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The uncertainty of the Si molar mass measurement is theoretically investigated by means of a two-isotope model, with particular emphasis to the role of this measurement in the determination of the Avogadro constant. This model allows an explicit calibration formula to be given and propagation of error analysis to be made. It also shows that calibration cannot correct for non-linearity.

We report on the progress and new results in the setup of the electron counting capacitance standard (ECCS) at Physikalisch-Technische Bundesanstalt (PTB), Braunschweig, Germany. Considerable progress has been made in the operation of the single-electron circuit and in the incorporation of a cryogenic capacitor into the millikelvin refrigerator setup. The single-electron tunneling (SET) circuit comprised a five-junction, single-electron R-pump that showed an electron retention time of more than 600 s, and the circuit was successfully used for the deterministic shuttle transfer of charge packets consisting of few electrons. In addition, the cryogenic capacitor was tested, and its performance was found to be suitable for a high-precision ECCS experiment.

We report on the development of a novel highly linear voltage ramp generator to be used for the traceable calibration of picoamperemeters. The generator is based on two digital-to-analog converters, one of them being used to compensate for the differential nonlinearity of the other one. The generator is completely controllable by a computer, its voltage slope dV/dt is adjustable between 1 and 1000 mV/s. During a ramp running between -10 and +10 V, the slope shows a relative variation of only 1.3 middot10-5 (relative standard deviation). Due to a small output filter time constant of only 10 ms, we are, for the first time, able to conduct dynamic measurements of picoamperemeters with no sacrifice of linearity.

A capacitance standard based on the definition of capacitance C=Ne/U is realized if 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, Physikalisch-Technische Bundesanstalt (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 progress in the setup with emphasis on the characterization of the single-electron tunneling elements. We describe the modifications of the single-electron circuit that are necessary to implement the capacitor charging experiment by using a four- or five-junction r-pump.

We present the comparison of results from the generation and the measurement of direct currents in the pA range, performed with traceable state-of-the-art methods at highest accuracy. The currents were generated with the capacitor charging method, and measured with the first prototype of a novel picoammeter developed at PTB. The results confirm the agreement between both methods and the linearity of the new picoammeter at an uncertainty level of few microA/A. Also, they shed light on the ac-dc difference of capacitors, crucial for current generation with the capacitor charging method., 2 pages, 1 figure. Contribution (summary paper, to appear in IEEE CPEM 2014 Conference Digest) accepted for presentation on the Conference on Precision Electromagnetic Measurements (CPEM) 2014 in Rio de Janeiro (Brazil), 24-29 August 2014

A new traceable low current source based on charging a capacitor by a ramp generator consisting of two digital-to-analog converters has been developed by MIKES. The current source has been compared with the ramp generator current source of PTB at currents between 10 fA and 100 pA. No significant deviations were observed at uncertainty levels ranging from about 20 µA/A at 100 pA to about 7 mA/A at 10 fA.

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 consistent with the value of the elementary charge., Comment: 16 pages, 9 figures, 1 table

We measure the frequency dependence of a sample of commercial air- and gas-dielectric capacitors between 1 kHz and ≈0.01 Hz. We find that the capacitance of sealed-gas capacitors can change by more than 100 µF/F over this range. This has important implications for the use of gas capacitors in reference sub-nA current generators.

Continuous-wave laser emission has been obtained in (14)NH(3) by using different excitation techniques. Two-photon infrared-microwave pumping led to laser emission with offsets between the virtual level and a real level up to 3 GHz. Raman laser emission could be demonstrated with offsets between the virtual level and a real level tip to 0.56 GHz. A new coincidence between (14)NH(3) and N(2)O could be used to generate far-infrared laser emission by resonant single-photon pumping.

We report on our new results in the setup of an experiment where a capacitor is charged by a well-known number of electrons. Considerable progress was made by using a single-electron R-pump for the controlled manipulation of single electrons for the first time, and by the successful implementation of a suitable cryogenic capacitor in the millikelvin dilution refrigerator setup.

For the calibration of picoammeters a novel highly linear voltage ramp generator has been constructed which is based on digital electronics and two digital-to-analog-converters (DACs). In contrast to our previous ramp generator constructed entirely in analog electronics the new design allows for the first time to perform dynamic measurements without any sacrifice of linearity.

As the sensors of many magnetometers, such as SQUID magnetometers, are not directly accessible, their spatial location is often known only approximately. To be able to position such sensors more accurately, a novel measuring setup has been developed to determine the sensor location by means of magnetic measurements. The system has a resolution of better than 0.1 mm. It can be used with virtually any magnetometer that is capable of working in inhomogeneous fields. Measurements with SQUIDs inside two different commercial Dewars yielded out-of-axis sensor displacements of 1.6 mm and 7.5 mm, which show clearly that the performing of such measurements is essential in experiments where the exact sensor location could be crucial.

An intercomparison of precision current sources was carried out for currents between 10 fA to 10 pA. The current sources of both PTB and VNIIM were based on the principle of charging a capacitor using a linear voltage ramp (Rozhdestvenskaya et al., 1979) and (Willenberg et al., 2003). The relative deviation for the values of the sources were found to be between 2.8middot10-4 and 3.1middot10-3, depending on the current range

A new calibration setup for picoamperemeters is presented. Owing to the use of a novel voltage ramp generator with increased linearity, the useful measuring time is increased to about 35 min, which reduces the calibration uncertainty of picomaperemeters with long time constants.

The European COUNT project exploits two complementary single electron tunneling devices for use in electrical current metrology: a single electron pump as a current source and a single electron counter as a current meter. An electron pump has been developed with on-chip resistors in order to suppress cotunneling. The intended accuracy is 1 ppm for a current of a few picoamperes. Apart from being a quantum current standard, the electron pump could also be the basis of a capacitance standard. A coaxial tunable cryogenic capacitor of 1 picofarad has been developed for this purpose. A passive electron counter based on a single electron transistor embedded in a resonant tank circuit has been further investigated and developed in order to reach both high sensitivity and high counting speed. The intended accuracy is 10 ppm for a current of a few picoamperes.

A novel design of a cryogenic vacuum capacitor has been developed which is to be used in our future SET charging experiment. Due to its co-axial design it shows better stability than previous parallel-plate designs. In addition it promises to be better adjustable to a decadic capacitance value.

For the first time, a EURAMET comparison was performed in the field of small DC currents below 1?nA. The capabilities of thirteen European and non-European National Metrology Institutes for traceable calibrations of picoammeters have been compared. For that purpose, two different commercial picoammeters were used as travelling instruments. They were calibrated at current values of ?100?fA, ?1?pA, ?10?pA and ?100?pA. The accuracy achieved was to a large extent limited by the stability of the travelling instruments. The expanded relative uncertainty (k = 2) of the reference values varied between 2.7 ? 10?4 and 1.9 ? 10?5, depending on the current ranges and the travelling instruments. There was a good agreement between the results of most of the participants. Main text. To reach the main text of this paper, click on Final Report. Note that this text is that which appears in Appendix B of the BIPM key comparison database kcdb.bipm.org/. The final report has been peer-reviewed and approved for publication by EURAMET, according to the provisions of the CIPM Mutual Recognition Arrangement (CIPM MRA).

Short FIR laser pulses of high repetition rate are obtained by pumping NH3 with the pulses of a passively Q-switched IR laser. The two cascade laser transitions observed show coupled relaxation oscillations. The pulse shapes and delay times are qualitatively in agreement with a four-level rate-equation model.

The semiclassical density matrix treatment is applied to serial four-level systems for the steady state. Phase and energy relaxations as well as Doppler effects and M degeneracy are accounted for. The calculations are restricted to parallel polarized fields, avoiding problems of quantum interference. The formalism is used to calculate the gain spectra of different four-level far-infrared (FIR) laser schemes: double resonance pumped laser, Raman laser, two-photon pumped laser, and hyper-Raman-laser.

The SI unit of current, the ampere, may be realized by combining the results of two different NMR experiments observing the precession frequencies of some nuclei. In contrast to the well-known methods used in some metrology institutes we suggest referring the magnetic flux densities produced by quite different coil arrangements in the two experiments to one coil, thus eliminating the first-order influence of its geometrical dimensions.

Infrared‐microwave pumping of two‐photon transitions in NH3 has led to cw laser emission of a number of NH3 transitions in the far infrared.

We have used the precise molecular constants of the V(2) vibration of (14)NH(3) and (15)NH (3) together with the accurately known frequencies of the various CO(2) and N(2)O laser lines to calculate the coincidences between pump laser lines and NH (3) absorption lines that could lead to cw FIR laser emission. We have experimentally examined the coincidences between NH(3) absorption lines and (12)C(16)O(2) laser lines, providing information about up to which quantum numbers J, K laser emission can be expected. FIR power measurements confirm the expected good efficiency of NH(3) FIR lasers.

The European COUNT project exploits two complementary single electron tunneling (SET) devices for use in electrical current metrology: a single electron pump as a current source and a single electron counter as a current meter. Apart from being a quantum current standard, the electron pump could be the basis of a capacitance standard.

We report on the progress achieved at PTB in setting up an experiment for the realization of a quantum capacitance standard based on the controlled charging of a capacitor by single electrons. An experiment of this kind was suggested and first performed by NIST. In order to enhance the accuracy of the experiment, we use a new kind of single-electron pump and a capacitor with improved design features. The main components for the experiment are presented and discussed.