Most stable, lowest noise voltage references?

[Twigg]

TL;DR Summary

What level of performance is state-of-the-art for very high stability, low noise voltage sources? Is something like a DC voltage with an SNR of $10^{17}$ at the 10s through 0.1s timescale possible? If not, what are the current technological limits?

Summary says it all, I think. If you just want to link me to a bunch of papers, that's fine by me.

All I was able to find out on my own is that mouser and digikey have a lot of off-the-shelf voltage references they want to sell me that get about order of $10^4$ SNR at those timescales. SNR might not be the right term for this, but I'm using it as an umbrella term to describe both inaccuracy and fluctuations. I didn't really find much beyond the wall of ads. What are some good search terms for this kind of stuff?

 

[berkeman]

Presumably you mean temperature-controlled voltage references? My initial searching finds around 1ppm to be available with standard products. I don't know about better performance from dedicated instruments though...

https://www.analog.com/en/technical-articles/how-to-choose-a-voltage-reference.html

https://www.electronicdesign.com/te...vides-voltage-reference-less-than-1ppmc-drift (looks like free login is required)

 

[Tom.G]

Even Josephson junctions are limited by the stability of the RF excitation frequency, which is around 1 part in 10¹². I suppose if you integrate long enough you could better that somewhat.

The above info from a quick skim of the Wikipedia article:
https://en.wikipedia.org/wiki/Josephson_voltage_standard

What I'm wondering is how you will know if you have met your requirements!

Cheers,
Tom

p.s. Since we are talking about superconducting here, I hope you have backing from someone with a substantial bank account.

 

[Baluncore]

Summary:: What level of performance is state-of-the-art for very high stability, low noise voltage sources? Is something like a DC voltage with an SNR of $10^{17}$ at the 10s through 0.1s timescale possible? If not, what are the current technological limits?

Liquid He? or at what temperature will you be operating ?

 

[Twigg]

Thanks all for the replies! Sorry my response is going to be short, long day.

@berkeman That article and adding "temperature-controlled" to the search terms helped a lot. Thanks!

@Tom.G I had no idea you could do that with josephson junctions. $10^{12}$ is a huge improvement over classical devices.

@Baluncore Sorry I didn't make this clearer earlier, but this is a pie in the sky question. Liquid helium, dilution fridges, all fair game.

For a little more context, I'm interested in stable voltages because I'm trying to estimate what's the most stable length scale you can produce with a piezoelectric crystal. For example, could you use a stable voltage with feedback (I realize the feedback is a whole other can of worms) to compensate out the bulk thermal displacements of a piezoelectric crystal, or would the applied voltage be too noisy? I figured step one would be having a crazy stable voltage source. This is interesting for design of high finesse optical cavities (think two mirrors, separated by a piezoelectric crystal).

Also, after double-checking my math, I realized I made a mistake. I don't actually need $10^{17}$ SNR, just $10^8$. So it seems Josephson junctions can already provide that level of stability. Thanks again, @Tom.G !

What I'm wondering is how you will know if you have met your requirements!

To do that, I'd check the stability of the optical cavity (voltage stability -> length stability of the piezo crystal -> apparent cavity linewidth) rather than the voltage directly. Either that or a lot of sad hours collecting voltage measurements with a noisy instrument to average down.

 

[Tom.G]

At the risk of sending you down another rabbit hole, take a look at these:
https://en.wikipedia.org/wiki/Adaptive_optics
https://en.wikipedia.org/wiki/Active_optics

(above found with:
https://www.google.com/search?&q=adaptive+optics+is+designed+to+compensate+for

You could also shorten that search string to get more information than you could possibly use.)

Have Fun! And let us know how you progress in your endeavor.

Cheers,
Tom

 

[DaveE]

If you want to know what the state of the art is in length stabilization, look into LIGO. No one's done it better than those guys.

 

[DaveE]

Also, I suspect you would get better performance if you could lock the cavity to a frequency standard or and atomic transition. It's much easier to get extremely accurate frequency measurements for your feedback system than voltages and such.

 

[Twigg]

@Tom.G huh I forgot about adapative/active optics. I'll have to take a look.

@DaveE You're a psychic! LIGO's active cooling of their mirrors' translational degrees of freedom got me thinking about this. I think you are right, that a piezo-controlled cavity won't get better performance than the current frequency standards. I'm just curious how far it falls short.

I'll chime in again if I get anything conclusive.

 

[KalleMP]

This YouTube video describes the design and construction of a DIY ovenised voltage reference.

 

[f95toli]

"Stable" is not really a well defined term unless you also state how long you are willing/able to measure so you would need to look at an Allan plot to determine if a method would work for you.
Josephson Voltage standards can indeed exceed 1 part in 10^8 and the main reason for that is that they are directly referencing the realisation of the second. You can probably improve on that by a quite a bit, but it also depends on the voltage you want to generate etc (standard arrays will usually give you 10V). These systems are commercially available but unless you work in a calibration lab it does not make sense to buy one (btw, these days they use cry-coolers; no liquid helium needed).

Voltage arrays at NMI's are typically just connected to the lab 10 MHz reference which turn comes from the same masers that generate the time signal.

However, it is pretty much always better to try to directly reference a time signal in your experiment if you can; even an off-the-shelf Rb reference will give you a short term stability better than 10^11, and if you buy one that is GPS disciplined the long term stability is also very good (assuming you can get the GPS signal into the lab...don't ask me how I know that this is not always easy)

 

[Twigg]

Thanks for that, @f95toli! My gut feeling is that using a Josephson voltage standard that depends on a time standard to develop a stable cavity for an atomic clock is like the experimental equivalent of circular reasoning and could only give worse performance than the original time standard. However, the math doesn't seem to add up, so let me run the numbers by you all.

Suppose I had a crystalline, piezoelectric cavity spacer that is 10cm long, and has a piezoelectric coefficient ($d_{33} = \frac{\mathrm{strain}}{E} = \frac{\Delta L}{V}$) of about 100 picocoulombs per Newton. Assuming I have a 10V source with $10^{8}$ stability at the timescale of interest (100ms - 10s) generated by a josephson array with a Rb reference ($10^{11}$ stability), that give voltage noise on the order of $100 \mathrm{nV}$. Since $\Delta L = d_{33} V$, that gives instability of the cavity length on the order of $10^{-15} \mathrm{cm}$. Dividing the 10cm cavity length by the instability, that's a fractional cavity stability of $10^{16}$. That cavity could be used to stabilize a laser's frequency, making a time standard with fractional stability of $10^{16}$. However, we said the rubidium reference was only stable at the $10^{11}$ level. There's obviously no free lunch, so what's really going on? Did I get my math horribly wrong somehow?

 

[Tom.G]

Did I get my math horribly wrong somehow?

Maybe.

piezoelectric coefficient () of about 100 picocoulombs per Newton.

Or maybe I did. I always thought that a Newton was a measure of force, not displacement.

 

[Twigg]

I always thought that a Newton was a measure of force, not displacement.

It made sense to me on the basis that $d_{33}$ was strain per unit electric field. Strain is unitless so $d_{33}$ has units of inverse electric field, and since electric field is Newtons per coulomb, $d_{33}$ would be coulombs per Newton?

 

[f95toli]

Suppose I had a crystalline, piezoelectric cavity spacer that is 10cm long, and has a piezoelectric coefficient ($d_{33} = \frac{\mathrm{strain}}{E} = \frac{\Delta L}{V}$) of about 100 picocoulombs per Newton. Assuming I have a 10V source with $10^{8}$ stability at the timescale of interest (100ms - 10s) generated by a josephson array with a Rb reference ($10^{11}$ stability), that give voltage noise on the order of $100 \mathrm{nV}$. Since $\Delta L = d_{33} V$, that gives instability of the cavity length on the order of $10^{-15} \mathrm{cm}$. Dividing the 10cm cavity length by the instability, that's a fractional cavity stability of $10^{16}$. That cavity could be used to stabilize a laser's frequency, making a time standard with fractional stability of $10^{16}$. However, we said the rubidium reference was only stable at the $10^{11}$ level. There's obviously no free lunch, so what's really going on? Did I get my math horribly wrong somehow?

I am certainly no expert on this. but I do know that lasers are sometimes stabilised using a signal from a frequency comb which in turn is generated by an atomic clock. As far as I know this is the most precise way to do this. However, you need to remember that laser stabilisation is a whole scientific field of its own and there are whole research groups specialise in building reference cavities. That is, there are going to be lots of tricks involved.
Also, Rb references are cheap and convenient but are not used in "proper" metrology (the kind done at NMIs) which seems to be what you are talking about. For that you would use a hydrogen maser either on its own (which is fine for short time stability) or used to "freewheel" as Cs fountain (or even an optical clock). Of course you are then talking about very specialised equipment.
A fractional stability of 1 part in 10^16 is one order of magnitude better then the "official" accuracy of a Cs clock; it is possible to do much better than this using optical clocks but there are certainly no "off the shelf" solutions.

 

[Twigg]

there are whole research groups specialise in building reference cavities.

That's me, or at least so they tell me For the purpose of this thread, I'm just curious what the limitations are on stability of piezo-driven cavities as a reference cavity for an optical atomic clock. Hope that clears up some of what my goals are.

I noticed one thing in my math. If instead of dividing the $10^{-15}\mathrm{cm}$ by the 10cm total length of the piezo crystal, I instead divide it by a typical $1\mathrm{\mu m}$ wavelength (typical for optical cavities which require the use of an electro-optic modulator to complete a Pound-Drever-Hall loop), I get back $10^{11}$ for the cavity stability. Intuitively, this feels right because $\frac {\delta L}{L}$ doesn't seem like it should represent a phase whereas $\frac{\delta L}{\lambda}$ feels like it should represent an optical phase. That seems to close that free lunch problem, but it seems awfully coincidental.