Compact structures for single-beam magneto-optical trapping of ytterbium.

At present, the best optical lattice clocks are based on the spectroscopy of trapped alkaline-earth-like atoms such as ytterbium and strontium. The development of mobile or even space-borne clocks necessitates concepts for the compact laser-cooling and trapping of these atoms with reduced laser requirements. Here, we present two compact and robust achromatic mirror structures for single-beam magneto-optical trapping of alkaline-earth-like atoms using two widely separated optical cooling frequencies.

Achromatic, planar Fresnel-reflector for a single-beam magneto-optical trap.

We present a novel achromatic, planar, periodic mirror structure for single-beam magneto-optical trapping and demonstrate its use in the first- and second-stage cooling and trapping for different isotopes of strontium. We refer to it as a Fresnel magneto-optical trap (MOT) as the structure is inspired by Fresnel lenses. By design, it avoids many of the problems that arise for multi-color cooling using planar structures based on diffraction gratings, which have been the dominant planar structures to be used for single-beam trapping thus far.

Improved Limits on the Coupling of Ultralight Bosonic Dark Matter to Photons from Optical Atomic Clock Comparisons.

We present improved constraints on the coupling of ultralight bosonic dark matter to photons based on long-term measurements of two optical frequency ratios. In these optical clock comparisons, we relate the frequency of the ^{2}S_{1/2}(F=0)↔^{2}F_{7/2}(F=3) electric-octupole (E3) transition in ^{171}Yb^{+} to that of the ^{2}S_{1/2}(F=0)↔^{2}D_{3/2}(F=2) electric-quadrupole (E2) transition of the same ion, and to that of the ^{1}S_{0}↔^{3}P_{0} transition in ^{87}Sr. Measurements of the first frequency ratio ν_{E3}/ν_{E2} are performed via interleaved interrogation of both transitions in a single ion.

Transportable clock laser system with an instability of 1.6 × 10.

We present a transportable ultra-stable clock laser system based on a Fabry-Perot cavity with crystalline AlGaAs/GaAs mirror coatings, fused silica (FS) mirror substrates, and a 20 cm-long ultra-low expansion (ULE) glass spacer with a predicted thermal noise floor of mod σ = 7 × 10 in modified Allan deviation at one second averaging time. The cavity has a cylindrical shape and is mounted at 10 points. Its measured sensitivity of the fractional frequency to acceleration for the three Cartesian directions are 2(1) × 10 /(ms), 3(3) × 10 /(ms), and 3(1) × 10 /(ms), which belong to the lowest acceleration sensitivities published for transportable systems.

Comparing ultrastable lasers at 7 × 10 fractional frequency instability through a 2220 km optical fibre network.

Ultrastable lasers are essential tools in optical frequency metrology enabling unprecedented measurement precision that impacts on fields such as atomic timekeeping, tests of fundamental physics, and geodesy. To characterise an ultrastable laser it needs to be compared with a laser of similar performance, but a suitable system may not be available locally. Here, we report a comparison of two geographically separated lasers, over the longest ever reported metrological optical fibre link network, measuring 2220 km in length, at a state-of-the-art fractional-frequency instability of 7 × 10 for averaging times between 30 s and 200 s.

Prospects and challenges for squeezing-enhanced optical atomic clocks.

Optical atomic clocks are a driving force for precision measurements due to the high accuracy and stability demonstrated in recent years. While further improvements to the stability have been envisioned by using entangled atoms, squeezing the quantum mechanical projection noise, evaluating the overall gain must incorporate essential features of an atomic clock. Here, we investigate the benefits of spin squeezed states for clocks operated with typical Brownian frequency noise-limited laser sources.

Transportable interrogation laser system with an instability of mod σ = 3 × 10.

We present an interrogation laser system for a transportable strontium lattice clock operating at 698 nm, which is based on an ultra-low-expansion glass reference cavity. Transportability is achieved by implementing a rigid, compact, and vibration insensitive mounting of the 12 cm-long reference cavity, sustaining shocks of up to 50 g. The cavity is mounted at optimized support points that independently constrain all degrees of freedom.

Phase noise of frequency doublers in optical clock lasers.

Frequency doublers are widely used in high-resolution spectroscopy to shift the operation wavelength of a laser to a more easily accessible or otherwise preferable spectral region. We investigate the use of a periodically-poled lithium niobate (PPLN) waveguide frequency doubler in an optical clock. We focus on the phase evolution between the fundamental (1396 nm) and frequency-doubled (698 nm) light and its effect on clock performance.

A compact and robust cooling laser system for an optical strontium lattice clock.

We present a simple and robust laser system for two-color, narrow-line cooling on the Sr (5s)S → (5s5p)P transition. Two hyperfine lines of this transition are addressed simultaneously with light from a single laser source, using sidebands created by an electro-optical phase modulator. A tapered amplifier system provides laser powers up to 90 mW.

Atomic clocks for geodesy.

We review experimental progress on optical atomic clocks and frequency transfer, and consider the prospects of using these technologies for geodetic measurements. Today, optical atomic frequency standards have reached relative frequency inaccuracies below 10, opening new fields of fundamental and applied research. The dependence of atomic frequencies on the gravitational potential makes atomic clocks ideal candidates for the search for deviations in the predictions of Einstein's general relativity, tests of modern unifying theories and the development of new gravity field sensors.

Test of Special Relativity Using a Fiber Network of Optical Clocks.

Phase compensated optical fiber links enable high accuracy atomic clocks separated by thousands of kilometers to be compared with unprecedented statistical resolution. By searching for a daily variation of the frequency difference between four strontium optical lattice clocks in different locations throughout Europe connected by such links, we improve upon previous tests of time dilation predicted by special relativity. We obtain a constraint on the Robertson-Mansouri-Sexl parameter |α|≲1.

Transportable Optical Lattice Clock with 7×10^{-17} Uncertainty.

We present a transportable optical clock (TOC) with ^{87}Sr. Its complete characterization against a stationary lattice clock resulted in a systematic uncertainty of 7.4×10^{-17}, which is currently limited by the statistics of the determination of the residual lattice light shift, and an instability of 1.

Improvement of an Atomic Clock using Squeezed Vacuum.

Since the pioneering work of Ramsey, atom interferometers are employed for precision metrology, in particular to measure time and to realize the second. In a classical interferometer, an ensemble of atoms is prepared in one of the two input states, whereas the second one is left empty. In this case, the vacuum noise restricts the precision of the interferometer to the standard quantum limit (SQL).

Ultra-stable clock laser system development towards space applications.

The increasing performance of optical lattice clocks has made them attractive for scientific applications in space and thus has pushed the development of their components including the interrogation lasers of the clock transitions towards being suitable for space, which amongst others requires making them more power efficient, radiation hardened, smaller, lighter as well as more mechanically stable. Here we present the development towards a space-compatible interrogation laser system for a strontium lattice clock constructed within the Space Optical Clock (SOC2) project where we have concentrated on mechanical rigidity and size. The laser reaches a fractional frequency instability of 7.

A clock network for geodesy and fundamental science.

Leveraging the unrivalled performance of optical clocks as key tools for geo-science, for astronomy and for fundamental physics beyond the standard model requires comparing the frequency of distant optical clocks faithfully. Here, we report on the comparison and agreement of two strontium optical clocks at an uncertainty of 5 × 10(-17) via a newly established phase-coherent frequency link connecting Paris and Braunschweig using 1,415 km of telecom fibre. The remote comparison is limited only by the instability and uncertainty of the strontium lattice clocks themselves, with negligible contributions from the optical frequency transfer.

8 × 10⁻¹⁷ fractional laser frequency instability with a long room-temperature cavity.

We present a laser system based on a 48 cm long optical glass resonator. The large size requires a sophisticated thermal control and optimized mounting design. A self-balancing mounting was essential to reliably reach sensitivities to acceleration of below Δν/ν<2×10(-10)/g in all directions.

Ultrastable laser with average fractional frequency drift rate below 5 × 10⁻¹⁹/s.

Cryogenic single-crystal optical cavities have the potential to provide high dimensional stability. We have investigated the long-term performance of an ultrastable laser system that is stabilized to a single-crystal silicon cavity operated at 124 K. Utilizing a frequency comb, the laser is compared to a hydrogen maser that is referenced to a primary caesium fountain standard and to the 87Sr optical lattice clock at Physikalisch-Technische Bundesanstalt (PTB).

Direct comparison of optical lattice clocks with an intercontinental baseline of 9000 km.

We have demonstrated a direct frequency comparison between two ⁸⁷Sr lattice clocks operated in intercontinentally separated laboratories in real time. Two-way satellite time and frequency transfer technique, based on the carrier-phase, was employed for a direct comparison, with a baseline of 9000 km between Japan and Germany. A frequency comparison was achieved for 83,640 s, resulting in a fractional difference of (1.

High accuracy correction of blackbody radiation shift in an optical lattice clock.

We have determined the frequency shift that blackbody radiation is inducing on the 5s2 (1)S0-5s5p (3)P0 clock transition in strontium. Previously its uncertainty limited the uncertainty of strontium lattice clocks to 1×10(-16). Now the uncertainty associated with the blackbody radiation shift correction translates to a 5×10(-18) relative frequency uncertainty at room temperature.

A compact and efficient strontium oven for laser-cooling experiments.

Here we describe a compact and efficient strontium oven well suited for laser-cooling experiments. Novel design solutions allowed us to produce a collimated strontium atomic beam with a flux of 1.0 × 10(13) s(-1) cm(-2) at the oven temperature of 450 °C, reached with an electrical power consumption of 36 W.

Collisional losses, decoherence, and frequency shifts in optical lattice clocks with bosons.

We have quantified collisional losses, decoherence and the collision shift in a one-dimensional optical lattice clock on the highly forbidden transition (1)S(0)-(3)P(0) at 698 nm with bosonic (88)Sr. We were able to distinguish two loss channels: inelastic collisions between atoms in the upper and lower clock state and atoms in the upper clock state only. Based on the measured coefficients, we determine the operation parameters at which a 1D-lattice clock with (88)Sr shows no degradation due to collisions on the fractional uncertainty level of 10(-16).

The A 1Sigmau+ state of K2 up to the dissociation limit.

We report an experimental study of the K(2) A (1)Sigma(u) (+) state. Long-range levels up to the dissociation limit were observed in a two laser spectroscopic experiment using a highly collimated molecular beam. We derive an analytical potential energy curve for the complete A state including long-range dispersion terms.

First Observation of Hyperfine Structure in K(2).

The hyperfine structure of the (v'-v") = (27-0) band of the b(3)Pi(u0(+)) <-- X(1)Sigma(+)(g) transition has been observed by laser excitation spectroscopy in a highly collimated molecular beam. Hyperfine parameters for magnetic dipole and electric quadrupole interaction are derived from least-squares fitting of the hyperfine pattern and deperturbation between A(1)Sigma(+)(u) and b(3)Pi(u0(+)). Copyright 2000 Academic Press.