Yb Lattice-Based Optical Clock
In order to load the atoms into the shallow lattice trap, we first cool the atoms with two stages of laser cooling/trapping. The initial stage loads several million atoms from a Yb beam into a magneto-optic trap using the strong 1S0→1P1 transition (Δν = 28 MHz) at 399 nm. The cooling light is generated with frequency-doubled semiconductor lasers. The trapped atoms have a temperature of a few mK, too warm for the lattice, so we transfer about 70 % of the atoms into a magneto-optic trap based upon the much narrower intercombination line (Δν = 182 kHz) at 556 nm. In this trap the atoms are cooled to 30-50 μK (depending on the isotope), suitable for lattice loading. We overlap a tightly focused lattice beam (1 W of power near 760 nm ) with the green magneto-optic trap for 30 ms, during which ~ 15000 atoms are loaded into the potential wells of the lattice at a temperature of ~ 15 μK. To excite the clock transition, a well-stabilized probe laser beam at 578 nm is overlapped with the lattice beams (although it is only a traveling wave since it passes through the retro-reflecting mirror). With the atoms trapped in the lattice, a probe pulse of 3-200 ms is used to excite the atoms. The degree of excitation is detected by measuring depletion of the ground state population with a resonant pulse at 399 nm as shown in the following measurement sequence:
Spectroscopy of the Clock Transition
The probe laser light was originally generated by a stabilized dye laser, but is now produced through sum frequency generation in a single-passed non-linear waveguide (for more details see "Stable Laser System for Probing the Clock Transition at 578 nm in Neutral Ytterbium"). The frequency of the light is pre-stabilized by locking it tightly to a reference fringe of a high finesse Fabry-Perot cavity. With our vertical reference cavity, we have achieved a short term laser stability of ~ 10-15 at 1 s with low drift rates. When we scan the laser over the clock resonance we see the expected sideband structure for lattice confined atoms :
In the center we see a narrow Doppler-free carrier with first-order sidebands located 90 kHz away. Zooming in on just the central feature, we see a spectrum that has been resolved with linewidths as narrow as 4 Hz (line Q > 1014):
We then use a spectroscopic feature such as this one to correct drifts of the reference cavity and give long term stability for the clock. Locking the frequency of the probe laser to a line such as the one shown above would yield a fractional frequency instability of less than 2 x 10-15 for 1 s averaging time, competitive with the best existing frequency standards. With the signals we can now derive with the normalized shelving detection scheme described above, we should be able to support an instability well below 10-15 for 1 s averaging time, given a sufficiently pre-stabilized probe laser.
One of the main concerns for lattice-based clocks is the inherent asymmetry built into the odd isotopes due to their non-zero nuclear spin. While with one dimensional lattices, the most obvious effects such as first-order sensitivities to magnetic fields and lattice light polarization, can be compensated by alternating between +/- m states, for three dimensional lattices, the situation is less clear. This leads to the idea of using the forbidden 1S0→3P0 transition in even isotopes, which have simpler atomic structure and can be easier the cool. The catch is how to excite these atoms since the transition is doubly forbidden and even isotopes for the clock candidates do not have a non-zero nuclear magnetic moment, which can slightly relax the selection rules. To address this issue, groups have proposed multi-photon excitation methods for using the even isotopes, but these are experimentally quite difficult to implement. In collaboration with A. Taichenachev and V. Yudin (affiliated with the Institute of Laser Physics of the Siberian Branch of the Russian Academy of Sciences and Novosibirsk State University) we have developed a new method that uses a small magnetic field (~ 1 mT or 10 G) to achieve the requisite level mixing . This technique is readily applied in the laboratory and has enabled construction of clocks with high stability (σ(τ) < 3 x 10-15τ-1/2) and small uncertainty (~ 10-15 ). We have performed absolute frequency measurements (see Figure below) for the clock transition against the Hg+ ion optical clock at NIST and the NIST timescale, which is calibrated by the NIST Cs fountain [5,6]. The resulting value was 518 294 025 309 217.8(0.9) Hz, where the uncertainty was primarily statistical in nature. The uncertainty due to systematic shifts in the clock was ~ 10-15, and was due to a variety of sources including collision effects, blackbody radiation shifts, and two other shifts that may ultimately limit lattice clocks based on even isotopes: second-order magnetic field shifts and AC Stark shifts due to the probe light. However, these last two effects will become less important as we progress towards systems with higher line Q, so the prospects for these clocks are still promising.
Spectroscopy in a Lattice With a Spin-1/2 Atom (171Yb)
More recently we have performed an evaluation of one of the Yb fermionic isotopes, 171Yb. This isotope has a nuclear spin of 1/2, which gives it the simplest sub-level structure available for a non-zero spin atom, and has the added advantage that we don't need to use a magnetic field to enable excitation of the clock transition. However, we do need to suppress first-order magnetic field shifts, which we do by alternating between the m = +/- 1/2 states through optical pumping of the atomic sample . Below is a spectroscopic scan of the clock transition for both m-states using linearly polarized light:
In (a) we see the two Zeeman peaks split by a 1 G magnetic field. By fixing our laser frequency to the average value of the two peaks, we make our clock insensitive to effects that depend on the m-level of the atom. The lower figure (b) shows a zoom-in on one of the peaks with a full-width half-max linewidth of ~ 5 Hz (or a line Q of 1015). With this system we have achieved an absolute frequency uncertainty of < 4 x 10-16 and have performed absolute frequency measurements with an uncertainty of less than 1 Hz (ν0 = 518 295 836 590 865.2(0.7)) . The uncertainty of the clock is limited by the extrapolation of the clock frequency to what it would be at zero degrees Kelvin. In fact, its reproducibility should be even better.
Prospects for Optical Lattice Clocks
In order to push lattice-based optical clocks to reach their full potential, several improvements in the current apparatus are underway. First, we are increasing the stability of the clock by improving the prestabilization of the clock laser with better reference cavities. Second, we are implementing higher-order dimensionality lattices in order to isolate the atoms in their own individual potential wells to suppress collision effects. This should enable the Yb lattice clocks to achieve uncertainties well below one part in 1016.
References (click on hyperlinks for pdf versions of the manuscripts) or visit the Division publication site for a updated listing of publications describing this work: Masao Takamoto, Feng-Lei Hong, Ryoichi Higashi, and Hidetoshi Katori, “An optical lattice clock”, Nature 435, 321 (2005).
 C. W. Hoyt, Z. W. Barber, C. W. Oates, T. M. Fortier, S. A. Diddams, and L. Hollberg, "Observation and absolute frequency measurements of the 1S0→3P0 optical clock transition in neutral ytterbium", Phys. Rev. Lett. 95, 083003 (2005).
 Z. W. Barber, C. W. Hoyt, C. W. Oates, L. Hollberg, A. V. Taichenachev, and V. I. Yudin, "Direct excitation of the forbidden clock transition in neutral 174Yb atoms confined to an optical lattice", Phys. Rev. Lett. 96, 083001 (2006).
 A. V. Taichenachev, V. I. Yudin, C. W. Oates, C. W. Hoyt, Z. W. Barber, and L. Hollberg, "Magnetic field-induced spectroscopy of forbidden transitions with application to lattice-based optical clocks", Phys. Rev. Lett. 96, 083002 (2006).
 Z. W. Barber, J. E. Stalnaker, N. D. Lemke, N. Poli, C. W. Oates, T. Fortier, S. A. Diddams, L. Hollberg, "Optical lattice induced light shifts in a Yb atomic clock", Phys. Rev. A 77, 00501(R) (2008).
 N. Poli, Z. W. Barber, N. D. Lemke, C. W. Oates, L. S. Ma, J. E. Stalnaker, T. Fortier, S. A. Diddams, L. Hollberg, J. C. Bergquist, A. Brusch, S. R. Jefferts, T. P. Heavner, and T. E. Parker, "Frequency evaluation of the doubly forbidden 1S0→3P0 transition in bosonic 174Yb", Phys. Rev. A 77, 00501(R) (2008).
 N. D. Lemke, A. D. Ludlow, Z. W. Barber, T. M. Fortier, S. A. Diddams, Y. Jiang, S. R. Jefferts, T. P. Heavner, T. E. Parker,
and C. W. Oates, "A spin-1/2 optical lattice clock", arXiv:0906.1219 (June 2009).
Chris Oates, NIST (email@example.com)