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.Comment: Final version with corrected and clarified discussion of g

RACE and Calculations of Three-dimensional Distributed Cavity Phase Shifts

The design for RACE, a Rb-clock flight experiment for the ISS, is described. The cold collision shift and multiple launching (juggling) have important implications for the design and the resulting clock accuracy and stability. We present and discuss the double clock design for RACE. This design reduces the noise contributions of the local oscillator and simplifies and enhances an accuracy evaluation of the clock. As we try to push beyond the current accuracies of clocks, new systematic errors become important. The best fountain clocks are using cylindrical TE(sub 011) microwave cavities. We recently pointed out that many atoms pass through a node of the standing wave microwave field in these cavities. Previous studies have shown potentially large frequency shifts for atoms passing through nodes in a TE(sub 013) cavity. The shift occurs because there is a small traveling wave component due to the absorption of the copper cavity walls. The small traveling wave component leads to position dependent phase shifts. To study these effects, we perform Finite Element calculations. Three-dimensional Finite Element calculations require significant computer resources. Here we show that the cylindrical boundary condition can be Fourier decomposed to a short series of two-dimensional problems. This dramatically reduces the time and memory required and we obtain (3D) phase distributions for a variety of cavities. With these results, we will be able to analyze this frequency shift in fountain and future space clocks

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 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 10 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 (PID) 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: H\"ansch-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

Spin waves and Collisional Frequency Shifts of a Trapped-Atom Clock

We excite spin-waves with spatially inhomogeneous pulses and study the resulting frequency shifts of a chip-scale atomic clock of trapped $^{87}$Rb. 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 the observed behaviors.Comment: Will appear soon in Physical Review Letters - Typos correcte