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Journal of Applied Physics

Josephson junction mixing

E. D. Thompson

Published Jul 1, 1973• 5 citations
Publisher

Abstract

It is shown that a Josephson junction, biased at a voltage V0 and driven simultaneously by two monochromatic sources at the frequencies ω1 and ω2, produces an output power at the frequency ω3 = ω1 — nω2 and that this frequency is independent of the Josephson frequency ω0 = 2eV0/ℏ. The power output depends upon the dc bias, showing fine structure with a voltage periodicity of ℏω2/2e.

DOI
10.1063/1.1662752

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•Sep 1, 1977•0 citations
It is shown that a Josephson junction, biased at a voltage V0 and driven simultaneously by two monochromatic sources at the frequencies ω1 and ω2, produces an output power at the frequency ω3 = ω1 — nω2 and that this frequency is independent of the Josephson frequency ω0 = 2eV0/ℏ. The power output depends upon the dc bias, showing fine structure with a voltage periodicity of ℏω2/2e.
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.
We have studied Josephson junctions with intrinsic energy ħIc/2e (Ic being the critical current) comparable to thermal energy kT and examined their potential for electromagnetic signal conversion. In this case, moderate thermal fluctuations are sufficient to destroy Josephson oscillations but do not entirely suppress the Josephson dynamics. We have numerically calculated the DC I–V curves, their derivatives dnV/dIn, and the DC and harmonic voltage responses Vn of such Josephson junctions to the AC currents Iωsinωt. We have found that Josephson junction with γ = 2ekT/ħIc ≥ 0.5 is a nonlinear resistance at frequencies ω below characteristic Josephson frequency ωc = 2eIcRn/ħ and all current biases I0. Frequency conversion in such junctions occurs due to the classical mechanism on the nonlinearity of the DC I–V characteristics at low signal frequencies. With increasing the signal frequencies to the characteristic Josephson frequency ωc = 2eIcRn/ħ and higher, the Josephson mechanism by frequency modulation of the Josephson current gradually replaces the classical one. The classical conversion mechanism demonstrates higher conversion efficiencies than the Josephson mechanism, although it operates within a narrower bandwidth. At zero DC bias i0 and in the range of γ-values from 0.1 to 2, we have found odd harmonics Vn emerging from low signal currents. Zero-bias values of the third harmonic V3 maximize at 0.18IcRn for JJs with γ = 0.5 and Iω = 2.5Ic. Based on these findings and high-Tc Josephson junctions, a family of low-noise square-law detectors, harmonic multipliers, and linear heterodyne receivers can be developed for emerging terahertz applications.
We consider a current biased, resistively shunted josephson junction irradiated at two frequencies. The perturbation technique introduced by Aslamasov and Larkin is used in the calculations. Both signals are treated as perturbations. The second order calculation yields the size of the mixing steps atV_{\pm}=h(\omega_{1}\pm\omega_{2})/2e. As in the case of a single frequency we show that subharmonic mixing steps are absent. The amplitude of the voltage oscillation at the difference and sum frequencies is shown to be non-zero at all voltages. We calculate the microwave resistance for one frequency ω2to third order in the perturbation. There are negative resistance regions nearV\pm(as well as nearV_{2}= h\omega_{2}/2e). Near V, the negative resistance region appears for bias voltage V just aboveV_{-}, while near V the region appears for V just belowV_{+}. This means that when an incident frequency mixes with a cavity mode the mixing step atV_{-}will be inverted compared to the cavity step itself.
Analog computer studies of a Josephson junction show that the microwave‐induced steps in the dc current‐voltage curve may be used as ideal (zero impedance) voltage sources with which to bias a second junction. Biased on one of these steps, the second junction is a microwave oscillator of precisely determined frequency. Because the biasing junction impedance →0 on a step, it contributes no noise to this second junction. A conceptual design using Dayem bridges fabricated as an integral part of a coplanar waveguide structure is proposed.
The possibility of using very-high-Q superconducting microwave cavities to obtain a strong coupling between the electromagnetic field and a Josephson junction has prompted a study of such systems. Expressions have been obtained describing the dc I-V characteristic of a junction biased so that the Josephson radiation frequency is near a resonance of the cavity in which it is located. The rf power coupled into an X-band (10 GHz) TE011 mode cavity from a weakly coupled junction is approximately 3×10−13 I02 Q W, where I0 is the critical current of the junction and Q is the cavity Q. When the coupling between the junction and cavity is large enough, the I-V characteristic becomes multiple valued and the power coupled to the cavity depends on the state of the system. The maximum power which can be coupled to the cavity is approximately 0.58I0Vdc, where Vdc is the voltage required to bias the junction to the resonant frequency of the cavity.
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)