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.
The reason I’m asking is because in RF we often need a stable reference, and these come in a clear $ for phase noise relationship: RC, LC, xtal, TCXO, GPSDO, YIG, Rubidium, …
Price-wise, all atomic clocks come after Rubidium. But would it be possible to build an atomic clock that sits between TCXO and Rb both for price and phase noise, by employing a non-exotic gas in a readily available lamp?
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.
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.
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.
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.
The Rb lamp is as simple as anything can possibly be, at least if you're not tasked with coming up with the right gas recipe.
Lasers, on the other hand, have to be frequency-stabilized for use in high-quality Rb clocks. Every time someone has tried to use an unstabilized laser to replace an Rb lamp, the results have been worse in one way or another.
Usually stabilization involves a separate loop with an Rb gas cell. A bit of an oversimplification if you count miniaturized Rb standards based on VCSELs, but those are at the very bottom end of the performance spectrum to begin with. As adrian_b suggests, the best crystal oscillators are superior in many respects to the worst rubidium standards.
So a good laser-based standard will never be more economical than a lamp-based standard unless someone finds a way to run the laser open-loop. AFAIK that hasn't happened yet, at least not with something I can order off the shelf from Edmund or Thor Labs.
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.
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 (the others are vanadium 50, tantalum 180 and lanthanum 138).
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 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. I'm not sure who will ever see the difference but really what a job well done!
Somewhat off-topic:
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.
The reason I’m asking is because in RF we often need a stable reference, and these come in a clear $ for phase noise relationship: RC, LC, xtal, TCXO, GPSDO, YIG, Rubidium, …
Price-wise, all atomic clocks come after Rubidium. But would it be possible to build an atomic clock that sits between TCXO and Rb both for price and phase noise, by employing a non-exotic gas in a readily available lamp?
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.
How do you discipline a crystal without introducing significant phase noise?
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.
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.
Your own answer is right. For atomic clocks, the integration times of the feedback loop are typically much longer than a second.
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.
There are ways using modulated lasers to read out small rubidium cells vs the complexities of the lamp approach.
The Rb lamp is as simple as anything can possibly be, at least if you're not tasked with coming up with the right gas recipe.
Lasers, on the other hand, have to be frequency-stabilized for use in high-quality Rb clocks. Every time someone has tried to use an unstabilized laser to replace an Rb lamp, the results have been worse in one way or another.
Usually stabilization involves a separate loop with an Rb gas cell. A bit of an oversimplification if you count miniaturized Rb standards based on VCSELs, but those are at the very bottom end of the performance spectrum to begin with. As adrian_b suggests, the best crystal oscillators are superior in many respects to the worst rubidium standards.
So a good laser-based standard will never be more economical than a lamp-based standard unless someone finds a way to run the laser open-loop. AFAIK that hasn't happened yet, at least not with something I can order off the shelf from Edmund or Thor Labs.
True, but it is unlikely that you could build one that is cheaper than a commercial miniature rubidium clock.
Already a rubidium vapor cell costs about two thirds of the cost of a commercial Rb clock.
Thank you for taking the time to elaborate.
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.
A clock, not only to measure time, but gravity as well. It’s impressive that it can measure time dilation due to a height difference of 5mm
Article in Nature https://www.nature.com/articles/s41586-026-11072-8
The most impressive part for me is:
Optical atomic clocks at the 10^-19 level are so precise they can detect the slowing of time caused by gravity over height differences of millimeters.
Lutetium-176, element 71, better than 1 part in 10^18.
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 (the others are vanadium 50, tantalum 180 and lanthanum 138).
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%).
My back of a envelope maths suggests it's accurate to about 1 second every 300 billion years.
43.5 ms over the age of the universe (13.8 billion years).
As long as we don’t go building a glass clock…
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. I'm not sure who will ever see the difference but really what a job well done!
Time-servers require hash sigs.
... And still come home late for supper
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