Proposed differential-frequency-readout system by hysteretic Josephson junctions.

Abstract

The Josephson relation V=nh\ensuremath{\nu}/2e has been verified experimentally to 3 parts in ${10}^{19}$ [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.