[time-nuts] Quartz crystall and beyond (was: What’s the BEST crystal?)

Sat Feb 29 21:58:10 UTC 2020

On Sat, 29 Feb 2020 20:23:56 +0000
"Poul-Henning Kamp" <phk at phk.freebsd.dk> wrote:

> --------
> In message <20200229210755.1abd900696f8aa85567d2151 at kinali.ch>, Attila Kinali writes:
> >On Sat, 29 Feb 2020 13:44:59 -0500
> 
> >But, there is not much we can do about absorption/desorption.
> 
> Actually, there are things you can do, but they are very
> expensive.
> 
> One of the early paths of experiments with optic fibers were
> to replace the absorbed hydrogen with deuterium which is
> slightly larger, in order to move the OH- absorption
> peak away from the 1.3 micrometer band. (Bake at 1000°C
> in a D2 atmosphere for a couple of hours).

While this might work with absorption lines (ie energy bands
that absorp light within atomic structures), the absorption
in crystals is really the material itself that is a problem.
The added weight and thickness lowers the frequency of the
crystal (or raises it, when the material leaves the crystal).
Changing it for a different isotope is not going to help.

> If you were *really* serious about it, you would start out growing
> your quartz from monoisotopic silicon and oxygen, picking the smaller
> silicon (28) and larger oxygen (18) in order to reduce the size
> of the gaps to begin with.  It will probably also do wonders for
> your Q that all bonds are identical.

I am not sure that is indeed the case. Or rather, I don't think
we can build quartz crystals well enough for this to matter.
Even high quality quartz is still full of crystal defects
and embedded ions. Even silicon crystal, the one crystal we
know best how to make pure and "free" of defects is still
a very rough thing. The surface of wavers is being molten and
reformed a few times to reshape the crystaline strucutre and
to remove impurities. Unfurtunately, this doesn't work with
quartz, as the heat of melting it woud disociate the Si-O bonds.

One way to grow quartz better, would be to do it in a high vacuum
at high temperature, with a gas of Si and O around, both in low
concentration such that the growth is slow. But the cost of this
would be way beyond what would be economically feasible.

> >The diameter of the blank has to be scaled with its thickness, in
> >order not to compromise the f*Q product. Which in turn makes it
> >a bit problematic in terms of packaging, but nothing unsolvable.
> 
> Isn't that where "whispering gallery" modes come into the picture ?

Different concept. Quartz oscillators are mechanical resonators.
Cryogenic sapphire oscillators are electro-magnetic resonators. 
The problem with those is, that they are large and need liquid He
for cooling. Not only is He expensive, but it also needs a cryostat
that will mechanically shake the CSO. But they get down to a few parts
in 10^-15 between 1s and ~1000s, I've even seen papers with a few parts
in 10^-16 in the same range(e.g. [1]) . There have been attempts to get
them to liquid nitrogen temperatures [2]. But they only got down to 1e-13
(i.e. where good crystal oscillators are). And not much happend since,
beside an attempt to get them working at room temperature [3]

But once we leave quartz oscillators, there are other possibilities.
My current favorite is the high-finesse cavity stabilized optical
frequency comb. [4] gives a good overview of what we know about these
beasts sofar. [5] gives a nice overview how the classical Ti:Sapphire
laser based frequency comb is constructed and [6] gives a more general
description. The stability they achieve is basically the one that the
laser cavity acheives and a few parts in 1e-16 have been reported [7].
The comb then acts as a frequency divider and divides the 100s of THz
of the light down to more convenient frequencies. NIST demonstrated
this in a synthesis chain down to 5MHz a few years back [8] and got
to a few parts in 1e-15 and astonishingly low phase noise numbers
(-150dBc/√Hz @1Hz offset 5MHz signal).

The big disadvantage of these things is that they are even larger
than CSOs. More expensive and more finicky to run. There have been
a few who boast that they were able to run them over a few days
without interruption, but not many. there are attempts to minaturize
the frequency combs by using small (mm to cm sized) discs as comb
generator, but they are still very new and not yet commercially available.
But even if the comb could be minaturized without loss of performance,
it would still need a high finess cavity that sits in vacuum, preferably
at cryogenic temperatures and is somewhere between 10 and 40cm long.
Kind of a thing inbetween is [9], which puts the frequency comb in
a cavity of CaF2. But even this would probably need another cavity
to get to the high stability figures we seek.

			Attila Kinali

[1] "Comparison of ultra-stable radio frequency signals synthesized
from independent secondary microwave frequency standards",
by Harnett, Parker, Ivanov, Povey, Nand, and le Floch, 2013
http://arxiv.org/abs/1302.0283

[2] "Frequency Stability of 1 X 10^-13 in a Compensated Sapphire
Oscillator Operating Above 77 K", by Santiago, Dick, Wang, 1996
https://tda.jpl.nasa.gov/progress_report/42-126/126G.pdf

[3] "Room temperature Dual-Mode Oscillator - First result",
By Torrealba, Tobar, Ivanov, Locke, Harnet, le Flock and Cros, 2005

[4] "20 years of developments in optical frequency comb technology and
applications", by Tara Fortier and Esther Baumann1,2, 2019
https://doi.org/10.1038/s42005-019-0249-y

[5] "Construction of a Femtosecond Mode-Locked Laser"
http://www.df.unipi.it/~fisapp/Gruppi/Metrologia/spiegazioni/boris.pdf

[6] "Femtosecond Optical Frequcny Comb Technology", 
by Ye and Cundiff, Springer 2005
https://doi.org/10.1007/b102450

[7] "A sub-40mHz-linewidth laser based on a silicon single crystal optical
cavity", Kessler, Hagemann, Grebin, Legero, Sterr, Riehle, Martin, Chen, Ye,
2012
https://doi.org/10.1038/nphoton.2012.217

[8] "State-of-the-Art RF Signal Generation From Optical Frequency Division",
by Hati, Nelson, Barnes, Lirette, Fortier, Quinlan, DeSalvo, Ludlow,
Diddams, and Howe, 2013
http://tf.boulder.nist.gov/general/pdf/2646.pdf

[9] "Ultra-low-noise monolithic mode-locked solid-state laser",
by Shoji, Xie, Silverman, Feldman, Harvey, Mirin, Shibli, 2016
https://doi.org/10.1364/OPTICA.3.000995

-- 
<JaberWorky>	The bad part of Zurich is where the degenerates
                throw DARK chocolate at you.