We evaluate the frequency error from distributed cavity phase in the caesium fountain clock PTB-CSF2 at the Physikalisch-Technische Bundesanstalt with a combination of frequency measurements and ab initio calculations. The associated uncertainty is 1.3E-16, with a frequency bias of 0.4E-16. The agreement between the measurements and calculations explains the previously observed frequency shifts at elevated microwave amplitude. We also evaluate the frequency bias and uncertainty due to the microwave lensing of the atomic wavepackets. We report a total PTB-CSF2 systematic uncertainty of 4.1E-16.
Improvements of the systematic uncertainty, frequency instability, and long-term reliability of the two caesium fountain primary frequency standards CSF1 and CSF2 at PTB (Physikalisch-Technische Bundesanstalt) are described. We have further investigated many of the systematic effects and made a number of modifications of the fountains. With an optically stabilized microwave oscillator, the quantum projection noise limited frequency instabilities are improved to $7.2 times 10^{-14} (tau/1,mathrm{s})^{-1/2}$ for CSF1 and $2.5 times 10^{-14} (tau/1,mathrm{s})^{-1/2}$ for CSF2 at high atom density. The systematic uncertainties of CSF1 and CSF2 are reduced to $2.74 times 10^{-16}$ and $1.71 times 10^{-16}$, respectively. Both fountain clocks regularly calibrate the scale unit of International Atomic Time (TAI) and the local realization of Coordinated Universal Time, UTC(PTB), and serve as references to measure the frequencies of local and remote optical frequency standards.
We introduce a scheme to coherently suppress second-rank tensor frequency shifts in atomic clocks, relying on the continuous rotation of an external magnetic field during the free atomic state evolution in a Ramsey sequence. The method retrieves the unperturbed frequency within a single interrogation cycle and is readily applicable to various atomic clock systems. For the frequency shift due to the electric quadrupole interaction, we experimentally demonstrate suppression by more than two orders of magnitude for the ${}^2S_{1/2} to {}^2D_{3/2}$ transition of a single trapped ${}^{171}text{Yb}^+$ ion. The scheme provides particular advantages in the case of the ${}^{171}text{Yb}^+$ ${}^2S_{1/2} to {}^2F_{7/2}$ electric octupole (E3) transition. For an improved estimate of the residual quadrupole shift for this transition, we measure the excited state electric quadrupole moments $Theta({}^2D_{3/2}) = 1.95(1)~ea_0^2$ and $Theta({}^2F_{7/2}) = -0.0297(5)~ea_0^2$ with $e$ the elementary charge and $a_0$ the Bohr radius, improving the measurement uncertainties by one order of magnitude.
We propose a method of joint interrogation in a single atom interferometer which overcomes the dead time between consecutive measurements in standard cold atomic fountains. The joint operation enables for a faster averaging of the Dick effect associated with the local oscillator noise in clocks and with vibration noise in cold atom inertial sensors. Such an operation allows achieving the lowest stability limit due to atom shot noise. We demonstrate a multiple joint operation in which up to five clouds of atoms are interrogated simultaneously in a single setup. The essential feature of multiple joint operation, demonstrated here for a micro-wave Ramsey interrogation, can be generalized to go beyond the current stability limit associated with dead times in present-day cold atom interferometer inertial sensors.
A caesium fountain clock is operated utilizing a microwave oscillator that derives its frequency stability from a stable laser by means of a fiber-laser femtosecond frequency comb. This oscillator is based on the technology developed for optical clocks and replaces the quartz based microwave oscillator commonly used in fountain clocks. As a result, a significant decrease of the frequency instability of the fountain clock is obtained, reaching 0.74E-14 at 100 s averaging time. We could demonstrate that for a significant range of detected atom numbers the instability is limited by quantum projection noise only, and that for the current status of this fountain clock the new microwave source poses no limit on the achievable frequency instability.
The residual cavity-pulling effect limits further narrowing of linewidth in dual-wavelength (DW) good-bad-cavity active optical clocks (AOCs). In this paper, we for the first time experimentally realize the cavity-length stabilization of the 1064/1470 nm DW-AOCs by utilizing the phase locking technique of two independent 1064 nm good-cavity lasers. The frequency tracking accuracy between the two main-cavities of DW-AOCs is better than $3 times {10^{ - 16}}$ at 1 s, and can reach $1 times {10^{ - 17}}$ at 1000 s. Each 1470 nm bad-cavity laser achieves a most probable linewidth of 53 Hz, which is about a quarter of that without phase locking. The influence of the asynchronous cavity-lengths variation between two DW laser systems is suppressed.