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Journal of Applied Physics

Theoretical and numerical analysis of very high harmonic superconducting tunnel junction mixers

Phichet Kittara, S. Withington, G. Yassin

Published Jan 15, 2007• 14 citations
Publisher

Abstract

We describe a procedure for modeling the nonlinear, quantum-mechanical behavior of very high harmonic superconductor-insulator-superconductor (SIS) mixers. A typical mixer is pumped by a strong microwave source at 10–15GHz, which causes high-harmonic (20–40) currents to flow, any one of which can be used as a local oscillator to downconvert a submillimeter-wave signal to a low microwave frequency, 1–8GHz. This mode of operation is attractive for measuring the beam patterns of conventional SIS mixers, because only a single submillimeter-wave source is needed. We conducted simulations using the 20th harmonic of a 13.5GHz microwave source, downconverting a 271.4GHz signal to a 1.4GHz intermediate frequency. These simulations clearly show that linear downconversion can be achieved even for relatively high levels of rf signal power; although, care is needed when choosing the operating point. The patterns of behavior seen in the simulations are in remarkable agreement with recently published experimental results.

DOI
10.1063/1.2424407

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When designing instruments for submillimeter-wave astronomy it is important to understand precisely how saturating superconducting tunnel-junction mixers behave. In this article, a procedure is described for calculating the behavior of tunnel-junction circuits when multitone high-level signals are applied. The procedure is based on a full quantum-mechanical description of photon-assisted tunneling, and uses Harmonic Newton to search for a set of voltages and currents that satisfy the circuit equations at every frequency present. A number of illustrative simulations are presented, and it is shown that Harmonic Newton can be used to model saturating superconductor–insulator–superconductor mixers in a robust and numerically efficient manner.

Journal of Applied Physics•Jun 6, 2003•15 citations
We describe a procedure for modeling the nonlinear, quantum-mechanical behavior of very high harmonic superconductor-insulator-superconductor (SIS) mixers. A typical mixer is pumped by a strong microwave source at 10–15GHz, which causes high-harmonic (20–40) currents to flow, any one of which can be used as a local oscillator to downconvert a submillimeter-wave signal to a low microwave frequency, 1–8GHz. This mode of operation is attractive for measuring the beam patterns of conventional SIS mixers, because only a single submillimeter-wave source is needed. We conducted simulations using the 20th harmonic of a 13.5GHz microwave source, downconverting a 271.4GHz signal to a 1.4GHz intermediate frequency. These simulations clearly show that linear downconversion can be achieved even for relatively high levels of rf signal power; although, care is needed when choosing the operating point. The patterns of behavior seen in the simulations are in remarkable agreement with recently published experimental results.
We present a numerical procedure for simulating the non-linear behaviour of Superconductor-Insulator-Superconductor (SIS) tunnel-junction mixers. Mixers of this kind are used extensively in high-performance submillimetre-wave astronomical receivers. The procedure is complete in that both the signal and local-oscillator voltages can be at high levels, with significant amounts of harmonic content; also, the full quantum mechanical behaviour of the tunnel junction is taken into account. The initial simulations show that multi-tone analysis can be carried out in a numerically efficient manner, and that saturation, and the attendant generation of IF harmonics, can be modelled rigorously. This work constitutes the first full non-linear model of an SIS mixer, and the theoretical and numerical procedures described, will be of great importance when designing the next generation of heterodyne astronomical receivers.
A harmonic Newton technique has successfully been used in the simulation of superconducting quasiparticle mixers in a five-port model. The steady-state large-signal waveform impressed across the tunnel junction by the incident local oscillator (LO) power is computed in the frequency domain. The three-frequency approximation provides the initial trial solution, which, together with the superlinear convergence property of Newton's method, ensures rapid convergence. A wide range of simulations based on the response function of a real superconductor-insulator-superconductor (SIS) junction is presented. The case of an SIS harmonic mixer (n=2) is also studied. Using a five-port model, the simulation explicitly takes the effect of the first harmonic into account. The algorithm and the principal results obtained for a hypothetical mixer incorporating the measured current-voltage characteristics of a real (SIS) junction are presented. The first results indicate that harmonic quasiparticle mixing may be very attractive in the submillimeter-wave band.>
A theoretical analysis of harmonic mixing in a quasiparticle tunnel junction at Vbias=0 shows that harmonic mixing for submillimeter frequencies is a viable alternative to fundamental mixing. It is also shown that the signal gain from the first harmonic above the pump frequency to the intermediate frequency is independent of the embedding admittance at the pump frequency. In fact, we show that the five-port model reduces to the three-port model as a result of the inversion symmetry of the I-V curve and, moreover, no large-signal analysis is necessary. Full simulations of harmonic mixing using a five-port model confirm these results. The simulations have been done for the case of a superconductor-insulator-normal junction in which there is no pair current interference. For this type of harmonic mixer we show that the local oscillator (LO) power requirement can be less than a fundamental mixer operating at the same signal frequency, which is particularly useful in circumventing the problems of high-frequency LO power generation.
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.
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.
When designing instruments for submillimeter-wave astronomy it is important to understand precisely how saturating superconducting tunnel-junction mixers behave. In this article, a procedure is described for calculating the behavior of tunnel-junction circuits when multitone high-level signals are applied. The procedure is based on a full quantum-mechanical description of photon-assisted tunneling, and uses Harmonic Newton to search for a set of voltages and currents that satisfy the circuit equations at every frequency present. A number of illustrative simulations are presented, and it is shown that Harmonic Newton can be used to model saturating superconductor–insulator–superconductor mixers in a robust and numerically efficient manner.