Since 1967 the primary time standard is the cesium atomic clock, based on a hyperfine transition in the microwave domain The development of ultrastable laser sources now allows one to operate on electronic transitions in the optical domain, corresponding to a 5-order-of-magnitude increase in the clock frequency This article reviews the spectacular accuracy and stability gains that can be obtained when working with laser cooled ions or neutral atoms It also discusses some important applications of these optical clocks, from geodesy to tests of fundamental theories to many-body physics

/pdf/optical-atomic-clocks-3jf2azdvlh.pdf

Optical atomic clocks

We briefly review basic properties of dielectric whispering gallery mode resonators that are important for applications of the resonators in optics and photonics.

Optical resonators with whispering-gallery modes-part I: basics

The polarized optical spectra of the ions Ti3+, V3+, Cr3+, Mn3+, Co3+, and Ni3+ in corundum single crystals have been studied at temperatures from 4.2° to 1200°K. A theory of the band strength based on the point‐charge model and p‐d mixing has been developed and applied to the data with results in fair agreement with experiment. The effects of temperature show that the vibrational‐electronic contribution to band strength is quite small at low temperature but may be appreciable at high temperatures. The crystal‐field parameters have been calculated as convergent lattice sums. The observed trigonal‐field parameter has the opposite sign from that calculated by the point‐charge model if the impurity ion is assumed to occupy an Al3+ ion position in the lattice, but has the same sign as calculated for an ion 0.1 A displaced along the c3 axis toward the empty octahedral site. Details of the spectra have been interpreted as showing that the surroundings of an ion are distorted in some electronic states.

Optical spectra of transition-metal ions in corundum

We present two ultrastable lasers based on two vibration insensitive cavity designs, one with vertical optical axis geometry, the other horizontal. Ultrastable cavities are constructed with fused silica mirror substrates, shown to decrease the thermal noise limit, in order to improve the frequency stability over previous designs. Vibration sensitivity components measured are equal to or better than $1.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}/\text{m}\text{ }{\text{s}}^{\ensuremath{-}2}$ for each spatial direction, which shows significant improvement over previous studies. We have tested the very low dependence on the position of the cavity support points, in order to establish that our designs eliminate the need for fine tuning to achieve extremely low vibration sensitivity. Relative frequency measurements show that at least one of the stabilized lasers has a stability better than $5.6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}16}$ at 1 s, which is the best result obtained for this length of cavity.

http://www.exphy.uni-duesseldorf.de/PDF/Millo%20et%20al.%20Ultrastable%20lasers%20based%20on%20vibration%20insensitive%20cavities%20Phys.%20Rev.%20A,%2079,%20053829%20(2009).pdf

Ultrastable lasers based on vibration insensitive cavities

Significant progress has been made in recent years on the development of gravitational wave detectors. Sources such as coalescing compact binary systems, low-mass X-ray binaries, stellar collapses and pulsars are all possible candidates for detection. The most promising design of gravitational wave detector uses test masses a long distance apart and freely suspended as pendulums on Earth or in drag-free craft in space. The main theme of this review is a discussion of the mechanical and optical principles used in the various long baseline systems being built around the world — LIGO (USA), VIRGO (Italy/France), TAMA 300 (Japan) and GEO 600 (Germany/UK) — and in LISA, a proposed space-borne interferometer.

/pdf/gravitational-wave-detection-by-interferometry-ground-and-45mm1uq4u9.pdf

Gravitational Wave Detection by Interferometry (Ground and Space)

We report a set of optical absorption measurements on x-irradiated high-purity sapphire. The results of the photothermal deflection absorption measurements at 1064 nm show an increase of the absorption at the x-irradiated areas. The x-ray damage recovery is achieved through annealing, where the absorption level at 1064 nm is brought from an average level of ~80 ppm cm-1 to ~24 ppm cm-1 . UV-Vis spectroscopy results suggest that the residual absorption at 1064 nm is due to complex clusters of Ti and Fe ions and oxygen vacancies. We suggest that a further reduction of Ti and Fe in sapphire (<0.1 ppm) as well as oxygen vacancies (through post growth oxidizing annealing) would further reduce the absorption. Moreover, the absorption level of 20 ppm cm-1 remains within the requirements of the second generation laser interferometric gravitational-wave detectors.

https://iopscience.iop.org/article/10.1088/0022-3727/33/6/301/pdf

X-ray induced absorption of high-purity sapphire and investigation of the origin of the residual absorption at 1064 nm

This paper presents a design for a Fabry–Perot optical frequency reference resonator which utilizes the high dimensional stability of cryogenically cooled sapphire. We show that cryogenic sapphire cavities can achieve substantial improvements in frequency stability compared with room‐temperature cavities. The design of a laser stabilization system based on such a resonator is discussed. Estimates of fundamental and practical limitations on the frequency stability of such a system suggest that a fractional frequency stability of 10−16 over integration times from 10 to 104 s is possible. The fundamental limits to stability from quantum shot noise, radiation pressure fluctuations, and thermal noise are overwhelmed by practical limits which arise due to mechanical, thermal, and optical effects.

Cryogenic, all‐sapphire, Fabry–Perot optical frequency reference

We describe a cryogenic Fabry-Perot cavity in which a frequency-temperature turning point at 43 K is created by differential thermal contraction between the mirrors and the spacer. The cavity uses a sapphire spacer and fused silica mirrors. The expansion coefficient of the spacer is balanced by a negative term arising from the outward flexing of the mirrors caused by differential radial expansion of the mirror substrate and spacer. A simple model indicates that is possible to construct cavities with shallow turning points of frequency-temperature at temperatures between 10 and 65 K.

https://iopscience.iop.org/article/10.1088/0022-3727/28/9/008/pdf

Temperature compensation for cryogenic cavity stabilized lasers

Cryogenic system for a sapphire Fabry-Perot optical frequency standard

Rayleigh scattering in sapphire test mass for laser interferometric gravitational-wave detectors. I. Measurement of scattering attenuation coefficient

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