# [time-nuts] NIST Optical lattice clocks

Anders Wallin anders.e.e.wallin at gmail.com
Thu May 30 13:29:17 EDT 2013

```According to Wikipedia, The optical clock based on it is exact to 17 digits
> after the decimal point!
> I hope that doesn't mean it is time to trade my HP 5370B in shortly...
> How do they measure down to these resolutions?
>

Short answer: instead of a few GHz (Cs clock or H-maser), go to 500 THz or
so.

You can think of these optical clocks as an exercise in laser
stabilization. A laser with the correct wavelength for the atomic species
chosen (Yb, Sr, Ca, and so on) is stabilized to a fabry-perot resonator
(two mirrors separated by a glass or silicon spacer). If the resonator
(mirrors+spacer) is kept in vacuum, temperature stabilized well, and
isolated from vibrations (seismic/acoustic), the mirror-separation (which
determines the resonance frequency) is stable to (roughly) 1 part in 10^16
or so for short time scales (<100s maybe).
If the resonator would be absolutely stable this alone would make a clock.
But there is ageing/creep in the spacer material, as well as thermal noise
in the spacer/mirrors that limits performance.

To get rid of the long-term drift of the reference-resonator these lasers
(oscillating at say 500 THz)  which are stable to <1Hz are locked to the
"clock transition" (an optical absorption resonance) of the atomic species
chosen.
If the atoms are cooled  and isolated from the environment (electric,
magnetic fields etc) a narrow absorption line can show a linewidth of one
or a few Hz.
Keep the 500 THz local-oscillator locked to the atomic reference with ~1 Hz
or better for a few hours/days and you have an optical clock!

The "clockwork" that converts laser light at 500 THz down to a reasonable
RF frequency is a femtosecond frequency comb - which is fairly standard
technology by now.

> http://tf.nist.gov/ofm/calcium/ybhome.htm
> I thought they are already able to capture an atom in its own well?
>

There are two approaches:
- ion-clocks that trap a single ion in an RF trap. It's easier to cool and
control a single atom/ion, but the signal for locking is weak.
- lattice-clocks trap neutral atoms in an optical standing-wave trap. SNR
scales with the number of atoms, so more is better, as long as you can cool
them all and ensure they experience the exact same environment so they all
show an identical clock-transition.

AFAIK the lattice-clocks trap maybe 100s or 1000s of atoms in one well, and
have a 1D lattice with many wells in order to get up to maybe 1e6 atoms in
total which are probed by the clock laser.

hope this helps :)
Anders
```