Annals of physics

The development of wave optics for light brought many new insights into our understanding of physics, driven by fundamental experiments like the ones by Young, Fizeau, Michelson-Morley and others. Quantum mechanics, and especially the de Broglie’s postulate relating the momentum p of a particle to the wave vector k of an matter wave: k = 2 λ = p/ℏ, suggested that wave optical experiments should be also possible with massive particles (see table 1), and over the last 40 years electron and neutron interferometers have demonstrated many fundamental aspects of quantum mechanics [1].

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Optics and interferometry with atoms and molecules

Advances in atomic physics, such as cooling and trapping of atoms and molecules and developments in frequency metrology, have added orders of magnitude to the precision of atom-based clocks and sensors. Applications extend beyond atomic physics and this article reviews using these new techniques to address important challenges in physics and to look for variations in the fundamental constants, search for interactions beyond the standard model of particle physics, and test the principles of general relativity.

Search for New Physics with Atoms and Molecules

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

The authors review progress in understanding the nature of atomic collisions occurring at temperatures ranging from the millidegrees Kelvin to the nanodegrees Kelvin regime. The review includes advances in experiments with atom beams, light traps, and purely magnetic traps. Semiclassical and fully quantal theories are described and their appropriate applicability assessed. The review divides the subject into two principal categories: collisions in the presence of one or more light fields and ground-state collisions in the dark.

Experiments and theory in cold and ultracold collisions

We give an overview of the work done with the Laboratoire National de Metrologie et d'Essais-Systemes de Reference Temps-Espace (LNE-SYRTE) fountain ensemble during the last five years. After a description of the clock ensemble, comprising three fountains, FO1, FO2, and FOM, and the newest developments, we review recent studies of several systematic frequency shifts. This includes the distributed cavity phase shift, which we evaluate for the FO1 and FOM fountains, applying the techniques of our recent work on FO2. We also report calculations of the microwave lensing frequency shift for the three fountains, review the status of the blackbody radiation shift, and summarize recent experimental work to control microwave leakage and spurious phase perturbations. We give current accuracy budgets. We also describe several applications in time and frequency metrology: fountain comparisons, calibrations of the international atomic time, secondary representation of the SI second based on the 87Rb hyperfine frequency, absolute measurements of optical frequencies, tests of the T2L2 satellite laser link, and review fundamental physics applications of the LNE-SYRTE fountain ensemble. Finally, we give a summary of the tests of the PHARAO cold atom space clock performed using the FOM transportable fountain.

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Progress in atomic fountains at LNE-SYRTE

We demonstate a laser-cooled Cs fountain which can be used as a frequency standard. The fountain has been used to measure the frequency shift due to ultracold Cs-Cs collisions at temperatures below 2.8 \ensuremath{\mu}K. The measured shift is -12.9\ifmmode\pm\else\textpm\fi{}0.7 mHz for a density of (2.7\ifmmode\pm\else\textpm\fi{}1.5)\ifmmode\times\else\texttimes\fi{}${10}^{9}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$ beginning with an even distribution (\ifmmode\pm\else\textpm\fi{}10%) among the F=3, ${\mathit{m}}_{\mathit{F}}$ states. For a fountain with 95% of the atoms in the ${\mathit{m}}_{\mathit{F}}$=0 states, we measure a frequency shift of -5.5\ifmmode\pm\else\textpm\fi{}0.5 mHz at a density of (3.5\ifmmode\pm\else\textpm\fi{}2.0)\ifmmode\times\else\texttimes\fi{}${10}^{8}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$.

Laser-cooled Cs frequency standard and a measurement of the frequency shift due to ultracold collisions.

We have captured 3.6 x 10(10) cesium atoms in a magneto-optic trap loaded from a vapor cell. The 300-fold increase in the number of trapped atoms compared with that of previous research was accomplished by using larger laser intensities and 4-cm-diameter laser beams. The loading time constant was as short as 0.2 s.

Improved magneto-optic trapping in a vapor cell

We measure a cold collision frequency shift in an 87Rb fountain clock that is fractionally 30 times smaller than that for Cs. The shift is -0.38(8) mHz for a density of 1.0(6)x10(9) cm(-3). We study the cavity pulling of the atomic transition and use it to cancel the cold collision shift. We also measure the partial frequency shifts of each clock state finding 2(lambda(10)-lambda(20))/(lambda(10)+lambda(20)) = 0.1(6).

Measurement and cancellation of the cold collision frequency shift in an 87Rb fountain clock

We evaluate the distributed cavity phase and microwave lensing frequency shifts, which were the two largest sources of uncertainty for the NPL-CsF2 cesium fountain clock. We report measurements that confirm a detailed theoretical model of the microwave cavity fields and the frequency shifts of the clock that they produce. The model and measurements significantly reduce the distributed cavity phase uncertainty to $1.1 \times 10^{-16}$. We derive the microwave lensing frequency shift for a cylindrical cavity with circular apertures. An analytic result with reasonable approximations is given, in addition to a full calculation that indicates a shift of $6.2 \times 10^{-17}$. The measurements and theoretical models we report, along with improved evaluations of collisional and microwave leakage induced frequency shifts, reduce the frequency uncertainty of the NPL-CsF2 standard to $2.3 \times 10^{-16}$, nearly a factor of two lower than its most recent complete evaluation.

Kurt Gibble

Papers

Progress in atomic fountains at LNE-SYRTE

Laser-cooled Cs frequency standard and a measurement of the frequency shift due to ultracold collisions.

Improved magneto-optic trapping in a vapor cell

Measurement and cancellation of the cold collision frequency shift in an 87Rb fountain clock

Improved accuracy of the NPL-CsF2 primary frequency standard: evaluation of distributed cavity phase and microwave lensing frequency shifts