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Journal of Applied Physics

High-frequency limits of superconducting tunnel junction mixers

Dag Winkler, T. Claeson

Published Dec 1, 1987• 35 citations
Publisher

Abstract

We have investigated high-frequency limits of superconducting quasiparticle mixers from experiments on Al/Al-oxide-In/Al (or Ag) tunnel junctions, and from calculations based on Tucker’s quantum theory of mixing (QTM). The small superconducting energy gap of Al enabled us to study mixer performance at around the junction gap frequency, fg =(Δ1+Δ2)/h≊87 GHz, of superconductor-insulator-superconductor (SIS) mixers, and at twice the junction gap frequency for S-I-normal metal (SIN) mixers ( fg =Δ1/h) with available millimeter wave sources. Because of the low transition temperature of Al (Tc ≊1.3 K), a dilution refrigerator was used for providing temperatures below 1 K. The best mixer conversion efficiency was obtained for a low-resistance (∼34 Ω) six-junction array SIS mixer operated at f/fg ≊1 (in this case 73 GHz). The coupled single sideband conversion gain (with no image rejection) was −13.8 dB and the available conversion gain was estimated to −8.4 dB. Complicating nonequilibrium phenomena made it difficult to compare the performance of these relatively high-current-density mixers to the QTM. However, good agreement between calculated and corresponding measured conversion efficiencies and dynamic resistance values was obtained for the low-current-density mixers. Noise due to switching between rf-induced Josephson steps and interference from Josephson mixing could be quenched by a magnetic field. Several high-frequency limits are considered in this paper (such as Josephson switching noise, nonequilibrium phenomena, pair breaking, and energy gap limitations). Our results indicate that submillimeter wave SIS mixer receivers are likely to perform well, at least up to their gap frequencies, i.e., the THz region for large gap superconductors. Our QTM calculations showed that conversion gain larger than unity should be possible up to twice the gap frequency. Above this frequency the conversion loss will increase rapidly.

DOI
10.1063/1.339038

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We have investigated high-frequency limits of superconducting quasiparticle mixers from experiments on Al/Al-oxide-In/Al (or Ag) tunnel junctions, and from calculations based on Tucker’s quantum theory of mixing (QTM). The small superconducting energy gap of Al enabled us to study mixer performance at around the junction gap frequency, fg =(Δ1+Δ2)/h≊87 GHz, of superconductor-insulator-superconductor (SIS) mixers, and at twice the junction gap frequency for S-I-normal metal (SIN) mixers ( fg =Δ1/h) with available millimeter wave sources. Because of the low transition temperature of Al (Tc ≊1.3 K), a dilution refrigerator was used for providing temperatures below 1 K. The best mixer conversion efficiency was obtained for a low-resistance (∼34 Ω) six-junction array SIS mixer operated at f/fg ≊1 (in this case 73 GHz). The coupled single sideband conversion gain (with no image rejection) was −13.8 dB and the available conversion gain was estimated to −8.4 dB. Complicating nonequilibrium phenomena made it difficult to compare the performance of these relatively high-current-density mixers to the QTM. However, good agreement between calculated and corresponding measured conversion efficiencies and dynamic resistance values was obtained for the low-current-density mixers. Noise due to switching between rf-induced Josephson steps and interference from Josephson mixing could be quenched by a magnetic field. Several high-frequency limits are considered in this paper (such as Josephson switching noise, nonequilibrium phenomena, pair breaking, and energy gap limitations). Our results indicate that submillimeter wave SIS mixer receivers are likely to perform well, at least up to their gap frequencies, i.e., the THz region for large gap superconductors. Our QTM calculations showed that conversion gain larger than unity should be possible up to twice the gap frequency. Above this frequency the conversion loss will increase rapidly.
An analysis of the frequency dependence of superconductor-insulator-normal (SIN) and superconductor-insulator-superconductor (SIS) quasiparticle mixers is presented. Power-law expressions for conversion loss and mixer shot-noise temperature for the double-sideband SIN mixer are derived from the Tucker theory for the case of a source conductance which is small compared to the conductance of the junction. For an ideal SIN tunnel junction at T=0 the mixer conversion efficiency is shown to decrease approximately linearly with frequency up to f=Δ/h. From f=Δ/h to 2Δ/h the conversion efficiency remains approximately constant, while above f=2Δ/h it rolls off as the inverse square of the frequency. Expressions for the shot-noise contribution to the mixer noise temperature are also derived. At frequencies up to f=Δ/h the noise temperature rises as the square root of the frequency. From f=Δ/h to f=2Δ/h the noise temperature of the mixer increases linearly with frequency, whereas above f=2Δ/h it rises as the cube of the frequency. Conversion efficiency and noise temperature are also calculated numerically for the SIN mixer. Good agreement is found between the frequency dependencies calculated analytically in the limit of small local oscillator power and the numerical calculations for optimal pumping. The frequency dependence of the nonideal SIS junction is also analyzed, and shown to yield similar results, with the characteristic frequencies Δ/h and 2Δ/h for a SIN mixer transformed into 2Δ/h and 4Δ/h, respectively. Expressions also are derived for the saturation power as a function of frequency.
We have tested the conversion efficiency of quasi-particle mixers at frequencies close to the superconducting gap frequency. We investigated arrays of aluminum SIS and SIN tunnel junctions at frequencies around 75 GHz and temperatures down to 0.3 K. This frequency corresponds to about 80% of the gap frequency. The experimental conversion loss was large due to severe impedance mismatches. However, we obtained a good agreement (within 1 dB) to the quantum theory of mixing, indicating that nonequilibrium effects do not play a significant role for these low current density junctions.
A computer simulation is constructed to describe the performance of superconductor-insulator-superconductor (SIS) quasiparticle heterodyne receivers in terms of photon-assisted tunneling theory. The results predict that conversion efficiencies greater than unity can be realized at millimeter wave frequencies, with noise temperatures approaching the fundamental quantum limit. The nonlinearity responsible for the mixing is the extremely rapid onset of quasiparticle tunneling current in SIS junctions near the full gap voltage 2Δ/e, and is independent of the Josephson pair currents. Substantial gain is expected under a variety of conditions and for a wide range of source and load impedances.
We have developed a low-noise 850 GHz superconductor–insulator–superconductor quasiparticle mixer with NbTiN thin-film microstrip tuning circuits and hybrid Nb/AlN/NbTiN tunnel junctions. The mixer uses a quasioptical configuration with a planar twin-slot antenna feeding a two-junction tuning circuit. At 798 GHz, we measured an uncorrected double-sideband receiver noise temperature of TRX=260 K at 4.2 K bath temperature. This mixer outperforms current Nb SIS mixers by a factor of nearly 2 near 800 GHz. The high-gap frequency and low loss at 800 GHz make NbTiN an attractive material with which to fabricate tuning circuits for SIS mixers. NbTiN mixers can potentially operate up to the gap frequency, 2Δ/h∼1.2 THz.
We have fabricated and tested submillimeter-wave superconductor–insulator–superconductor (SIS) mixers using very high-current-density Nb/AlN/Nb tunnel junctions (Jc≈30 kA cm−2). The junctions have low-resistance-area products (RNA≈5.6 Ω μm2), good subgap-to-normal resistance ratios Rsg/RN≈10, and good run-to-run reproducibility. From Fourier transform spectrometer measurements, we infer that ωRNC=1 at 270 GHz. This is a factor of 2.5 improvement over what is generally available with Nb/AlOx/Nb junctions suitable for low-noise mixers. The AlN-barrier junctions are indeed capable of low-noise operation: we measure an uncorrected double-sideband receiver noise temperature of TRX=110 K at 533 GHz for an unoptimized device. In addition to providing wider bandwidth operation at lower frequencies, the AlN-barrier junctions will considerably improve the performance of THz SIS mixers by reducing rf loss in the tuning circuits.
We experimentally investigate different mixing regi-mes in Nb/AlOx/Nb and Nb/AlN/NbN tunnel superconductor-insulator-superconductor (SIS) junctions. The SIS mixers were studied with regard to the following modes of operation: in an extremely low-frequency range (0.1-20 GHz) and as high harmonic mixers; n ≈ 20-30 at signal frequencies of about 500 GHz that requires high power of a local oscillator. The quasiparticle and Josephson mixing regimes have been compared. We demonstrate that, in some applications requiring high conversion efficiency, the Josephson regime can be more preferable than the quasiparticle regime due to a larger output signal and better signal-to-noise ratio. As an example of such an application, we consider the phase locking of a THz oscillator using a cryogenic harmonic phase detector, which only ought to realize all of its benefits under the Josephson mixing regime. In addition, we demonstrate that the presence of the Josephson effect results in considerable increase in conversion efficiency at the expense of the dynamic range decrease; it was measured for low-frequency up- and down-convertors, which are promising for cryogenic multiplexing systems.