route towards quantum based standards for current …
Schemes aimed at transferring individual electrons in semiconductor devices and detecting possible transfer errors have increasing importance for metrological applications. We study the coupling of a superconducting Josephson-junction-based charge detector to an electron island defined by field-effect in silicon. The flexibility of our device allows one to tune the coupling using the detector as an additional gate electrode. We study the reliability of the electron sensor in different device configurations and the suitability of various operation modes for error detection in electron pumping e…
