Progress toward a microwave frequency standard based on laser-cooled large scale ${}^{{\rm{171}}}{\rm{Y}}{{\rm{b}}^{\rm{+}}}$ ion crystal

In recent years, numerous atomic clocks have been developed that offer precise and stable time frequency signals. Such signals are crucial for both basic physics dzuba2016strongly ; safronova2018search and practical applicationshinkley2013 . In particular, with the excellent performance, atomic clocks operating with a cloud of trapped ions are showing extremely strong promise in the quest for high precision. For instance, optical clocks based on $\rm{Al}^{+}$ exhibit a systematic uncertaintybrewer2019al+ of $9.4\times{10^{-19}}$. Whereas $\rm{Hg}^{+}$ microwave clock liu2020progress demonstrate a frequency instability of $1.5\times{10^{-13}}/\sqrt{\tau}$burt2021demonstration . In targeting the microwave spectral region, $\rm{Hg}^{+}$burt2021demonstration ; berkeland1998laser , $\rm{Cd}^{+}$miao2021precision ; miao2015high , $\rm{Yb}^{+}$mulholland2019compact ; king2012absolute , and $\rm{Ba}^{+}$pino2020demonstration trap systems have been investigated meticulously during the past few decades. The investigations show that while ensuring a decent performance, an atomic microwave frequency standard based on trapped ions has great potential in high transportability because their interaction time are long and the structure of the system is relative simple. For these reasons, microwave ion clocks are being touted as promising candidates for the next generation of practical atomic clocks.

Much progress on microwave clocks based on ytterbium ions (${}^{{\rm{171}}}{\rm{Y}}{{\rm{b}}^{\rm{+}}}$) has been achieved. For the buffer gas cooled $\rm{Yb}^{+}$ microwave clock, an instability of $10^{-11}/\sqrt{\tau}$ has been demonstrated, which was limited by collision and pressure related shifts. The instability of the laser-cooled $\rm{Yb}^{+}$ microwave clock was measured to be $2.09\times{10^{-12}}/\sqrt{\tau}$ and was limited by second-order Zeeman effectsphoonthong2014determination . In absolute terms, the frequency instability potential of a laser-cooled $\rm{Yb}^{+}$ microwave clock is the same as for the microwave clocks based on $\rm{Hg}^{+}$ and $\rm{Cd}^{+}$jau2012low ; schwindt2016highly ; warrington1999csiro ; schwindt2018operating . Lately, researchers at the National Physical Laboratory (NPL) have built a prototype of a laser-cooled ${}^{{\rm{171}}}{\rm{Y}}{{\rm{b}}^{\rm{+}}}$ microwave clock that is both compact and portable. The entire system fits into a 6U 19-inch rack unit $(51\times 49\times 28)$ $\rm{cm}^{3}$, verifying the feasibility of such miniaturized Ytterbium-based clocks.mulholland2019laser .

In this study, we report the design and prototyping of a laser-cooled ${}^{{\rm{171}}}{\rm{Y}}{{\rm{b}}^{\rm{+}}}$ microwave clock, based on the ground-state hyperfine transition of ${}^{{\rm{171}}}{\rm{Y}}{{\rm{b}}^{\rm{+}}}$ at 12.6 GHz. The clock system is well integrated into a single physical package and operates successfully in the laboratory environment. More than $10^{5}$ ytterbium ions are stably trapped in the system enabling it to offer a high signal-to-noise ratio (SNR) Ramsey signal of the ground-state transition. The short-term stability of the ${}^{{\rm{171}}}{\rm{Y}}{{\rm{b}}^{\rm{+}}}$ microwave clock has been improved to $8.5\times{10^{-13}}/\sqrt{\tau}$, a current record level, and its performance in practice demonstrates that the laser-cooled ${}^{{\rm{171}}}{\rm{Y}}{{\rm{b}}^{\rm{+}}}$ clock has promising potential that is as good as other types of ion trap systems. Our research is helpful for developing a compact microwave clock device that can used in ground-based time-keeping, navigation station networking, and terrestrial network synchronizing.

The specifics of the operation of an microwave clock are determined by the electronic energy-level structure of the trapped ions. The simple energy-level structure of single ${}^{{\rm{171}}}{\rm{Y}}{{\rm{b}}^{\rm{+}}}$ is shown in Fig.1. To cool the ions and probe their states, a 369 nm laser is used to cycle between the transition states labeled ${}^{2}{S_{1/2}}(F=1)$ and ${}^{2}{P_{1/2}}(F=0)$. The neutral Yb atoms are ionized using a combination of two laser beams of wavelengths 369 nm and 399 nm. An extra 935 nm laser is used to drive ions out of the long-lived state ${}^{2}{D_{3/2}}(F=0)$yu2000lifetime . Moreover, to drive ions out of the state ${}^{2}{S_{1/2}}(F=1)$ during cooling, microwave radiation of 12.6 GHz is also applied. The ground state hyperfine splitting, $({}^{2}{S_{1/2}}(F=1)\to{\rm{}}{}^{2}{S_{1/2}}(F=0))$ of 12.6 GHz, is used as the clock transition.

In regard to the clock system (Fig. 2), an ${}^{{\rm{171}}}{\rm{Y}}{{\rm{b}}^{\rm{+}}}$ cloud is trapped in a well-designed linear Paul trap. Details of the ion trap are given elsewhere han2021toward , and hence only a brief description is presented here. The trap is made up of four trisected cylindrical electrodes made of copper. The radius of each electrode is ${r_{e}}=7.1$ mm, and the shortest distance between the electrodes and the ion trap center is ${r_{o}}=6.2$ mm. The ratio of ${\raise 3.01385pt\hbox{${{r_{e}}}$}\!\mathord{\left/{\vphantom{{{r_{e}}}{{r_{o}}}}}\right.\kern-1.2pt}\!\lower 3.01385pt\hbox{${{r_{o}}}$}}$ is optimized and set at 1.15, to reduce RF heating effects and to increase the number of trapped ionsdenison1971operating . The lengths of the electrode sections are 20, 40, and 20 mm. Direct current (DC) voltage is applied across adjacent sections, whereas a radio frequency (RF) voltage, with frequency fixed at 1.144 MHz, is assigned to the central section. Usually, the amplitude of the RF voltage is set below 200 V, implying that the trapping $q$ parameter is smaller than 0.11. A DC voltage of 4 V is adopted to provide fine axial confinement of the ion cloud. Besides the ion pump, a titanium sublimation pump is added to enhance the vacuum degree because ${}^{{\rm{171}}}{\rm{Y}}{{\rm{b}}^{\rm{+}}}$ is found to bond rapidly with some molecules such as ${{\rm{O}}_{2}}$, ${{\rm{H}}_{2}}$, and ${{\rm{H}}_{\rm{2}}}{\rm{O}}$sugiyama1995disappearance ; hoang2020ybh+ [see Fig. 2(a)]. A background pressure below ${10^{-9}}$ Pa is maintained during clock operations. For the Helmholtz coil system, three orthogonal pairs of coils are arranged compactly around the vacuum chamber and provide a steerable magnetic field that compensates the residual magnetic field and performs the Zeeman sublevel splitting. An extra ${\rm{700}}$ ${\rm{\mu T}}$ external magnetic field, generated by a pair of coils, is also placed in the north-south direction to induce a precession in the dipole moments of the ions and to destabilize the dark statesberkeland2002destabilization .To minimize the second-order Zeeman (SOZS) shift, a magnetic shield, composed of three layers Permalloy, wraps the vacuum chamber and coils. The shielding factors in the north-south, east-west, and up-down directions are measured to be 1000, 2000, and 300, respectively.

In regard to the laser system setup [Fig. 2(b)], all wavelengths of the various laser beams, corresponding to the different state transitions, were found by using saturated absorption spectroscopy that employed a Yb hollow cathode lamp. For accuracy, a high-resolution wavemeter (HighFinesse WS8-2) together with a proportional–integral–derivative controller was used to measure and stabilize the lasers. The 399 nm and 935 nm lasers are respectively extended-cavity-diode and distributed-feedback (DFB) lasers. Because the 369 nm laser beam plays a pivotal role in both cooling and probing, to enhance the aseismic capacity and large mode-hop-free tuning range, this beam is generated by a frequency-tripled laser—the 1108 nm DFB fiber laser—and two periodically poled crystals. Reviewing the laser system, the 369 nm laser beam is separated into two beams by a polarization beam splitter. One of the beams is combined by a dichromatic mirror with the 935 nm laser beam and passed from above into the vacuum chamber. The other beam is combined with the 399 nm laser beam and directed in the opposite direction to the 935 nm laser beam. Because the extra strong magnetic field is recommended to be at a certain oblique angle relative to the polarization of the laser beams, all beams are linearly polarized by half-wave plates. Our lasers can provide power outputs up to 70 mW, 100 mW, and 80 mW for the 369 nm, 399 nm, and 935 nm beams, respectively, propagating in free space. The spatial configuration of the ion cloud is captured by an electron-multiplying charge-coupled device (EMCCD). A photomultiplier tube (PMT) is used to record the number of photons emitted by the ions. The microwave radiation is generated by a commercial microwave synthesizer (Agilent E8257D), referenced by the 10 MHz signal obtained from an oven-controlled crystal oscillator (OCXO).