The full quantum theory of mixing has been widely developed by Tucker. From theoretical analysis it allows one to predict the optimal performances of a quasiparticle superconducting insulator-superconducting junction mixer from knowing the junction current-voltage characteristics. This theory, however, considers only quasiparticle processes and neglects pair effects. At frequencies close to the superconductor energy gap, the Josephson currents become unavoidable and are reputed to be the cause of strong instabilities and noise. We present here a theoretical calculation of the Josephson noise and losses, which is consistent with experimental results. The width of the Josephson noise peaks is discussed.
The full quantum theory of mixing has been widely developed by Tucker. From theoretical analysis it allows one to predict the optimal performances of a quasiparticle superconducting insulator-superconducting junction mixer from knowing the junction current-voltage characteristics. This theory, however, considers only quasiparticle processes and neglects pair effects. At frequencies close to the superconductor energy gap, the Josephson currents become unavoidable and are reputed to be the cause of strong instabilities and noise. We present here a theoretical calculation of the Josephson noise and losses, which is consistent with experimental results. The width of the Josephson noise peaks is discussed.
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.
Josephson currents have been observed to drain instabilities and decrease the sensitivity of a heterodyne superconductor-insulator-superconductor (SIS) receiver operated at submillimeter wavelengths. A static magnetic field is usually applied on the SIS junction to reduce the magnitude of its critical Josephson currents and enable quasiparticle mixing. We measured the SIS mixer output power at the intermediate frequency (IF) versus the dc bias voltage of an array of two 1 μm2 Nb/Al–Al2O3/Nb junctions. We show evidence of additional, magnetic-field-sensitive noise, peaked at the Shapiro steps voltages, which is due to high-frequency Josephson currents converted to the IF by quasiparticle mixing.
We have made a systematic study of the gain and noise in superconductor-insulator-superconductor mixers employing Ta based, Nb based, and Pb-alloy based tunnel junctions. These junctions displayed both weak and strong quantum effects at a signal frequency of 33 GHz. The effects of energy gap sharpness and subgap current were investigated and are quantitatively related to mixer performance. Detailed comparisons are made of the mixing results with the predictions of a three-port model approximation to the Tucker theory. We have measured mixer performance with a novel test apparatus which is accurate enough to allow for the first quantitative tests of theoretical noise predictions. We find that the three-port model of the Tucker theory underestimates the mixer noise temperature by a factor of about 2 for all of our mixers. In addition, predicted values of available mixer gain are in reasonable agreement with experiment when quantum effects are weak. However, as quantum effects become strong, the predicted available gain diverges to infinity, which is in sharp contrast to the experimental results. Predictions of coupled gain do not always show such divergences.
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. This thesis describes both theoretical and experimental investigations into the dynamics and noise processes of Josephson junctions, with the intent of evaluating their potential as mixers in heterodyne instruments for submillimeter-wave (i.e., the frequency range from 300 GHz to 3THz) detection. Superconducting tunnel junctions utilizing the nonlinearity due to photon-assisted tunneling of quasiparticles (SIS mixers) have become the state-of-the-art technology for sensitive heterodyne detection up to frequencies of about 700 [...]. Recent progress in the fabrication of high [...], superconductors has led to Josephson-effect devices with [...] products of up to ten millivolts, which might be suitable for mixing at frequencies of many terahertz. The key question for weighing the prospects for high-frequency Josephson mixers is that of the sensitivity which can be attained. Previous experimental work on Josephson mixing suggests the existence of an "excess" noise, which degrades the sensitivity. Theoretical modeling of mixer performance, based on the resistivelyshunted junction (RSJ) model for the dynamics of the device, also indicates the presence of larger noise than expected. The origin of this noise was not clearly understood, however, nor was its exact magnitude or expected scaling with frequency or junction characteristics known. In addition, previous experiments utilized crude devices of the point-contact type, which were unstable and thus undesirable for real applications. In the first part of this thesis research, extensive numerical simulations were performed with the RSJ model, including calculations of mixer noise and conversion efficiency. These calculations have revealed that the source of excess noise is the AC Josephson oscillations of the device, which can be completely incoherent, with a linewidth comparable to their frequency. Thus they appear as a broadband noise source. While this noise is intrinsic and unavoidable, an optimized mixer is still shown to be capable of interesting sensitivity levels, and the excess noise is expected to become relatively less important as the operating frequency is increased. Secondly, a process has been developed for the fabrication of stable, well-characterized, and reproducible Josephson devices based on resistively-shunted Nb and NbN tunnel junctions. The devices utilize submicron-area, high current-density tunnel junctions and a AuGe shunt resistor to yield completely non-hysteretic I-V curves, normal-state resistances of about [...] products of about half a millivolt. These devices should be nearly optimal for mixing at [...]. Heterodyne measurements using these junctions have been performed in a waveguide mixer mount. Receiver temperatures as low as 190 K (DSB), with -6 dB conversion efficiency, have been obtained at 100 [...], but these results are still a factor of about four higher than those predicted by the RSJ simulations. Accurate measurements of the available noise power of the junctions at the intermediate frequency of 1.5 [...] were made, and confirmed that the receivers were limited by elevated junction output noise. The deviations of the noise from theoretical predictions are shown to be caused by the nonlinear interaction of the junction with the embedding circuit. While this work points out some of the complexity introduced by the strong nonlinearity of Josephson devices, it is still expected that Josephson-effect mixers may be useful for heterodyne detection at very high frequencies.
Superconductor-insulator-superconductor (SIS) mixers are currently the lowest-noise devices available for mixing in the 26–110 GHz frequency range. However, a major source of noise is anticipated to be the increased effects of Josephson oscillations within the mixer as higher operating frequencies are achieved. Simulations have been done to demonstrate these effects. Results indicate that the commonly used three-port analysis is valid over a wide range of conditions, but that even minimal Josephson oscillations have a deleterious effect on mixer performance. The junction shunt capacitance, which serves to short out the Josephson oscillations, is thus an extremely important parameter. However, the characterization of the mixer in terms of an ‘‘ωRC’’ product appears to be an oversimplification. A more elaborate approach to mixer characterization is suggested.
Virtually all analyses of the superconductor-insulator-superconductor (SIS) quasiparticle mixer have employed the quantum theory of mixing in its three-frequency approximate form. This approximation is valid only in the limit of very large junction capacitance. For finite capacitance, these analyses may be seriously in error. To remedy this, a computer program has been developed which uses the quantum theory of mixing in its most general form, treating the large-signal properties of the mixer in the time domain. The terminating impedances at the harmonics of the local oscillator frequency and their sidebands can be arbitrary. Using this analysis, the effect of finite junction capacitance on one SIS mixer's performance is described. This gives an insight into the range of validity of the three-frequency model.