Study of Ytterbium Optical Lattice Clocks in China
MIN ZHOU AND XINYE XU
STATE KEY LABORATORY OF PRECISION SPECTROSCOPY AND DEPARTMENT OF PHYSICS
EAST CHINA NORMAL UNIVERSITY, CHINA
This brief review introduces optical clocks based on neutral ytterbium atoms stored in an optical lattice. The discussion covers laser cooling and trapping of ytterbium atoms, state selection by quantum manipulation, and precision clock spectroscopy in a magic optical lattice. Recent progress on laser stabilization to clock resonance and the frequency stability measurement is reported.
Optical atomic clocks, ytterbium atoms, optical lattices, quantum manipulation, precision measurements.
Optical atomic clocks, which provide unprecedented precision for frequency-based measurements with stability better than cesium-fountain clocks, have become a hot area of research over the past decade. Great efforts have been made to improve the clocks' performance. Both the fractional frequency inaccuracy and instability have been brought down to the 10-17 or even 10-18 level. At this level, the precise comparison between local clocks can go beyond the uncertainty of the International System of Units (SI) second, enabling tests for fundamental physics such as gravitational redshift  and the search for the temporal variation of fundamental constants [2-4]. In addition, at this level there are also possible practical applications for global satellite navigation systems. Furthermore, a redefinition of the SI second based on optical atomic transitions could occur in the future. On the other hand, ultra-long fiber links and transportable clock systems for remote or international comparison are currently under active investigation [5, 6]. In this system, accurate optical clocks would be connected to form an intercontinental network, which would facilitate applications in geodesy and in fundamental sciences.
Optical transitions with an extremely high quality factor Q (i.e. ν/Δν) lie at the heart of optical atomic clocks. These clock transition lines are available either in neutral atoms confined in an optical lattice or a single ion contained in a radiofrequency trap. It is generally believed that, the optical lattice clocks have an edge over single ion clocks in terms of stability, because the optical lattice clocks embrace more quantum absorbers. For optical lattice clock realization, the ytterbium atom is recognized as one of the most promising candidates, and most of the ytterbium optical lattice clocks use the spin-1/2 system with 171Yb. To the best of our knowledge, 171Yb lattice clocks have been demonstrated at the National Institute of Standards and Technology (NIST) [7, 8], at the National Metrology Institute of Japan (NMIJ) and the National Institute of Advanced Industrial Science and Technology (AIST) , at the Korea Research Institute of Standard and Science (KRISS) , and at the Institute of Physical and Chemical Research (RIKEN) . Recently, the group at Istituto Nazionale di Ricerca Metrologica (INRIM) has also reported the absolute frequency measurement of a clock transition . To date, outstanding results of the 171Yb optical clocks have been obtained with a frequency uncertainty of few parts in 10-17  and an instability of few parts of 10-18 in only seven hours of averaging .
In this article, we will describe our accomplishments on the study of ytterbium optical clocks. Two nearly identical clock systems are being developed for performance evaluation below 10-16. The cold-atom preparation is reported followed by the quantum manipulation in an optical lattice. The laser is stabilized to the clock resonance based on precision clock spectroscopy. We will then present the fractional frequency stability measurement and discuss some systematic frequency shifts.
PREPARATION OF COLD ATOM SAMPLES
Since atoms in a gas move very quickly, the direct excitation of the clock transition is impossible. The laser cooling and trapping techniques offer possibilities to reduce the Doppler effects. The magneto-optical trap (MOT), formed by three pairs of counter-propagation beams in a standard σ+- σ- configuration in conjunction with a quadrupole magnetic field, is widely used for obtaining cold neutral atoms. Fig. 1 depicts the relevant energy levels of 171Yb with the transitions and the wavelengths used in an optical lattice clock. In principle, the ytterbium atoms can be continuously cooled in two MOTs.
As shown in Fig.1, the blue MOT is based on the 1S0→1P1 dipole transition at 399 nm. This is a strong cycling transition. It has a broad linewidth of 29 MHz, and the corresponding Doppler-limited temperature is 690 μK. The 399-nm
laser beam is mainly split into four parts for the Zeeman slower, the MOT, the two-dimensional optical molasses (2D-OM) and the 399-nm probe for fluorescence detection, respectively. Acousto-optic modulators (AOMs) are used to shift laser frequency and to chop laser beams. For frequency stabilization of a 399-nm laser we use the modulation transfer spectroscopy technique with a ytterbium hollow cathode lamp. For each clock system, an atomic beam of ytterbium effuses from a heated oven at 400°C. After mechanical collimation, the thermal beam is further transversely collimated in the 2D-OM. Then the Zeeman slower decelerates the atoms from 300 m/s to 15 m/s in the longitudinal direction. Here, the Zeeman slower consists of an increasing magnetic field and a 399-nm circularly-polarized light. Finally, the atoms interact with three pairs of the 399-nm laser beams and are cooled in the blue MOT . The fluorescence of the trapped ytterbium atoms is collected with the photomultiplier and imaged onto an intensified CCD. As many as 107 of 171Yb atoms are cooled down to about 1 mK.
Fig. 1: Relevant energy levels of 171Yb for the lattice clock realization. The 1S0 → 3P0 clock transition at 578 nm has a natural linewidth of about 10 mHz. The magic lattice trap is operated at 759 nm and the induced Stark shifts of the clock states 1S0 and 3P0 are indicated by the single arrows. The first-order Zeeman shift and the vector lattice shift are cancelled by averaging the hyperfine Zeeman transition frequencies ƒ-1/2 and
ƒ+1/2. Energy levels are not to scale.
The ytterbium atoms are further cooled in a green MOT based on the 1S0 → 3P1 intercombination transition at 556-nm. The transition is completely closed and it has a narrow linewidth of 182 kHz with a Doppler limit of about 4 μK. The 556-nm laser is obtained by frequency doubling of a 1111.6-nm source generated by a diode laser and a fiber amplifier. A waveguide in a single-pass configuration provides up to 40 mW of 556-nm radiation. The Pound-Drever-Hall (PDH) locking technique is utilized to stabilize the frequency on a Fabry-Perot (FP) cavity. The stabilized laser is measured to have a linewidth of 3 kHz , which is feasible for narrow line cooling. The 556-nm MOT beams are overlapped with 399-nm MOT beams using dichroic mirrors in three dimensions. To switch the phase from the blue MOT to the green MOT, the 399-nm beams are turned off and the quadrupole magnetic field is turned down. Typically 50% of precooled atoms are transferred into the green MOT and the atom temperature is about 15 μK.
STATE SELECTION AND HERTZ-LEVEL CLOCK SPECTROSCOPY IN A MAGIC LATTICE
Optical frequency standards using a free expanding MOT approach have some problems. The spectroscopic time is constrained due to gravity. Meanwhile, Doppler and recoil related shifts still contaminate the Q factor, thus limiting the accuracy at the 10-16 level. To eliminate these effects, a successful approach is to limit the motion of the atoms during the time of clock interrogation to regions much smaller than a wavelength, which is the so-called Lamb-Dicke regime. This key technique has been applied in single ion clocks. Similarly, the use of an optical lattice eliminates the Doppler related systematics for free-falling atoms and it can provide a long interrogation time. It is noted that, the resulting AC Stark shift by the lattice is significantly larger than the target precision for the clock transition. Furthermore, the AC Stark shift is generally different for the ground state and the excited state of the clock transition. An ingenious way to circumvent this problem is to tune the lattice at the Stark-shift free (magic) wavelength.
Fig. 2 shows a schematic diagram of the experimental setup for one 171Yb optical lattice clock. The vacuum chamber and the two-stage cooling systems are omitted for clarity. The lattice laser is obtained from a continuous Ti:sapphire laser system. A small part is sent to a FP cavity for frequency stabilization via the PDH method. The main part is delivered to the atoms with a polarization-maintaining (PM) fiber for mode clearing. The output of about 1.5 W is focused down to a waist radius of 30 μm and retro-reflected by a curved mirror to form a standing wave. The optical lattice is oriented at about 35.2° with respect to the horizontal plane. After the two-stage cooling, typically about 105 atoms are loaded into the 1D optical lattice at the magic wavelength of 759.3 nm . At this moment, the atoms are all populated at the 1S0 ground state and are ready for clock interrogation.
Fig. 2: Schematic diagram of the experimental setup for one 171Yb optical lattice clock. Signal processing for 578-nm laser stabilization to the clock resonance is highlighted. The clock laser is pre-stabilized on the high-finesse cavity via the PDH method, where AOM1 is used for fast locking. After driving the clock transition, the fluorescence collected by the PMT is sent to the computer for data processing. The digital servos determine the error signals of the signal generators driving the AOM2 and AOM3.
The clock transition 1S0 → 3P0 at 578-nm is strictly dipole-forbidden, yet it becomes allowable in odd isotopes such as fermionic 171Yb due to hyperfine state mixing of the 3P0 sublevels. Thus, the clock transition is accessible with a non-zero natural linewidth of about 10 mHz and efficient excitation is possible while maintaining a large Q factor. The clock laser at 578-nm is generated by sum frequency mixing a 1319-nm Nd:YAG laser with a 1030-nm fiber laser in a periodically poled lithium niobate (PPLN) waveguide. The obtained 578-nm laser is then referenced to a high-finesse FP cavity for active frequency stabilization. The slow feedback signal is sent to the PZT of the 1310-nm laser and the fast feedback signal is sent to AOM1. The stabilized light with a linewidth of about 1 Hz  is then delivered to the cold atom sample through a 15-m long PM fiber. The fiber noise cancellation technique is employed to cancel the random phase noise induced by the fiber length fluctuation. AOM3 bridges the frequency difference between the laser and the clock transition. The clock laser is aligned coaxially with the lattice laser and their polarizations are linearized by the same Glan-Laser polarizer, which has an approximated extinction ratio of 105:1. For the initial clock spectroscopy, the clock-transition absorption profile is measured using the electron shelving technique . If the clock laser is close to the resonance, a fraction of atoms in the 1S0 ground state are excited into the long-lived 3P0 state. As a result, there are population losses in the 1S0 ground state during the measurement. As shown in Fig. 2, a 399-nm probe is used to detect the fluorescence signal of atoms remaining in the 1S0 ground state. The clock laser is tuned with a step of 100 Hz by scanning the frequency of the double-pass AOM3. The fluorescence reduction is shown in Fig. 3a. The data fitting yields a spectral linewidth of 1.7 kHz. Each data point is averaged four times.
Fig. 3: Clock spectroscopy in an optical lattice operated at the magic wavelength. (a) Clock-transition absorption profile with the electron shelving technique . (b) Carrier-sideband spectroscopy with the atom number normalization scheme. (c) Hz-level Fourier-limited spectroscopy. (d) Two scans over the Zeeman substates with different polarization of optical pumping. The applied bias magnetic field Bbias is 1.15 Gs.
To eliminate the noise from the shot-to-shot atom-number fluctuation, an atom number normalization scheme is implemented. The fluorescence I1 by the first 399-nm probe accounts for the unexcited atoms; then, they are swept out of the lattice. Those atoms on the 3P0 state are pumped back to the 1S0 ground state using the 649-nm and 770-nm
lasers. A second 399-nm probe is used to observe the fluorescence I2. Both the 649-nm and 770-nm lasers are frequency stabilized to the FP cavity shared by the 759-nm laser stabilization (see Fig.2). The excitation fraction is expressed by (I2 - I0) / (I1 + I2 - 2I0), where I0 is the background fluorescence signal induced by a third 399-nm probe. In order to observe the full carrier-sideband structure, the excitation of the clock transition is oversaturated. A typical clock-transition spectrum of 171Yb atoms in a 1D optical lattice is shown in Fig. 3b. Clock transitions between motional states are clearly resolved. The carrier corresponds to the |n > → |n > transition and the red (blue) sideband corresponds to the |n > → |n -1> (|n+1 >) transition. The longitudinal motional frequency is read from the sharp edge of each sideband and the temperature can be extracted by modeling the spectrum. As shown in Fig. 3c, by removing the power broadening and Zeeman broadening effects, the carrier linewidth shows a decrease from a few kHz to about 6 Hz .
As a few tens of cold atoms are trapped at each lattice site, atom-atom interactions may occur through s- or p-wave collisions. According to the Pauli exclusion principle, the s-wave and higher even-partial-wave collisions can be suppressed by employing ultracold fermions. To this end, the cold ytterbium atoms are spin polarized at one Zeeman substate, 1S0(mF = -1/2) or 1S0(mF = +1/2), using a pumping laser at 556-nm. A bias magnetic field Bbias is applied perpendicular to the lattice beam axis. The pump laser is chosen to be near resonant with the 1S0, F = 1/2 → 3P1, F = 3/2 transition and the alternating between the σ+ and σ- polarization is realized by reversing the direction of Bbias. In the presence of Bbias, the Zeeman degeneracy in the 3P1, F = 3/2 state is lifted. In one cycle, the σ+ polarized beam drives the atoms at 1S0(mF = -1/2) into 3P1(mF = +1/2). Some atoms that decay on a σ+ transition are pumped again and the others that decay on a π transition remain in the 1S0(mF = +1/2) dark state, where all atoms will be finally populated. Similarly in the next cycle, the σ- polarized beam pumps all atoms into 1S0(mF = -1/2). Spin polarization prevents the average population in the two Zeeman substates of 1S0, therefore the contrast of clock spectroscopy is improved by a factor of two. Moreover, the first-order Zeeman shift as well as the vector light shift is removed by averaging the hyperfine Zeeman transition frequencies ƒ-1/2 and ƒ+1/2. Spin polarization is implemented using a σ+ polarized laser operating on the 1S0, F = 1/2 → 3P1, F = 3/2 transition with an applied bias magnetic field Bbias . After finishing the optical pumping, a π-polarized pulse of 578-nm laser interrogates the clock transition. The spectra of two π transitions are as shown in Fig. 3d.
PERFORMANCE CHARACTERIZATION OF THE CLOCK
An optical frequency standard is operated in such a way that the clock laser must be steered by the atomic transition frequency ƒ171Yb . Fig. 2 highlights the signal processing for stabilizing the clock laser frequency to the atomic resonance. To remove the first-order Zeeman shift and the vector lattice shift, and to possibly be more pronounced for suppressing the collisional shift, the laser is locked to the average of 1S0(mF = ±1/2) → 3P0(mF = ±1/2), ΔmF =0 transitions. For this purpose, two independent digital servos are used to lock the two peaks. AOM3 is responsible for frequency hopping and the overall frequency correction is realized using AOM2. The timescale involved in one cooling-interrogation-detection cycle is about 1.3 s. In the first and second cycles, we alternately set the AOM3 frequency at each half maximum of the first peak. The excitation fraction difference of two measurements gives the error signal δƒ1 in the digital servo. For the second peak, another digital servo outputs the error signal δƒ2 in the third and fourth cycles. The average of δƒ1 and δƒ2 provides the frequency correction of AOM2. Meanwhile, a feedforward by fitting the updating frequency of AOM2 compensates frequency drifts of the clock laser. The first-order Zeeman splitting may vary due to the stray magnetic field fluctuation. Therefore, the common-mode value of δƒ1 and δƒ2 is the feedforward to AOM3 to improve the locking robustness. Finally, the clock laser is locked to the center of the atomic resonance.
Fig. 4: Fractional frequency instability of a 171Yb optical clock by evaluating the clock laser independently locked to the two Zeeman components.
In general, the two Zeeman components of the clock transition can be regarded as independent references. As the clock laser is alternately locked to each Zeeman component, self-comparison of one optical clock can be implemented by comparing the two frequencies ƒ-1/2 and ƒ+1/2. Fig. 4 shows the fractional instability of one optical clock from the difference (ƒ-1/2 - ƒ+1/2)/2. The Allan deviation follows the dependence of 4.2×10-15 / √τ, which shows there is no significant fluctuation of the magnetic field during the entire locking. To evaluate the true stability of the optical clock, the second optical lattice clock is employed as a reference. Direct comparison of the two 171Yb clocks shows similar behavior with the stability measurement in Fig. 4.
Fig. 5: The observed frequency difference between two 171Yb optical clocks. Relative frequency shifts are measured by varying the lattice power for eight lattice frequencies. Each line is a linear fit to determine the magic frequency where the relative frequency shift crosses zero for any lattice power. The labelled frequencies are all relative to 394,798,150 MHz.
The clock transition is affected by various systematic shifts that should be corrected. Here we are concerned with several terms, including the lattice laser shift, the collisional shift and the blackbody radiation (BBR) shift. At present, the lattice light shift is the most prominent contribution in our optical lattice clocks. The clock-transition frequency difference between two optical lattice clocks is measured by varying the lattice power for eight lattice frequencies in one clock system. The observed frequency shifts are shown in Fig. 5. Each group of data is linearly fitted to give a slope of line. The line has a slope of zero corresponds to the magic frequency. The uncertainty of the scalar Stark shift is therefore evaluated to be 1.7×10-16.
The collisional shift is not a negligible issue in our optical lattice clocks, as we note that it may contribute to the relative shift between two clocks when varying the lattice depth. The other group has measured small collisional shifts in spin-polarized 171Yb optical lattice clocks . The light-atom interaction may introduce inhomogeneous excitation, thus leading the fermions to be distinguishable . The worse thing for ytterbium is that the achievable temperature from the narrow-line cooling is comparable to the centrifugal p-wave barrier of 30 μK, which means atoms in the optical lattice are not cold enough to freeze out the p-wave collision. As a result, the initially identical fermions are likely to become distinguishable as well. Suppression of the p-wave collisions is demonstrated by choosing the specific excitation fraction with Ramsey spectroscopy . An over-π pulse interrogation scheme with Rabi spectroscopy is also proposed . Toward the p-wave collisions cancellation, we plan to lower the atom temperature in advance using Raman sideband cooling. In the optical lattice, the motion of atoms is quantified by motional states
|n > (n=0,1,2...) and the resolved transition corresponding to |n > → |n'> can be addressed by the clock laser at 578-nm. A 578-nm laser pulse excites the atoms in the |n > motional state of 1S0(mF = ±1/2) into the |n -1> motional state of 3P0(mF = ±1/2). The 3P0 state has a very long lifetime so atoms would never decay spontaneously. Therefore, two extra beams at 649-nm and 770-nm pump the atoms in 3P0(mF = ±1/2) to the upper 3S1 state. They can decay back to the ground state via the 3S1 → 3P1 → 1S0 path. Through this process, atoms finally accumulate in the |n = 0> motional state of 1S0(mF = ±1/2).
The BBR shift is an obstacle to obtaining an optical lattice clock with 10-16 uncertainty or below. It can be evaluated theoretically from the Stark effect over a broad spectrum. The dominating differential static polarizability of two clock states of 171Yb has been measured with high accuracy . Meanwhile, the small dynamic correction has also been considered . However, problems still remain for complete knowledge of the temperature around the atoms. In our experiments, several calibrated sensors attached on the surface of the vacuum chamber are used to measure the temperature during the experimental period. The temperature distribution around the cold ytterbium atoms is numerically simulated based on the chamber structure and the measured temperature data. The total BBR shift is -1.289(7) Hz, and the corresponding uncertainty is 1.25×10-17 .
The most recent progress on the study of 171Yb optical clocks in China has been reported. The Hz-level spectroscopy in an optical lattice operated at the magic wavelength is demonstrated. The fractional frequency instability is measured by locking the clock laser to the atomic resonance. To operate as an optical frequency standard, a complete evaluation of systematic effects is demanded and the absolute frequency needs to be measured. The BBR shift is accurately evaluated at the 10-17 level by numerically simulating the temperature distribution around the atoms. Direct comparison of two optical clocks enables us to investigate the systematic uncertainties, such as the uncertainty from the lattice laser. In the next step, all frequency shifts will be further corrected, and the absolute frequency of the clock transition of the ytterbium optical lattice clock will be measured.
Acknowledgements: We would like to thank L. Ma, Z. Bi, Y. Jiang, J. Liu, J. Wang et al. for their contributions and J. Ye, H. Katori, F. Hong, K. Gibble, N. Treps, J. Li, Y. Wang, T. Li et al. for their fruitful discussions. This work is supported by the National Key Basic Research and Development Program of China (2016YFA0302103 and 2012CB821302), the National Natural Science Foundation of China (11134003 and 10774044), the National High Technology Research and Development Program of China (2014AA123401) and the Shanghai Excellent Academic Leaders Program of China (12XD1402400).
 C. W. Chou et al., Science 329,1630(2010).
 T. Rosenband et al., Science 319,1808(2008).
 S. Blatt et al., Phys. Rev. Lett. 100,140801(2008).
 R. M. Godun et al.,. Phys. Rev. Lett. 113,210801(2014).
 K. Predehl, et al., Science 336,441(2012).
 N. Poli et al., Appl. Phys. B 117, 1107(2014).
 N. D. Lemke et al., Phys. Rev. Lett. 103, 063001(2009)
 N. Hinkley et al., Science 341, 1215(2013).
 M. Yasuda et al., Appl. Phys. Express 5,102401(2012).
 C. Y. Park et al., Metrologia 50,119(2013).
 N. Nemitz et al., Nat. Photon. 10, 258(2016).
 M. Pizzocaro et al., arXiv:1609.01610v1(2016).
 X. Y. Xu et al., Front. Phys. China 4, 160(2009).
 M. Zhou et al., Chin. Opt. Lett. 11, 121402(2013).
 M. Zhou et al., Chin. Phys. B 22, 103701(2013).
 S. Fang et al., Appl. Phys. Lett. 102, 231118(2013).
 N. Chen et al., Chin. Phys. B 22, 090601(2013).
 X. H. Zhang et al., Laser Phys. Lett. 12, 025501(2015).
 N. Lemke et al., Phys. Rev. Lett. 107, 103902(2011).
 N. Chen and X. Y. Xu, Laser Phys. Lett. 12, 015501(2015).
 A. D. Ludlow et al., Phys. Rev. A 84,052724(2011).
 L. Sangkyung et al., New J. of Phys. 18, 033030(2016).
 J. A. Sherman et al., Phys. Rev. Lett. 108, 153002(2012).
 K. Beloy et al., Phys. Rev. A 86, 051404(2012).
 Y. L. Xu and X. Y. Xu, Chin. Phys. B 25,103202(2016).
Min Zhou received his PhD in optics from East China Normal University in 2014. Since 2014, he has worked as a research assistant at the State Key Laboratory of Precision Spectroscopy at East China Normal University. His research focuses on cold atom physics, laser physics and precision spectroscopy measurements.
Xinye Xu is a professor of physics at the State Key Laboratory of Precision Spectroscopy at East China Normal University, China. He obtained his PhD from the Shanghai Institute of Optics and Fine Mechanics (SIOM), Chinese Academy of Sciences (CAS) in 1997. He is currently the group leader of the ytterbium optical clock group at East China Normal University. His research interests include lasers physics, cold atom physics, atomic fountain and optical clocks, atom interferometers, atomic gyroscopes and precision spectroscopy measurements.