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Physics Procedia

Double rf-SQUIDs Operating in a Non-Adiabatic Regime: A Dream Comes True?

Boris Chesca

Published Jan 1, 2012• 2 citations
Publisher

Abstract

At a time when the supremacy of SQUIDs as the most sensitive magnetometers is being challenged by the recent progress of optically pumped atomic magnetometers operating at room temperature, looking into new opportunities to further improve SQUIDs sensitivity would probably be most welcomed by the SQUID community. By far the most promising such opportunity is to operate a double (D) rf SQUID (an rf-SQUID in which a dc-SQUID is used instead of a single Josephson junction) in a non-adiabatic regime at frequencies of about a few GHz. At these relatively high frequencies required to assure an ultra-high SQUID sensitivity the SQUID-design complexity and the cost of the electronics involved (current generator and SQUID amplifier) are still kept at reasonable levels. The advantages of using this concept, as presented in my contribution in more detail now, are overwhelming. Ironically, although this idea in its preliminary shape has been around for some time now [1], the opportunity has never been explored experimentally! I am just wondering what else needs to be done to get this message across the SQUID community and have this concept finally tested experimentally?

DOI
10.1016/j.phpro.2012.06.248

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At a time when the supremacy of SQUIDs as the most sensitive magnetometers is being challenged by the recent progress of optically pumped atomic magnetometers operating at room temperature, looking into new opportunities to further improve SQUIDs sensitivity would probably be most welcomed by the SQUID community. By far the most promising such opportunity is to operate a double (D) rf SQUID (an rf-SQUID in which a dc-SQUID is used instead of a single Josephson junction) in a non-adiabatic regime at frequencies of about a few GHz. At these relatively high frequencies required to assure an ultra-high SQUID sensitivity the SQUID-design complexity and the cost of the electronics involved (current generator and SQUID amplifier) are still kept at reasonable levels. The advantages of using this concept, as presented in my contribution in more detail now, are overwhelming. Ironically, although this idea in its preliminary shape has been around for some time now [1], the opportunity has never been explored experimentally! I am just wondering what else needs to be done to get this message across the SQUID community and have this concept finally tested experimentally?
The operation and noise limitations of de and RF SQUID's are outlined, and recent advances in their sensitivity are discussed. A model of the dc SQUID predicts an energy noise level per hertz referred to the SQUID of approximately8 k_{B}TL/R \approx 8 k_{B}T(\piLC)^{1/2}, whereL, R,andCare the SQUID inductance and the shunt resistance and capacitance of each Josephson junction. Some examples of dc SQUID's are described to show that their performance is generally in reasonable agreement with the model. The noise energy has improved from about 2 × 10-30J. Hz-1for a device withL = 1nH and a tunnel junction area of 104µm2to about 2 × 10-33J . Hz-1for a device withL = 0.1nH and a microbridge resistance of 40 Ω. Further improvements axe expected in the near future. The model of the RF SQUID predicts a noise energy per hertz referred to the SQUID of[(\pi\alpha^{2}\phi\min{0}\max{2}/2L) + 2 \pi \alpha k_{B}T\min{a}\max{(eff)}]/\omega_{RF}, where α is the intrinsic width of the distribution of flux transitions,T\min{a}\max{(eff)}is an effective amplifier noise temperature, and ωRFis the pump frequency. With one exception, the performance of the seven types of RF SQUID listed is in reasonable agreement with the model. The noise energy ranges from about 1.5 × 10-29J . Hz-1for a 20-MHz toroidal SQUID to 3.5 × 10-31J . Hz-1for 9-GHz reentrant toroidal SQUID; a somewhat better sensitivity has been reported for a 430-MHz device, apparently in conflict with the theory. In both dc and RF SQUID's, 1/fnoise (fis frequency) is likely to extend to higher frequencies as the white-noise level is decreased.
The dc SQUID had been presented for use in the rf SQUID instead of a weak link. The new device, referred to as “double SQUID”, possesses a large output signal (hundreds of microvolts) in operating in a hysteretic mode. For making an operating mode a double SQUID is coupled to a circuit traditional for rf SQUIDs containing a tank circuit and an rf current pumping generator. The magnetic flux being measured is recognized by the dc SQUID quantization loop which results in changing its critical current. As a result the height of the flat part of the tank circuit I–V characteristics coupled to a double SQUID is modulated. It is this modulation that is the SQUID output signal. The experimental investigations of the double SQUID showed the validity of the assumptions under consideration. Output signals up to 690 μV, noise spectral density ≈2×10−5ϕ0/ Hz 1/2 (ϕ0 is the flux quantum) and energy resolution ≈1.4×10−29 J/Hz have been obtained.
SQUIDs are an attractive candidate for the amplification of low-level rf and microwave signals. Compared to semiconductor amplifiers, they offer lower noise and much lower power dissipation. Especially at frequencies below 1 GHz, the improvement in noise temperature compared to the best cold semiconductor amplifiers can be as high as 50; noise temperatures only slightly above the quantum limit have been achieved in this frequency range. This article will review the current status of radio-frequency amplifiers based on dc SQUIDs and provide detailed discussions of amplifier noise temperature, input and output impedance, and nonlinearities.
Conventional rf SQUIDs (superconducting quantum interference devices) consist of a superconducting loop interrupted by one weak link, and when read out via a tank circuit they produce output signals in the order of a few tens of microvolts. When the single weak link is replaced by a dc SQUID (a superconducting loop with two junctions) a so-called double quantization loop SQUID is formed. In this paper it is shown theoretically, and supported experimentally with thin-film devices of three different designs, that the general behaviour can be explained by a simplified picture of the fixed critical current of the single junction of the rf SQUID being replaced by an effective critical current of a dc SQUID loop that is varied by the applied magnetic flux (i.e., we have a rf SQUID with a variable β parameter). A more detailed analysis of the experimental data and the theory of this novel device reveals its interesting nonlinear character and shows the deviations from this simple picture. It is demonstrated experimentally that output signals in the order of ≥1 mV can be obtained with a suitable read-out mode for the tank circuit, a clear advantage when compared to conventional rf SQUIDs. With respect to dc SQUIDs, the coupling to integrated planar input coils will be unproblematic since no microwave resonances should occur in the structures.
Abstract An analysis of the measurement of the magnetic flux in superconducting qubits based on RF SQUIDs was carried out with an 800 MHz bandwidth low-power-consumption cryogenic high-electron-mobility transistor amplifier. The preliminary experimental results obtained at temperatures 2 K and 4 K for RF SQUIDs in hysteretic, and in two non-hysteretic, regimes with a pump frequency of about 30 MHz are discussed. Parameters of RF SQUIDs in the hysteretic and non-hysteretic modes are analyzed within the framework of the resistively and capacitively shunted junction model for Josephson junctions. Its sensitivity at a temperature of 30 mK and frequency band (speed) are calculated and optimized to read the states of a flux qubit used as a single microwave photon counter. It is shown that an RF SQUID, operated in an adiabatic non-hysteretic mode for qubit readout, allows us to minimize its back-action effect and the dark count rate. This is due to the absence of Josephson generation, the small amplitude of the resonator electromagnetic field, and the selection of the pump frequency that does not coincide with the characteristic frequencies of the flux qubit.
Two new SQUID variants have been made and tested using nanobridges as Josephson contacts. The first is a dc SQUID whose hysteretic weak links are inductively shunted such that it operates as a relaxation oscillator with a frequency depending on the applied magnetic flux. When standard ICs are used for FM detection, the readout electronics are cheap and compact, of the size of a matchbox. The second variant is a microwave-biased rf SQUID incorporated into a λ/2 stripline resonator, which is capacitively coupled to a coaxial cable leading to the room-temperature electronics. Peak-to-peak modulation voltages of several hundred μV were obtained in the investigated frequency range of 3 to 4.2 GHz. For both SQUID variants, white flux noise values of some 10−5Φ0/Hz1/2 have been found.