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Physical Review A

Proposed differential-frequency-readout system by hysteretic Josephson junctions

L. Z. Wang, R. V. Duncan

Published Oct 1, 1992• 0 citations
Publisher

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.

DOI
10.1103/physreva.46.3617

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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.
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.
Measurements have been made of the low-frequency spectral density of the voltage noise in current-biased resistively shunted Josephson tunnel junctions under conditions in which the noise mixed-down from frequencies near the Josephson frequency (${\ensuremath{\nu}}_{J}$) to the measurement frequency ($\ensuremath{\ll}{\ensuremath{\nu}}_{J}$) is in the regime $h{\ensuremath{\nu}}_{J}>{k}_{B}T$. In this limit, quantum corrections to the mixed-down noise are important. The spectral densities measured on junctions with current-voltage characteristics close to the Stewart-McCumber model were in excellent agreement with the predicted values, with no fitted parameters. The mixed-down noise for a wide range of bias voltages was used to infer the spectral density of the current noise in the shunt resistor at frequency $\ensuremath{\nu}$. With no fitted parameters, this spectral density at frequencies up to 500 GHz was in excellent agreement with the prediction $(\frac{2h\ensuremath{\nu}}{R})coth(\frac{h\ensuremath{\nu}}{2{k}_{B}T})$. The presence of the zero-point term, $\frac{2h\ensuremath{\nu}}{R}$, at frequencies $h\ensuremath{\nu}>{k}_{B}T$ was clearly demonstrated. The current-voltage characteristics of a junction with ${\ensuremath{\beta}}_{L}\ensuremath{\equiv}\frac{2\ensuremath{\pi}{L}_{s}{I}_{0}}{{\ensuremath{\Phi}}_{0}}\ensuremath{\sim}1$ and ${\ensuremath{\beta}}_{C}\ensuremath{\equiv}\frac{2\ensuremath{\pi}{I}_{0}{R}^{2}C}{{\ensuremath{\Phi}}_{0}}\ensuremath{\ll}1$, where I0{I}_{0}I0​ is the critical current, CCC is the junction capacitance, and Ls{L}_{s}Ls​ is the shunt inductance, showed structure at voltages where the Josephson frequency was near a subharmonic of the LsC{L}_{s}CLs​C resonant frequency. The additional nonlinearity of the $I\ensuremath{-}V$ characteristic caused mixing down of noise near higher harmonics of the Josephson frequency, thereby greatly enhancing the voltage noise. The measured noise was in good agreement with that predicted by computer simulations.
Experiments are reported in which two millimeter-wave signals incident on point-contact Josephson junctions produced changes in the junction dc voltage versus current characteristic and an intermediate frequency output whose amplitude depended sensitively on both junction bias and applied power. Equations are derived, based on Josephson's phenomenological equations, for the Josephson current in a junction exposed to two applied rf signals. When the applied signals differ appreciably in frequency, additional constant-voltage steps in the $V\ensuremath{-}I$ curve are predicted which are spaced at the difference frequency. These steps have been observed in experiments employing sources at 64 and 72 Gc/sec. Results of mixing experiments utilizing two sources nearly equal in frequency are reported at 23 and at 72 Gc/sec. In this case the two waves beat together and are equivalent in their effect to a single signal amplitude modulated at the difference frequency. Also explained on the same basis are experiments in which the third harmonic of a signal at 24 Gc/sec mixed with a signal at 72 Gc/sec. These results demonstrate the existence of the Josephson mixing mechanism as opposed to classical nonlinear mixing, and they show that it is operative at microwave and millimeter-wave frequencies over a wide range of power.
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)
Josephson oscillations in a large series array of Josephson junctions designed as a superconducting microwave transmission line are studied. For descriptions of the Josephson junctions both the Stewart–McCumber model and the Werthamer model are used. The attenuation of the Josephson oscillations in the considered array is composed of two terms rising from the stripline and from the Josephson junctions. The latter one is of increasing significance for lower than usually applied drive frequencies.