Quantum metrology

V. Giovannetti, S. Lloyd, L. Maccone, Quantum metrology, Phys. Rev. Lett. 96 (2006) 010401. 

QUANTUM METROLOGY ATOM NANO OPTICS, GASES... 

Quantum Metrology Group National Bureau of Standards Washington, D,C. 20234... 

This experimental development was matched by rapid theoretical progress, and the comparison and interplay between theory and experiment has been important in the field of metrology, leading to higher precision in the determination of the fundamental constants. We feel that now is a good time to review modern bound state theory. The theory of hydrogenic bound states is widely described in the literature. The basics of nonrelativistic theory are contained in any textbook on quantum mechanics, and the relativistic Dirac equation and the Lamb shift are discussed in any textbook on quantum electrodynamics and quantum field theory. An excellent source for the early results is the classic book by Bethe and Salpeter [6]. A number of excellent reviews contain more recent theoretical results, and a representative, but far from exhaustive, list of these reviews includes [7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17]. 

For almost three decades, the S-2S two-photon transition in atomic hydrogen with its natural linewidth of only 1.3 Hz has inspired advances in high-resolution spectroscopy and optical frequency metrology. This resonance [the 1S-2S transition] has become a de facto optical frequency standard. More importantly, it is providing a cornerstone for the determination of fundamental constants and for stringent tests of quantum electrodynamic theory. In the future, it may unveil... 

The setup shown in Fig. 5.100 is also used for experiments based on parametric downconversion. A nonlinear crystal produces photon pairs the energy of which is equal to the energy of the pump photons. The measurement then delivers a correlation peak on a baseline of randomly detected background photons. The effect can be used for tests of quantum mechanics and a number of metrological applications [70]. The measurement of absolute detector quantum efficiencies by parametric downconversion [301, 356, 357, 358, 423, 536] is shown in Fig. 6.28, page 242. 

Magnetic Resonance has greatly contributed to the fields of Nuclear Magnetic Moments, Molecular Structure, Quantum Field Theory, Particle Physics, QED, Chemical Analysis, Chemistry, Navigation on Earth and in Space, Biology, Time, Frequency, Astronomy, Seismology, Metrology, Tests of Relativity, Medicine, MRI and fMRI. There is every reason in the future to expect even better contributions. 

The possibilities of Doppler-free two-photon spectroscopy for metrology and fundamental physics has been impressively demonstrated by precision measurements of the 1S-2S transition in atomic hydrogen [260-263]. Precise measurements of this one-photon forbidden transition with a very narrow natural linewidth of 1.3 Hz yield accurate values of fundamental constants and can provide stringent tests of quantum electrodynamic theory (Sect. 9.7). A comparison of the 1S-2S transition frequency with the 2S-3P frequency allows the precise determination of the Lamb shift of the 15 ground state [261], whereas the 2S Lamb shift was already measured long ago by the famous Lamb-Rutherford experiments where the RF transition between 25 1/2 and 2P /2 were observed. Because of the isotope shift the 15-25 transitions of and differ by... 

The above characteristics make these systems very promising for radiation effect studies and in particular for metrological applications such as the measurement of the Rydberg constant directly in frequency units. One can indeed expect very narrow resonances between circular states, with spectral lines only quadratically sensitive to stray electric fields and frequencies depending only slightly upon the atomic ion core properties and being easily related to the hydrogen frequencies via the determination of very small quantum defects corrections. 

I hope to have shown in this brief review that Rydberg atom radiation experiments are of central interest in a variety of studies not only in fundamental Quantum Optics, but also in the technology of new radiation sources and detectors and in metrology. 

Traceability guarantees comparability. The comparability of measurements between different places on earth is achieved by comparisons performed by the National Metrology Institutes (NMIs). The comparability over time was given in the past because the NMIs have realized and maintained the units for long times. Currently, there is an effort to define the base units as far as possible on the basis of quantum effects and fundamental physical constants, which are, to our knowledge, stable in time. 

An interesting phenomenon known as the quantum Hall ejfect, which occtus in the two-dimensional electron gas in, for example, MOSFETs (metal-oxide-semiconductor-fleld-effect transistors), is becoming extremely valtrable in metrology. At very low temperatirres and strong magnetic fields, it is possible to exploit the effect to make absolute measurements of /h (in effect, the atomic fine-stmctine constant) to very high precision. 

The first of the macroscopic quantum effects to be demonstrated was the ac Josephson effect, whereby 2e/h is established via the invariant ratio nV/V for irradiation at frequency V and noting the n th step voltage, V. This has been a powerful tool in the service of electrical measurements. The history, which has been well reviewed by Petley, shows a rapid evolution from laboratory curiosity through a significant determination of a to the role of maintenance of the operational unit of voltage [16]. Incidentally, the early history of this area of work is an instance in which electrical metrology made a distinct impact on atomic physics. It will be recalled that a key issue of the early 1960 s was the discrepancy between values of a obtained from fine-structure measurement and those deduced from hyperfine structure. This story is well told in the widely known summary, due to Taylor,... 

Fig. 2 Summary of values for the fine-structure constant without using quantum electrodynamic theory. The recommended value is characterized by the dotted lines, and the measured values of a (including one standard deviation) using the %-method and the h/e -method ( quantum Hall effect) are plotted as vertical lines. The national laboratories are NBS (National Bureau of Standards, U.S.), NIM (National Institute of Metrology, China), VlIIIM (Mendeleev Institute, USSR), and NPL (National Physics Laboratory, U.K.)...

This value is based on the assumption that q 14 is correct The uncertainty arises mainly from instabilities in the value of the calibrated reference resistor necessary for the determination of a (see Fig.3). A large number of theoretical papers discuss the question whether microscopic details of the semiconductor may influence the accuracy of Eq.l4. Up to now, no corrections to the value of the quantized Hall resistance are known, and the good agreement of the a- value deduced from the quantum Hall effect (Eq.l5) with the recommended value (Eq.l) and data obtained from other experiments ( q 4, Eq.7) demonstrates that corrections to the quantized Hall resistance (if any) should be smaller than the experimental uncertainty of about lO" . We believe that Eq.l4 is correct even at a higher level of accuracy and that the QHE can be used on one hand as a standard resistor (if the value for h/e is known or defined for metrological applications) and on the other hand for the determination of the fine-structure constant with an uncertainty corresponding to the uncertainty of the reference resistor. 

---