It should be noted that this is a rare isotope of lutetium, which must be separated from the abundant isotope, so it is much more expensive than normal lutetium, which is already very expensive.
Nonetheless, the amount used in the clock is extremely small, so it does not influence much the cost, which is determined by a much more expensive set of lasers and optical components.
Lutetium 176 is very rare because chemical elements with an odd number of protons normally do not have isotopes with an even atomic mass, because those are unstable vs. beta decay.
Lutetium 176 is also radioactive, but its half-life time happens to be long enough so that a small amount of it has survived since the formation of the Solar System, like it also happened with the radioactive potassium 40 that is contained in the bodies of all living beings, which is another one of the 5 radioactive isotopes with even atomic mass of chemical elements with an odd atomic number.
2.6% natural abundance is more than enough to load an ion trap. Photoionization is so selective that one can load 46Ca from a sample with natural abundance (0.004%).
I’ve often wondered if a hobby-class atomic clock can be built with “a less accurate gas” that is easy to excite and measure in a feedback loop simply because it’s available in a handy package that lends itself for experimentation without having to mess with melting glass and bottles of pressurised gas. E.g. neon, nitrogen or mercury vapour.
There are different types of atomic clocks, but in most common types, the output comes from a crystal oscillator, or more generally frequency synthesizer, which is then slaved to some spectral feature in the "physics package". That is to say, the phase noise is as good as that of the crystal in the unit, but the longer term frequency stability is much improved by the slaving.
An exception is an active hydrogen maser, which directly outputs the frequency of atomic transition. It has very good phase noise, but is a rare beast, which is only used where it is absolutely necessary.
You can pull the frequency of a crystal resonator circuit by changing the loading capacitance, for example. You may use a varactor or any semiconductor junction. Doing so doesn't really affect phase noise.
I'm probably missing the right terminology. I would have thought the feedback loop creates jitter of its own. Phase locked VCOs are generally noisier than a crystal alone. But maybe I'm overthinking it and the loop bandwidth can be made very narrow with trimmed crystal and long integration times or whatever.
The contribution of the crystal to the overall tank circuit Q is vastly higher, by several orders of magnitude, than the contribution of the varactor diode.
So while making an oscillator steerable inevitably increases its phase noise slightly, the increase is either ignorable in practice or cancelled by the control loop itself.
A very good 10 MHz ovenized crystal oscillator, Hewlett Packard 10811D, ages by up to a few Hertz per year, and has a mechanical capacitor for trimming the frequency by up to 10 Hz, and an electronic frequency adjustment by 1 Hz using a varactor. I am sure the varactor does not improve jitter, but considering that the full range of adjustment is 0.1 ppm, it also should not add that much jitter, assuming everything is well designed.
So we are talking about a reasonably high stability crystal to begin with, and a very narrow adjustment range. In an atomic clock, the feedback loop uses the electronic frequency adjustment to more or less completely remove the aging. This requires a very tiny and a rather slow acting feedback.
In the atomic clock, the output of the crystal is used as a reference for a microwave sweep generator, which then scans the spectrum of atomic transitions. The absorption peak in a cesium clock is something like a kiloherz wide, but with a good signal to noise ratio and with a lot of averaging, one can measure the position of the peak to a very tiny fraction of its width. Comparing the measured and the expected positions reveals the deviation of the reference frequency from its design value, and that is what generates the tuning feedback for the crystal. I do not know off the top of my head how slow the feedback is exactly -- it is something that one could look up in the Hewlett-Packard service manual, but I am sure it is slow enough to be irrelevant for the cycle-per-cycle jitter.
GPSDO is about as good as it gets for hobby folks.
>But would it be possible to build an atomic clock
Time and frequency metrology gets expensive as people start to model aging characteristics of electronic components, relativistic drift, and thermal noise.
An off-the-shelf chip-scale atomic clock module will cost an order of magnitude less. =3
It would be possible to build a hobby-class optical atomic clock using a quartz cell with iodine vapor and modulation transfer spectroscopy, which would be much more accurate than a rubidium clock, but it would be significantly more expensive. A iodine cell would be almost $800 and the rest of the components would add several thousand $ in costs.
Optical clocks are much more expensive than microwave clocks, because they need an optical frequency comb, which is a special kind of pulsed oscillator with a laser, to divide the optical frequency down to a frequency in the hundreds of MHz range, where you can use digital counters to measure time and frequency.
For a microwave clock, currently only 4 options are widespread, active or passive hydrogen masers, cesium clocks, rubidium clocks and clocks with mercury ions.
Clocks with trapped mercury ions, which can steer the frequency of an oscillator that provides a 40 GHz signal (typically after a frequency multiplication) are the most compact and reliable, but few hobbyists would succeed to build one. There are research articles that describe prototypes of such mercury clocks intended for use in satellites, which show how one could be made.
There is no option to make something cheaper than a commercial miniature rubidium frequency standard, unless you do some successful research and discover a completely new method.
Nonetheless, high-quality OCXO (oven-controlled quartz oscillators) are cheaper than rubidium clocks, and if used correctly they can be more accurate than miniature rubidium or cesium clocks.
For short time intervals, the rubidium clocks and the cesium clocks are no better than the quartz oscillators included in them, which are likely to be worse than a high-quality separate OCXO.
For times longer than a day the miniature rubidium and cesium clocks will have a lower drift, but you can achieve better than them if you compare periodically your OCXO clocks with good NTP servers and you create a model of your OCXO, measuring its aging rate and possibly also the influence of the ambient temperature.
After you accumulate enough statistics to characterize well your OCXO, even without Internet access you could maintain with it a more accurate clock and frequency standard than with a miniature rubidium or cesium clock.
This means that you would use a program to transform the accumulated ticks from the OCXO into time, taking into account the variation of its frequency with time and ambient temperature, modeled with low-order polynomials. Even using just linear dependencies would remove most of the OCXO error. Similarly, if you use it as a frequency standard, you would use a program to compute the current frequency, based on the current time and the current ambient temperature.
Most chip-scale Rubidium oscillators sport relatively poor phase noise at the low end (because they typically have a crystal oscillator internally) despite ultra-high frequency stability.
OCXOs are the "in between TCXO for both price and phase noise" - really good, specifically-cut OCXOs beat Rubidium in phase noise.
I mean you think to yourself "one second of error per million years must be quite enough overkill" and then these beautiful people come to show you wrong.
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[ 0.24 ms ] story [ 14.6 ms ] threadNonetheless, the amount used in the clock is extremely small, so it does not influence much the cost, which is determined by a much more expensive set of lasers and optical components.
Lutetium 176 is very rare because chemical elements with an odd number of protons normally do not have isotopes with an even atomic mass, because those are unstable vs. beta decay.
Lutetium 176 is also radioactive, but its half-life time happens to be long enough so that a small amount of it has survived since the formation of the Solar System, like it also happened with the radioactive potassium 40 that is contained in the bodies of all living beings, which is another one of the 5 radioactive isotopes with even atomic mass of chemical elements with an odd atomic number.
I’ve often wondered if a hobby-class atomic clock can be built with “a less accurate gas” that is easy to excite and measure in a feedback loop simply because it’s available in a handy package that lends itself for experimentation without having to mess with melting glass and bottles of pressurised gas. E.g. neon, nitrogen or mercury vapour.
An exception is an active hydrogen maser, which directly outputs the frequency of atomic transition. It has very good phase noise, but is a rare beast, which is only used where it is absolutely necessary.
So while making an oscillator steerable inevitably increases its phase noise slightly, the increase is either ignorable in practice or cancelled by the control loop itself.
So we are talking about a reasonably high stability crystal to begin with, and a very narrow adjustment range. In an atomic clock, the feedback loop uses the electronic frequency adjustment to more or less completely remove the aging. This requires a very tiny and a rather slow acting feedback.
In the atomic clock, the output of the crystal is used as a reference for a microwave sweep generator, which then scans the spectrum of atomic transitions. The absorption peak in a cesium clock is something like a kiloherz wide, but with a good signal to noise ratio and with a lot of averaging, one can measure the position of the peak to a very tiny fraction of its width. Comparing the measured and the expected positions reveals the deviation of the reference frequency from its design value, and that is what generates the tuning feedback for the crystal. I do not know off the top of my head how slow the feedback is exactly -- it is something that one could look up in the Hewlett-Packard service manual, but I am sure it is slow enough to be irrelevant for the cycle-per-cycle jitter.
GPSDO is about as good as it gets for hobby folks.
>But would it be possible to build an atomic clock
Time and frequency metrology gets expensive as people start to model aging characteristics of electronic components, relativistic drift, and thermal noise.
An off-the-shelf chip-scale atomic clock module will cost an order of magnitude less. =3
Optical clocks are much more expensive than microwave clocks, because they need an optical frequency comb, which is a special kind of pulsed oscillator with a laser, to divide the optical frequency down to a frequency in the hundreds of MHz range, where you can use digital counters to measure time and frequency.
For a microwave clock, currently only 4 options are widespread, active or passive hydrogen masers, cesium clocks, rubidium clocks and clocks with mercury ions.
Clocks with trapped mercury ions, which can steer the frequency of an oscillator that provides a 40 GHz signal (typically after a frequency multiplication) are the most compact and reliable, but few hobbyists would succeed to build one. There are research articles that describe prototypes of such mercury clocks intended for use in satellites, which show how one could be made.
There is no option to make something cheaper than a commercial miniature rubidium frequency standard, unless you do some successful research and discover a completely new method.
Nonetheless, high-quality OCXO (oven-controlled quartz oscillators) are cheaper than rubidium clocks, and if used correctly they can be more accurate than miniature rubidium or cesium clocks.
For short time intervals, the rubidium clocks and the cesium clocks are no better than the quartz oscillators included in them, which are likely to be worse than a high-quality separate OCXO.
For times longer than a day the miniature rubidium and cesium clocks will have a lower drift, but you can achieve better than them if you compare periodically your OCXO clocks with good NTP servers and you create a model of your OCXO, measuring its aging rate and possibly also the influence of the ambient temperature.
After you accumulate enough statistics to characterize well your OCXO, even without Internet access you could maintain with it a more accurate clock and frequency standard than with a miniature rubidium or cesium clock.
This means that you would use a program to transform the accumulated ticks from the OCXO into time, taking into account the variation of its frequency with time and ambient temperature, modeled with low-order polynomials. Even using just linear dependencies would remove most of the OCXO error. Similarly, if you use it as a frequency standard, you would use a program to compute the current frequency, based on the current time and the current ambient temperature.
OCXOs are the "in between TCXO for both price and phase noise" - really good, specifically-cut OCXOs beat Rubidium in phase noise.