Clock-Line-Mediated Sisyphus Cooling.

We demonstrate subrecoil Sisyphus cooling using the long-lived ^{3}P_{0} clock state in alkaline-earth-like ytterbium. A 1388-nm optical standing wave nearly resonant with the ^{3}P_{0}→^{3}D_{1} transition creates a spatially periodic light shift of the ^{3}P_{0} clock state. Following excitation on the ultranarrow clock transition, we observe Sisyphus cooling in this potential, as the light shift is correlated with excitation to ^{3}D_{1} and subsequent spontaneous decay to the ^{1}S_{0} ground state. We observe that cooling enhances the loading efficiency of atoms into a 759-nm magic-wavelength one-dimensional (1D) optical lattice, as compared to standard Doppler cooling on the ^{1}S_{0}→^{3}P_{1} transition. Sisyphus cooling yields temperatures below 200 nK in the weakly confined, transverse dimensions of the 1D optical lattice. These lower temperatures improve optical lattice clocks by facilitating the use of shallow lattices with reduced light shifts while retaining large atom numbers to reduce the quantum projection noise. This Sisyphus cooling can be pulsed or continuous and is applicable to a range of quantum metrology applications.

A many-channel FPGA control system.

We describe a many-channel experiment control system based on a field-programmable gate array (FPGA). The system has 16 bit resolution on 10 analog 100 megasamples-per-second (MS/s) input channels, 14 analog 100 MS/s output channels, 16 slow analog input and output channels, dozens of digital inputs and outputs, and a touchscreen display for experiment control and monitoring. The system can support ten servo loops with 155 ns latency and MHz bandwidths, in addition to as many as 30 lower bandwidth servos. We demonstrate infinite-impulse-response (IIR) proportional-integral-differential filters with 30 ns latency by using only bit-shifts and additions. These IIR filters allow timing margin at 100 MS/s and use fewer FPGA resources than straightforward multiplier-based filters, facilitating many servos on a single FPGA. We present several specific applications: Hänsch-Couillaud laser locks with automatic lock acquisition and a slow dither correction of lock offsets, variable duty cycle temperature servos, and the generation of multiple synchronized arbitrary waveforms.

Cs Fountain Clocks for Commercial Realizations-An Improved and Robust Design.

We report on the design, assembly, testing, and delivery of a series of new cesium fountain primary frequency standards built through commercial and scientific collaboration with international users. The new design, based on proven National Physical Laboratory solutions, improves reliability, simplicity of operation, and transportability. The complete system consists of a novel physics package, a specially developed optical package, and dedicated electronics for system control. We present results showing that despite their simplified and more compact design, the new fountains have state-of-the-art performance in terms of signal-to-noise ratio and robust long-term operation. With a sufficiently low-noise local oscillator, they are capable of reaching a short-term stability below 3×10-14 (1 s) and have potential accuracy in the low 10-16 range, similar to the best cesium fountains currently in operation. This cost-effective solution could be used to increase the availability of accurate frequency references and timescales and provide redundancy in critical locations.

Atomic Clock Measurements of Quantum Scattering Phase Shifts Spanning Feshbach Resonances at Ultralow Fields.

We use an atomic fountain clock to measure quantum scattering phase shifts precisely through a series of narrow, low-field Feshbach resonances at average collision energies below 1 µK. Our low spread in collision energy yields phase variations of order ±π/2 for target atoms in several F, m_{F} states. We compare them to a theoretical model and establish the accuracy of the measurements and the theoretical uncertainties from the fitted potential. We find overall excellent agreement, with small statistically significant differences that remain unexplained.

s-Wave collisional frequency shift of a fermion clock.

We report an s-wave collisional frequency shift of an atomic clock based on fermions. In contrast to bosons, the fermion clock shift is insensitive to the population difference of the clock states, set by the first pulse area in Ramsey spectroscopy, θ(1). The fermion shift instead depends strongly on the second pulse area θ(2). It allows the shift to be canceled, nominally at θ(2)=π/2, but correlations perturb the null to slightly larger θ(2). The frequency shift is relevant for optical lattice clocks and increases with the spatial inhomogeneity of the clock excitation field, naturally larger at optical frequencies.

Scattering of cold-atom coherences by hot atoms: frequency shifts from background-gas collisions.

Frequency shifts from background-gas collisions currently contribute significantly to the inaccuracy of atomic clocks. Because nearly all collisions with room-temperature background gases that transfer momentum eject the cold atoms from the clock, the interference between the scattered and unscattered waves in the forward direction dominates these frequency shifts. We show they are ≈ 10 times smaller than in room-temperature clocks and that van der Waals interactions produce the cold-atom background-gas shift. General considerations allow the loss of the Ramsey fringe amplitude to bound this frequency shift.

Spin waves and collisional frequency shifts of a trapped-atom clock.

We excite spin waves with spatially inhomogeneous Ramsey pulses and study the resulting frequency shifts of a chip-scale atomic clock of trapped 87Rb. The density-dependent frequency shifts of the hyperfine transition simulate the s-wave collisional frequency shifts of fermions, including those of optical lattice clocks. As the spin polarizations oscillate in the trap, the frequency shift reverses and it depends on the area of the second Ramsey pulse, exhibiting a predicted beyond mean-field frequency shift. Numerical and analytic models illustrate these observed behaviors.

Progress in atomic fountains at LNE-SYRTE.

We give an overview of the work done with the Laboratoire National de Métrologie et d'Essais-Systèmes de Référence 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 (87)Rb 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.

Direct observation of resonant scattering phase shifts and their energy dependence.

We scan the collision energy of two clouds of cesium atoms between 12 and 50 µK in an atomic fountain clock. By directly detecting the difference of s-wave scattering phase shifts, we observe a rapid variation of a scattering phase shift through a series of Feshbach resonances. At the energies we use, resonances that overlap at threshold become resolved. Our statistical phase uncertainty of 8 mrad can be improved in future precision measurements of Feshbach resonances to accurately determine the Cs-Cs interactions, which may provide stringent limits on the time variation of fundamental constants.

Rydberg spectroscopy in an optical lattice: blackbody thermometry for atomic clocks.

We show that optical spectroscopy of Rydberg states can provide accurate in situ thermometry at room temperature. Transitions from a metastable state to Rydberg states with principal quantum numbers of 25-30 have 200 times larger fractional frequency sensitivities to blackbody radiation than the strontium clock transition. We demonstrate that magic-wavelength lattices exist for both strontium and ytterbium transitions between the metastable and Rydberg states. Frequency measurements of Rydberg transitions with 10(-16) accuracy provide 10 mK resolution and yield a blackbody uncertainty for the clock transition of 10(-18).

Evaluation of Doppler shifts to improve the accuracy of primary atomic fountain clocks.

We demonstrate agreement between measurements and ab initio calculations of the frequency shifts caused by distributed cavity phase variations in the microwave cavity of a primary atomic fountain clock. Experimental verification of the finite element models of the cavities gives the first quantitative evaluation of this leading uncertainty and allows it to be reduced to δν/ν=±8.4×10(-17). Applying these experimental techniques to clocks with improved microwave cavities will yield negligible distributed cavity phase uncertainties, less than ±1×10(-17).

Decoherence and collisional frequency shifts of trapped bosons and fermions.

We perform exact calculations of collisional frequency shifts for several fermions or bosons using a singlet and triplet basis for pairs of particles. The "factor of 2 controversy" for bosons becomes clear-the factor is always 2. Decoherence is described by singlet states and they are unaffected by spatially uniform clock fields. Spatial variations are critical, especially for fermions which were previously thought to be immune to collision shifts. The spatial variations lead to decoherence and a novel frequency shift that is not proportional to the partial density of internal states.

A quantum scattering interferometer.

The collision of two ultracold atoms results in a quantum mechanical superposition of the two possible outcomes: each atom continues without scattering, and each atom scatters as an outgoing spherical wave with an s-wave phase shift. The magnitude of the s-wave phase shift depends very sensitively on the interaction between the atoms. Quantum scattering and the underlying phase shifts are vitally important in many areas of contemporary atomic physics, including Bose-Einstein condensates, degenerate Fermi gases, frequency shifts in atomic clocks and magnetically tuned Feshbach resonances. Precise experimental measurements of quantum scattering phase shifts have not been possible because the number of scattered atoms depends on the s-wave phase shifts as well as the atomic density, which cannot be measured precisely. Here we demonstrate a scattering experiment in which the quantum scattering phase shifts of individual atoms are detected using a novel atom interferometer. By performing an atomic clock measurement using only the scattered part of each atom's wavefunction, we precisely measure the difference of the s-wave phase shifts for the two clock states in a density-independent manner. Our method will enable direct and precise measurements of ultracold atom-atom interactions, and may be used to place stringent limits on the time variations of fundamental constants.

Difference between a photon's momentum and an atom's recoil.

When an atom absorbs a photon from a laser beam that is not an infinite plane wave, the atom's recoil is less than variant Planck's k in the propagation direction. We show that the recoils in the transverse directions produce a lensing of the atomic wave functions, which leads to a frequency shift that is not discrete but varies linearly with the field amplitude and strongly depends on the atomic state detection. The same lensing effect is also important for microwave atomic clocks. The frequency shifts are of the order of the naive recoil shift for the transverse wave vector of the photons.

Locking lasers with large FM noise to high-Q cavities.

We demonstrate that a laser can be directly locked to a cavity when the laser linewidth is much greater than the cavity linewidth. We lock an external-cavity diode laser with more than 1 MHz of added frequency noise to a 3.5 kHz wide cavity resonance. Our analog servo acquires lock even though the laser frequency sweeps through the cavity resonance in less than the cavity buildup time. Our theoretical analysis fully describes our measurements and explains why lock can be acquired.