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Superconductor Science and Technology

Measurement accuracy of macroscopic quantum circuits with RF-biased Josephson junction arrays

David H. Dunlap, R. V. Duncan

Published Sep 1, 1991• 0 citations
Publisher

Abstract

The DC voltage output from a hysteretic Josephson junction which is locked to an AC frequency source differs from the ideal Josephson relation if the junction drives a current about a closed superconducting circuit. The difference in voltage Delta V from two hysteretic Josephson junctions driven in series opposition is proportional to the difference in their driving frequencies Delta omega if the junctions are each biased to the nth voltage step. It is shown here, however, that Delta V is systematically smaller than the voltage difference Delta V 0 predicted by the ideal Josephson relation Delta V 0 =(nh(cross)/2e) Delta omega . If the loop inductance approaches zero, the smallest detectable voltage difference Delta V 0 between two junctions is limited by the intrinsic Josephson inductance. For arrays of more than one junction, however, Delta V 0 remains proportional to the loop inductance.

DOI
10.1088/0953-2048/4/9/008

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The DC voltage output from a hysteretic Josephson junction which is locked to an AC frequency source differs from the ideal Josephson relation if the junction drives a current about a closed superconducting circuit. The difference in voltage Delta V from two hysteretic Josephson junctions driven in series opposition is proportional to the difference in their driving frequencies Delta omega if the junctions are each biased to the nth voltage step. It is shown here, however, that Delta V is systematically smaller than the voltage difference Delta V 0 predicted by the ideal Josephson relation Delta V 0 =(nh(cross)/2e) Delta omega . If the loop inductance approaches zero, the smallest detectable voltage difference Delta V 0 between two junctions is limited by the intrinsic Josephson inductance. For arrays of more than one junction, however, Delta V 0 remains proportional to the loop inductance.
The Josephson relation V=nh\ensuremath{\nu}/2e has been verified experimentally to 3 parts in 1019{10}^{19}1019 [A. K. Jain, J. E. Lukens, and J.-S. Tsai, Phys. Rev. Lett. 58, 1165 (1987)]. Motivated by this result, we propose a differential-frequency-readout system by two sets of hysteretic Josephson junctions rf biased at millimeter wavelengths. Because of the Josephson relation, the proposed differential-frequency-readout system is not limited by photon fluctuation, which limits most photon-detection schemes. In the context of the Stewart-McCumber model [W. C. Stewart, Appl. Phys. Lett. 12, 277 (1968); D. E. McCumber, J. Appl. Phys. 39, 3113 (1968)] of Josephson junctions, we show theoretically that the differential frequency of the two milliwave biases can be read out by the proposed system to unprecedented accuracy. The stability of the readout scheme is also discussed. The measurement uncertainty of the readout system resulting from the intrinsic thermal noise in the hysteretic junctions is shown to be insignificant. The study of two single junctions can be extended to two sets of Josephson junctions connected in series (series array) in this measurement scheme provided that junctions are separated by at least 10 \ensuremath{\mu}m [D. W. Jillie, J. E. Lukens, and Y. H. Kao, Phys. Rev. Lett. 38, 915 (1977)]. The sensitivity for the differential frequency detection may be increased by biasing both series arrays to a higher constant-voltage step.
Pulse-driven Josephson junction arrays (PD JJAs) are used for the generation of arbitrary waveforms with quantum accuracy. The main requirement for quantum operation is that all the Josephson junctions have quantum locking ranges (QLRs) with respect to the power and frequency of the radio frequency (RF) bias and constant voltage over a range of dc bias currents. In this paper we investigate the QLR of PD JJAs for the generation of dc voltage. Our results demonstrate that in proximity to the QLR for RF power, the dc current-voltage characteristics can show apparent quantization of the voltage with statistical properties almost indistinguishable from those in the QLR.
The RF power at approximately 300 GHz coupled to a 52- Omega load by a one-dimensional DC series biased Josephson junction array has been measured using an on-chip Josephson detector. The array was fabricated using the planarized all-refractory technology for low-T/sub c/ superconductivity (PARTS). From the measured RF power and DC voltage levels, it is concluded that the 100 junctions in this array were locked in-phase. The effects of the finite inductance, associated with the junction's shunt resistor, on the array output power and detector's current-voltage characteristics are also discussed.>
The Josephson primary DC voltage standard is very successful quantum standard. Recently it has become possible to divide Josephson arrays up into binary segments, thereby creating the possibility of developing a digital to analogue converter with quantum accuracy. These new arrays are based upon non-hysteretic Josephson junctions, which allow the voltage to be changed almost instantaneously. In this paper we will investigate the properties of two different types of Josephson arrays, one type is an intrinsically shunted array of junctions or so-called SINIS array, while the second type is externally shunted via small on-chip resistors. The arrays are biased using a purpose built computer controlled bias source discussed in a separate paper in this conference. We will discuss the accuracy of the generated voltage and investigate the ac properties.
This final report of ONR Contract No. N00014-76-C-0609 describes some initial experimental work and then calculations on an analogue computer of properties of Josephson junctions used as a frequency agile source. The results of the calculations show that a junction may be used as a nearly ideal (zero impedance) dc voltage source with which to bias a second junction. The junctions must be isolated rf-wise from each other and the inductance level between them must not exceed about 10 to the minus 8 power H for operation at liquid helium temperatures. The second junction will then oscillate at a frequency determined by this bias voltage. Additionally the same junction bias source was shown to be capable of biasing a series array of junctions. The series array was shown to oscillate phase coherently at a frequency determined by the divided bias voltage across each junction. (Author)