# Superconducting Resonator matches 3 Degree Kelvin Spectrum

1. Jan 27, 2016

### wavepax

Carver Mead writes in his book, "Collective Electrodynamics", that experimental evidence indicates a superconducting ring and capacitor resonator circuit will increase from zero voltage (scalar potential difference) to an energy matching a 3 degree Kelvin black body radiation spectrum. Unfortunately, he doesn't cite a reference, Also, the same circuit resonating at an energy more than that of a 3 Kelvin black body radiator will decrease in energy until it reaches that of a 3 degree Kelvin black body. Carver doesn't indicate whether this is independent of the superconductor temperature, although he seems to implicitly assume this (as long the temperature is in the superconducting range, i.e., less than Tc)

I want to read the papers describing this experimental evidence. I was unable, after an hour on scholar.google.com, to find anything about this. Can any of you provide good references (preferably a link to a pdf) to these experiments (or provide the search terms that lead directly to good references)?

Carver then proceeds to indicate the resonator is gaining energy by coupling to the rest of the universe that has zero proper time separation from the resonator (which could be a very far 3-space distance away if the time difference was large enough).

This evidence would be on par with other "spooky action at a distance" experimental evidence in quantum mechanics.

2. Jan 27, 2016

### f95toli

I don't understand the description of the experiment.
They way it is described here would seem to suggest that there is some sort of "equilibrium" temperature for superconducting resonators which is obviously not true; we can do experiments at whatever temperatures we want as long as we are below Tc and there is no tendency for anything to drift as long as the batch temperature stays the same. The energy scale is simply set by the resonance frequency compared to kBT (i.e. if kB*T is larger than h*f0 there the resonator can be thermally excited)

Also, why 3K of all temperatures? That corresponds to an energy of about 60 GHz which would be very high for a superconducting resonator; most operate below 20 GHz.

3. Jan 27, 2016

### wavepax

Let me quote directly from the source (p. 80, "Collective Electrodynamics", Carver Mead, 2000 MIT ed.)

In our investigation of radiative coupling, we use a superconduct-
ing resonator as a model system. The resonator is a coherent quan-
tum system, interacting within itself in a purely electromagnetic
manner. In this sense, it can be viewed as a “giant atom.” As a
model system, however, it is much simpler than either an atom or
a free particle. Its lowest mode of oscillation has a single degree of
freedom, the configuration of which is known to astounding pre-
cision. Its orientation in space is known and controlled. Its phase
can be measured to extreme accuracy. We can build such a res-
onator from a superconducting loop and a capacitor, as described
in Section 3.2.3 (p. 53). If we suspend the resonator in free space,
far from any other matter, we obtain the following experimental
results:
1. If the resonator is initialized to zero amplitude, its average
amplitude of oscillation increases with time until it fluctuates
around a mean amplitude V0
2. If the resonator is initially oscillating at an amplitude that is
large compared with V0 , the amplitude decreases with time
until it fluctuates around V0 .
3. For large amplitudes, the rate of decrease of amplitude is pro-
portional to the amplitude, leading to an exponential damp-
ing of the oscillation.
4. The final approach to V0 from either direction is, on aver-
age, exponential, with the same time constant as the large-
amplitude decay.
5. The value of V0 is dependant on the frequency ω of the res-
onator; the dependence on frequency is that of a black body
at ≈ 3 kelvin

_________________________________________________

The above is what I'm trying to better understand, and I figure the best way to understand this evidence is to go to the literature that describes these experiments in detail. My question again is, what is a good reference for the above experiments? I find this experimental evidence (if true) to be VERY interesting.

4. Jan 28, 2016

### f95toli

I still don't understand what is suppose to be going on. I have never heard of such an experiment (and I have worked with superconducting resonators for about 10 years), have never observed such effects and I can't see which physical effects he might be getting at. And I still don't understand what the experimental setup is supposed to look like, or even what type of resonator he is referring to.

Mead has -according to Google scholar- never published anything about this and when he was active he was working on VLSI design, not anything related to this topic. Hence, I am inclined to believe that this is a case of sophisticated crackpottery,.

5. Jan 28, 2016

### Daz

I’m no expert so this is just a wild guess.

It seems to me that there may be a subtlety in the author’s use of language. He doesn’t describe the resonator as being “closed” or “isolated” but rather “suspended in free space far from other matter”. In other words, it has nothing to interact with that could excite or dampen its field — except the cosmic microwave background.

Could it be that the author is suggesting that the resonator will eventually attain thermal equilibrium with the CMB which, I believe, has a characteristic temperature of a few Kelvin?

6. Jan 28, 2016

### f95toli

But how can the resonator even see the CMB?
Even if it is decoupled It must be in a cryostat meaning it will be quit well insulated or otherwise it would heat up. The walls of the cryostat would presumably be held at a temperature lower than 3K (lets say 1.6K for a pumped He4 cryostat) for the experiment to make any sense at all, .so would be the equilibrium temperature of the system would be that of the walls.
You can use superconducting resonators to look at the CMB (google "kinetic inductance detector"), but that requires that you install some sort of window or waveguide in your cryostat.

7. Jan 28, 2016

Staff Emeritus
That's the part I don't get either. If it can see the CMB, it can surely see the much hotter laboratory that it's in.

8. Jan 28, 2016

### Daz

Not if it’s “suspended in free space far from other matter” - it wouldn’t be in a hot laboratory. Nor for that matter, would you need to worry about cryostats and windows, etc.

I don’t know whether the author is describing a thought-experiment, but he mentions experimental observations so I guess it could be something like this. The instruments which map and measure the CMB consist of resonators which are excited into oscillation by the CMB; and the Cobe satellite is pretty close to the author’s description of it being "suspended if free space."

This would also tally with the comments at the end of post #1 where it is mentioned that the resonator is interacting with the distant past of an excitation source arbitrarily far away. (The big bang?)

But like I said, this is all a wild guess.

9. Jan 28, 2016

### f95toli

And how would you keep it cold? If you put a resonator in an insulated space it won't see the CMB anymore than it would see the room temperature radiation from the lab with the cryostat. You can't cool anything down to low temperatures without shielding from EM radiation and that includes the CMB.

The author mentions "experimental observations" and if it only meant to be a thought experiment is certainly a convoluted one. Why would it even be relevant that it was a superconducting resonator?

Also, I am pretty no one has yet used a superconducting resonator as a detector in a satellite; I believe COBE used a standard bolometric detector.
But as I mentioned above that is irrelevant; no one disputes that fact that you COULD see CMB with a superconducting resonator (although the way that happens has to do with pair breaking changing the kinetic inductance, so you don't need a quantum mechanical description of the resonator); but so what?

10. Jan 28, 2016

### Daz

I think that excerpt is actually describing a thought-experiment. If so, I don’t like the author’s use of the phrase “... we obtain the following experimental result...”

I suspect that the only relevance of the superconducting resonator is to have a very high Q so that it can resolve the line-shape of a black-body curve at 3K.

11. Jan 29, 2016

### wavepax

Yes. Thanks for the clarification. Carver specified the exponential behavior toward steady state, furthering the impression that he was talking about something more than a thought experiment.. Perhaps he was relying on the linearity of the governing equations to make that prediction.

"Superconducting detectors and mixers for millimeter and submillimeter astrophysics", JONAS ZMUIDZINAS and PAUL L. RICHARDS, PROCEEDINGS OF THE IEEE, VOL. 92, NO. 10, OCTOBER 2004

is a nice summary of superconducting devices used in the measuring the CMB and other radiation extending into the mm and shorter wavelengths. Did not see superconducting ring-capacitor resonators. Yes, high Q definitely a pro of these resonators.

12. Jan 29, 2016

### wavepax

I scholar googled "kinetic inductance detector". Very interesting. Thanks.

13. Jan 29, 2016

### f95toli

This is getting a bit off topic.
However, the resonators Zmundias et al are talking about in the review article are mainly of the kinetic inductance type I mentioned above . These are tiny on-chip thin film resonators and definitely not of the type discussed by Carver (I still don't understand how what Carver describes could even work as a resonator) .
Note also that the Q value has nothing as such to do with the detection process, but the high Q value is nice because it makes it possible to frequency multiplex many resonators (i..e several pixels) and read them all out using a single microwave line (whenever a photon is absorbed the kinetic inductance changes, which in turn changes the resonance frequency of the resonator which is easy to detect).
However, the actual detection process (creation of extra quasi particles) is more or less the same as for e.g. SPD detectors that have been used for optical frequencies for a few years.

I work with exactly the same type of devices as Zmuidzinas, albeit we do not primarily use them as photon detectors (the review article mentioned above does refer to some of our papers).