In the search for stable and accurate atomic clocks, many-atom lattice clocks have shown higher precision than clocks based on single trapped ions, but have been less accurate; here, a stable many-atom clock is demonstrated that has accuracy better than single-ion clocks. Whether for the definition of SI units, testing the laws of physics or for applications yet to be dreamt of, scientists will always want more stability and more accuracy in their atomic clocks. Many-atom lattice clocks have achieved better precision than clocks based on single trapped ions, but their accuracy has so far been relatively poor. This study from the National Institute of Standards and Technology (NIST) demonstrates a many-atom clock that achieves better accuracy than single-ion-based clocks, and at the same time reduces the required measurement time by two orders of magnitude. Based on thousands of neutral strontium atoms trapped in a laser beam, this new 'optical lattice' clock has the stability, reproducibility and accuracy that make it a prime contender for consideration as a primary standard. It would neither gain nor lose one second in about 5 billion years — although the Earth is unlikely to last that long. Progress in atomic, optical and quantum science1,2 has led to rapid improvements in atomic clocks. At the same time, atomic clock research has helped to advance the frontiers of science, affecting both fundamental and applied research. The ability to control quantum states of individual atoms and photons is central to quantum information science and precision measurement, and optical clocks based on single ions have achieved the lowest systematic uncertainty of any frequency standard3,4,5. Although many-atom lattice clocks have shown advantages in measurement precision over trapped-ion clocks6,7, their accuracy has remained 16 times worse8,9,10. Here we demonstrate a many-atom system that achieves an accuracy of 6.4 × 10−18, which is not only better than a single-ion-based clock, but also reduces the required measurement time by two orders of magnitude. By systematically evaluating all known sources of uncertainty, including in situ monitoring of the blackbody radiation environment, we improve the accuracy of optical lattice clocks by a factor of 22. This single clock has simultaneously achieved the best known performance in the key characteristics necessary for consideration as a primary standard—stability and accuracy. More stable and accurate atomic clocks will benefit a wide range of fields, such as the realization and distribution of SI units11, the search for time variation of fundamental constants12, clock-based geodesy13 and other precision tests of the fundamental laws of nature. This work also connects to the development of quantum sensors and many-body quantum state engineering14 (such as spin squeezing) to advance measurement precision beyond the standard quantum limit.

An optical lattice clock with accuracy and stability at the 10 −18 level

An iterative formula for the directional hemispherical apparent reflectivity of an opaque isothermal cavity with an arbitrary surface is derived on the basis of an integral equation representing the apparent reflectivity. Nested integrals in the formula are computed by the hit-or-miss Monte Carlo method. The formula is applied to right circular cylinders whose surfaces are diffuse and to cylindrical cones whose surfaces are characterized by a uniform specular-diffuse model. For the cylinders, a table is given from which one can easily calculate the apparent emissivities of the center of the bottoms for arbitrary surface reflectivities. An analytical recalculation of I2 of Quinn gives corrected values that agree with those produced by the Monte Carlo method. For the cylindrical cones the directional apparent emissivities of the bottoms are obtained by varying the apex angle and the fraction of specular component. We point out that angles of 120° and 70° have advantages even for cavities with moderate specular components. Results are analyzed by studying numerically the individual terms of the iterative formula. The validity of an approximation for the directional apparent emissivity is discussed in terms of the constant asymptotic distribution of impact points of rays in cavities.

Calculation of the directional emissivities of cavities by the Monte Carlo method

Local, hemispherical, effective emissivities and integrated cavity emissivities are computed for isothermal and nonisothermal diffuse cylindro-cones (a cylindrical section of radius R2 and length L2 joined to a conical base of length L1 and half-angle θ), with and without lids, and are compared with corresponding values for the limiting cases of right circular cones and cylinders. The local emissivities everywhere along the walls are considerably higher in a cylindro-cone with a lid than in a similar one without, and also increase rapidly with decreasing cone angle. They are considerably higher in a cylindro-cone than in a cone of length L1 or in a cylinder of length L2. On the other hand, for cavities of the same total length, the cylinder has the highest local emissivities except at and near the base, where the emissivity of the cone is highest. There is a regular transition between these two extremes through various intermediary cylindro-cones. The normal integrated cavity emissivities are higher than the hemispherical emissivities for cavities for which (L1 + L2)/2R2 ≳ 0.8. The local and integrated spectral emissivities of nonisothermal cylindro-cones change markedly with wavelength and somewhat with cavity reference temperature. Approximate local emissivities for nonisothermal cylindro-cones can be obtained from corresponding isothermal ones in a simple manner, with useful accuracy.

Emissivities of diffuse cavities, II: Isothermal and nonisothermal cylindro-cones

In this work, Kirchhoff’s law (Kirchhoff G. Monatsberichte der Akademie der Wissenschaften zu Berlin, sessions of Dec. 1859, 1860, 783–787) is being revisited not only to mark its 150th anniversary but, most importantly, to highlight serious overreaching in its formulation. At the onset, Kirchhoff’s law correctly outlines the equivalence between emission and absorption for an opaque object under thermal equilibrium. This same conclusion had been established earlier by Balfour Stewart (Stewart B. Trans. Royal Soc. Edinburgh, 1858, v. 22(1), 1–20). However, Kirchhoff extends the treatment beyond his counterpart, stating that cavity radiation must always be black, or normal: depending only on the temperature and the frequency of observation. This universal aspect of Kirchhoff’s law is without proper basis and constitutes a grave distortion of experimental reality. It is readily apparent that cavities made from arbitrary materials (" < 1) are never black. Their approach to such behavior is being driven either by the blackness of the detector, or by black materials placed near the cavity. Ample evidence exists that radiation in arbitrary cavities is sensitive to the relative position of the detectors. In order to fully address these issues, cavity radiation and the generalization of Kirchhoff’s law are discussed. An example is then taken from electromagnetics, at microwave frequencies, to link results in the resonant cavity with those inferred from the consequences of generalization.

Kirchho 's Law of Thermal Emission: 150 Years

The influence of energetic species on thin film growth mechanism is a long-term issue in the field of low-pressure plasma-based magnetron sputtering technology. Several species may contribute to the energy flux such a plasma ions, electrons and neutrals, film-forming species, photons, etc. Several research groups have designed probes capable of quantifying energy fluxes in these particular working conditions and experimental strategies to get a better insight on the relationship between the plasma working parameters, the energy flux, the film growth mechanism and the coating properties. In this paper we aim at showing how the thermopile-based probe developed at GREMI laboratory can contribute to this field thanks to its time resolved capability (~ms) and sensitivity (~mW/cm2). We show how such a probe can be used to identify and quantify energetic contributions such as gas conduction, chemical reactions on surfaces such as oxidation, but also radiations emitted from a (hot) sputter target during DC, pulsed-DC and High-power Impulse Magnetron Sputtering (HiPIMS) processes. Both non-reactive and reactive sputtering discharges are studied. Ultimately, we present data on the relationship between the phase composition and the energy deposited during the synthesis of two technologically important thin film materials, namely Titania and Zirconia. Through the reported examples, the advantage and limitations of energy flux measurements and the interest to couple the obtained data to those derived from conventional plasma diagnostics are discussed. The relative importance of various energetic contributions is investigated in a purpose to identify the key parameters driving the film properties.

https://hal.archives-ouvertes.fr/hal-02381748/document

Energy flux measurements during magnetron sputter deposition processes

Total radiant power emission from various diffuse wall cavity sources is calculated without approximation. In addition, a useful radiometric quantity, ∊O-d, the fraction of blackbody power received by a distant viewer, is precisely defined and calculated. Extensive tabulation of numerical results and tutorial background are included. A new method, faster and more accurate than traditional quadrature methods, for the numerical solution of integral equations is described in an appendix. Results are applied to the practical problems of cavity design and analysis.

Radiometric properties of isothermal, diffuse wall cavity sources.

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Radiometric properties of isothermal, diffuse wall cavity sources.