Fundamental electrical standards and the quantum metrological triangle

The advent of the fundamental constants R_K (the von Klitzing constant) and K_J (the Josephson constant) in electrical metrology and the growing development of nanotechnologies have totally changed the vision and the practice of the National Metrology Institutes (NMIs), opening a modern era of metrology and arousing a growing interest in a possible re-definition of the international system of units (SI). The Josephson effect (JE) and the Quantum Hall effect (QHE), at the origin of these fundamental constants, constitute the keystone of a new approach to electrical units, when one considers the very high level of reproducibility of these units, never seen before. On the other hand, the Watt balance experiment in which these constants play a part could be the origin of a new SI definition, replacing the mass unit ‘the kilogram’ as a fundamental unit by the Planck constant h. It thus seems that the implementation of experiments aimed at demonstrating the coherency between the theoretical and phenomenological values of these constants is a major objective. In this framework the metrological triangle experiment associating QHE, JE and single electron tunnelling effect would play a major role in checking the consistency of these fundamental constants in terms of the Planck and electron charge constants. This article gives briefly an outline of these quantum phenomena and their metrological applications in NMIs for the realisation of electrical units and the determination of the fundamental constants. To cite this article: F. Piquemal et al., C. R. Physique 5 (2004).     

The Elementary Charge for the Definition and Realization of the Ampere

The elementary charge e is one of the seven defining constants in the revised International System of Units (SI). Here, the determination of the elementary charge with the highest precision is discussed, including the results of the special CODATA adjustment leading to the fixed value of e. The various options to realize the ampere and the other electrical units in the revised SI, either through the counting of electrons by using single‐electron tunneling devices or through the Josephson and quantum Hall effect, respectively, are further elucidated.     

Quantum Hall effect: The resistivity of a 2D electron gas—a thermodynamic approach

Based on a thermodynamic approach, we have calculated the resistivity of a 2D electron gas, assumed dissipationless in a strong quantum limit. Standard measurements, with extra current leads, define the resistivity caused by a combination of Peltier and Seebeck effects. The current causes heating (cooling) at the first (second) sample contacts, due to the Peltier effect. The contact temperatures are different. The measured voltage is equal to the Peltier effect-induced thermoemf which is linear in current. As a result, the resistivity is non-zero as I→0. The resistivity is a universal function of magnetic field and temperature, expressed in fundamental units h/e². The universal features of magnetotransport data observed in the experiment confirm our predictions.     

The anomalous magnetic moment of the electron in hydrogenlike ions

The precise determination of the anomalous magnetic moment of the electron bound in hydrogen-like ions allows for a stringent test of quantum electrodynamics (QED)in the presence of strong electric fields. g-factor measurements on the electron bound in hydrogen-like ions ¹²C⁵⁺ and ¹⁶O⁷⁺, using single ions confined in a Penning trap, have yielded values in agreement with theory on the ppb level. If the QED calculations are considered correct, the results can in turn be used for a determination of fundamental constants like the electron mass m_e, the fine structure constant α or nuclear parameters. We report about presentdevelopments towards g-factor measurements also in medium-heavy and heavy highly-charged ions.     

Resistance metrology based on the quantum Hall effect

The Quantum Hall effect (QHE), a macroscopic effect of solid state physics, provides a universal representation of the unit of resistance which depends on the elementary charge e and the Planck constant h only. If implemented according to specific technical guidelines, the quantum resistance standard can be reproduced with a relative uncertainty below one part in 10⁹. Calibrations of wire resistors in terms of the QHE can be carried out with similarly low uncertainties by using resistance bridges equipped with cryogenic current comparators, the performance of which relies on the magnetic flux sensitivity of superconducting quantum interference devices (SQUID). Using a special connection technique, the fundamental properties of the QHE allow the fabrication of arrays combining a large number of single Hall bars connected in series or in parallel and which demonstrate quantum accuracy. Similar to the case of voltage metrology with Josephson array voltage standards, an improvement of resistance metrology is expected from the availability of quantum Hall array resistance standards (QHARS). The QHE Wheatstone bridge, which is another application of the same connection technique, opens the way to new universality tests of the QHE with a relative uncertainty below one part in 10¹¹. At frequencies in the kilohertz range, the recent progress in the application of coaxial bridges to the QHE allows metrologists to operate a quantum resistance standard with alternating current reaching an accuracy of some parts in 10⁸. Finally, the discovery of the QHE in graphene opens new horizons for the resistance metrology.     

Physics with high energy electron-positron colliding beams with the MARK J detector

This report reviews the experimental investigation of high energy e⁺e^? interactions by the MARK J collaboration at PETRA, the electron-positron colliding beam accelerator at DESY in Hamburg, Germany. The physics objectives include studies of several purely electromagnetic processes and hadronic final states, which further our knowledge of the nature of the fundamental constituents and of their strong, electromagnetic and weak interactions. Before discussing the physics results, the main features and the principal components of the MARK J detector are discussed in terms of design, function, and performance. Several aspects of the on-line data collection and the off-line analysis are also outlined. Results are presented on tests of quantum electrodynamics using e⁺e^? → e⁺e^?, μ⁺μ^? and τ⁺τ^?, on the measurement of R, the ratio of the hadronic to the point-like muon pair cross section, on the search for new quark flavors, on the discovery of three jet events arising from the radiation of hard noncollinear gluons as predicted by quantum chromodynamics, and on the determination of the strong coupling constant α_s.     

Electromagnetic momentum in frontiers of modern physics

We review the role of the momentum of the electromagnetic (EM) fields P _e in several areas of modern physics. P _e represents the EM interaction in equations for matter and light waves propagation. As an application of wave propagation properties, a first order optical experiment which tests the speed of light in moving rarefied gases is presented. Within a classical context, the momentum P _e appears also in proposed tests of EM interactions involving open currents and angular momentum conservation laws. Moreover, P _e is the link to the unitary vision of the quantum effects of the Aharonov-Bohm (AB) type and, for several of these effects, the strength of P _e is evaluated. These effects provide a quantum approach to evaluate the limit of the photon mass m _ph. A new effect of the AB type, together with the scalar AB effect, provides the basis for table-top experiments which yield the limit m _ph = 9.4 × 10⁻⁵²g, a value that improves the results achieved with recent classical and quantum approaches.      

<Emphasis Type="Italic">CPT</Emphasis> Symmetry and Quantum Mechanics Tests in the Neutral Kaon System at KLOE

The neutral kaon system offers a unique possibility to perform fundamental tests of CPT invariance, as well as of the basic principles of quantum mechanics. The most recent limits obtained by the KLOE experiment at the DAΦNE e ⁺ e ⁻ collider on several kinds of possible CPT violation and decoherence mechanisms, which in some cases might be justified in a quantum gravity framework, are reviewed. No deviation from the expectations of quantum mechanics and CPT symmetry is observed, while the precision of the measurements, in some cases, reaches the interesting Planck scale region. Finally, prospects for this kind of experimental studies at KLOE-2 are presented.     

On neutrinoless double e capture problem

Resonance effects in neutrinoless double e capture are considered. It is shown that observation of these effects in future experiments is a fundamental test of QED. However, preparation of the experiment requires new technologies to be applied in nuclear physics.     

On the conductance of finite systems in the ballistic regime: Dependence on Fermi energy,magnetic field,frequency, and disorder

It is shown that the dc-conductance of a ballistically behaving electron system of a finite width is quantised in units ofe ²/h. The quantisation is independent of the length of the system, and can be observed experimentally by changing the Fermi energy, the geometrical width, and the magnetic field, alternatively. Two novel quantum phenomena are predicted. In the presence of weak disorder there are anti-resonances which separate neighboring conductance plateaus. The ac-conductance shows oscillations which can be assigned to interference of free electron states.     

A three‐level dark state and double‐control single‐photon logic gates via quantum coherent control

Multilevel quantum coherence and its quantum‐vacuum counterpart, where a three‐level dark state is involved, are suggested in order to achieve new photonic and quantum optical applications. It is shown that such a three‐level dark state in a four‐level tripod‐configuration atomic system consists of three lower levels, where constructive and destructive quantum interference between two control transitions (driven by two control fields) arises. We point out that the controllable optical response due to the double‐control tunable quantum interference can be utilized to design some fascinating new photonic devices such as logic gates, photonic transistors and switches at quantum level. A single‐photon two‐input XOR logic gate (in which the incident “gate” photons are the individual light quanta of the two control fields) based on such an effect of optical switching control with an EIT (electromagnetically induced transparency) microcavity is suggested as an illustrative example of the application of the dark‐state manipulation via the double‐control quantum interference. The present work would open up possibility of new applications in both fundamental physics (e.g., field quantization and relevant quantum optical effects in artificial systems that can mimic atomic energy levels) and applied physics (e.g., photonic devices such as integrated optical circuits at quantum level).     

A Possible New Value for the Electron Mass from g-Factor Measurements on Hydrogen-Like Ions

The mass of the electron in atomic units (m _e) represents the largest error contribution in an experiment to determine the g-factor of the electron bound in hydrogen-like carbon. Recent progress in the calculation reduces the uncertainty of the theoretical value to such a low value that m _e can be determined from a comparison of experimental and theoretical g-factors. The present preliminary value of the electron mass agrees with the accepted value but reduces the uncertainty by about a factor 2. This revised version was published online in July 2006 with corrections to the Cover Date.     

The structure of the nucleon

We assume that nucleons are made of quarks which are made of subquarks which are made of more fundamental subquarks, etc. Thus, finally, the proton and the neutron may be composed of an infinite number of pointlike quarks and antiquarks. The limit particle has quantum numbers of spinJ=1/2, isospinI=1/2, third component of isospinI ₃=1/2, and fractional electric chargeQ=(l/2)¦e¦, where ¦e¦ is the electron charge. All quantum numbers are thus just one-half and this fermion will behave as if it was lepton, since the baryon number approaches zero at an infinite sublayer level. Sum rules in lepton-nucleon scattering have been evaluated using this model. The predicted values are not incompatible with the experimental results.     

Energy relaxation of electrons in the (100) n-channel of a Si-MOSFET: II. Surface phonon treatment

The electron energy relaxation is investigated as a function of the “electron temperature” T_e in the n-channel of a (100) surface silicon MOSFET device by inspecting the phenomenological energy relaxation time τ_ε(T_e). τ_ε is determined theoretically and compared to experimental results in order to identify the energy relaxation mechanism(s) present at the interface. Two dimensional electron transport is assumed. Single activation temperature (θ) Rayleigh wave scattering and acoustic Rayleigh wave scattering are studied as possible energy loss processes. The effects of electric subbanding near the surface are included. τ_ε is calculated for T_e ? 15 K in the electric quantum limit. We find that a single θ = 12.0 K Rayleigh phonon fits theory to experiment for a single electron inversion density (N_inv) case, but can not provide a fit simultaneously for more than one N_inv value. Theory and experiment disagree when Rayleigh wave acoustic scattering is assumed.     

Pragmatic versus semantic contextuality in quantum physics

An approach to quantum physics (QP) is proposed that is characterized by the attempt to give up the verificationist theory of truth underlying the standard interpretation of QP. As a first step, anobservatively minimal language L is constructed that is endowed with a Tarskian truth theory. Then, a set of axioms is stated by means of L that hold both in classical physics and in QP, and the further language L_e of all properties is constructed. The concepts ofmeaning andtestability do not collapse in L and L_e, hence quantum logic is interpreted as a theory of testability in QP, and QP turns out to be semantically incomplete. Furthermore, semantic and pragmatic compatibility of physical properties are distinguished in L_e, and the concepts of testability and conjoint testability of statements are introduced. In this context some known quantum paradoxes can be avoided, and a new general principle (MGP) characterizes the truth mode of empirical physical laws. MGP invalidates the Bell theorem and, presumably, the Bell-Kochen-Specker theorem, and introduces apragmatic contextuality in QP in place of thesemantic contextuality that should occur because of these theorems.     

Electron Magnetic Moment in Highly Charged Ions: The ARTEMIS Experiment

The magnetic moment (g‐factor) of the electron is a fundamental quantity in physics that can be measured with high accuracy by spectroscopy in Penning traps. Its value has been predicted by theory, both for the case of the free (unbound) electron and for the electron bound in a highly charged ion. Precision measurements of the electron magnetic moment yield a stringent test of these predictions and can in turn be used for a determination of fundamental constants such as the fine structure constant or the atomic mass of the electron. For the bound‐electron magnetic‐moment measurement, two complementary approaches exist, one via the so‐called “continuous Stern–Gerlach effect”, applied to ions with zero‐spin nuclei, and one a spectroscopic approach, applied to ions with nonzero nuclear spin. Here, the latter approach is detailed, and an overview of the experiment and its status is given.     

0.7 structure in long quantum wires

While quantized conductance steps in short quantum wires are understood through a single electron picture, additional structure often observed in high-quality one-dimensional systems near g=0.7×(2e²/h) is commonly interpreted as arising due to many-body interactions. Most studies of conductance structure below 2e²/h use short one-dimensional wires where transport is known to be ballistic. We report transport measurements for both short (0.5 μm) and long (5 μm) quantum wires, and use both conductance and nonlinear transport to explore the behavior of one-dimensional wires.     

Sensitivity to new physics: a e versus a μ

At present it is generally believed that “new physics” effects contribute to leptonic anomalous magnetic moment, a _l , via quantum loops only and they are proportional to the squared lepton mass, m _l ². An alternative mechanism for a contribution by new physics is proposed. It occurs at the tree level and exhibits a linear rather than quadratic dependence on m _l . This leads to a much larger sensitivity of a _e to the new physics than was expected so far.     

Quantized charge transport in adiabatic pumping by a driven double δ-barrier

We investigate the condition that the charge carried by quantum parametric pumping per cycle is quantized in units of the electron charge e and the role of adiabaticity in charge quantization. Using a driven double-δ-potential model and a Floquet scattering approach, it is found that the quantization phenomenon occurs only at very low frequencies of the oscillating potential and adiabaticity of the potential modulation is crucial for quantization.     

Electric charge as a quantum of flux

Ratio of electron charge radius and Compton wavelength of electron is known to be equal to the dimensionless electromagnetic coupling constant e²/? c. It is pointed out that the coupling constant has two alternative interpretations: as a ratio of two angular momenta since Planck constant has the dimension of angular momentum, and two flux quanta e and hc/e. We argue that it has deep physical significance such that the electronic charge becomes flux itself and at a fundamental level fractional spin of quantized vortex. A unified perspective of the three interpretations of the coupling constant is presented invoking the new interpretation of the magnetic moment of the electron comprising three terms. A critical discussion on the magnetism and flux quantum is given and the implication on the spintronics is pointed out.