[time-nuts] How Rubidiums make their frequency

Magnus Danielson cfmd at bredband.net
Wed Apr 19 17:04:50 EDT 2006

From: "Matt Ettus" <boyscout at gmail.com>
Subject: Re: [time-nuts] How Rubidiums make their frequency
Date: Wed, 19 Apr 2006 12:55:01 -0700

> Since we can now make DDS's with arbitrary frequency resolution, could
> you make an Rb oscillator without the magnetic field adjustment?
> Wouldn't that reduce a source of error in frequency?  Then we'd be
> left with the ideal resonance frequency, right?

No. First of all you have cavity pull from the missmatch of the resonant cavity
and the actual frequency, you have wall shift as the Rubidium atoms hit the
wall and you also have a pull in frequency due to the buffert gas. The
frequency pull of the buffert gas can be made to compensate the wall-shift
where as the cavity pull is harder since it is a per unit and temperature
thing.

Then, the real reason for a C-field is to separate several hyperfine levels
appart so that you can monitor the interesting one. In the case of Rubidium
you have the energy-levels for (F=1, mf = +2), (F=1, mf = +1), (F=1, mf = 0),
(F=1, mf = -1) and (F=1, mf = -2) falling down to (F=0, mf = +1),
(F=0, mf = 0) and (F=0, mf = -1). Since the mf = 0 is only weakly dependent on
the C-field and mf = +/- n is mostly linearly dependent on the C-field we only
want to monitor the {F=1, mf = 0} downto {F=0, mf = 0} transition (actually we
will monitor the transition from the lower to the higher state, ah well).
Early Cesium tubes used a too weak C-field and as a consequence they had
problems with interfering responses.

Also, you almost always have a field, so you better have one you control well.

Then again, for a Rubidium the other sources of error needs compensation and
with a C-field you can tune both up and down and not only in one direction.

> Are there any other influences on the resonance frequency?  I assume
> temperature and density don't matter.

Temperature doesn't matter you may think, but it will shift the physical size
of the resonance cavity which will then shift its cavity pull. Darn!

Cheers,
Magnus