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IEEE Transactions on Magnetics

An analytic investigation of the superconductor quasiparticle mixer in the low power limit

M. J. Feldman

Published Mar 1, 1991• 11 citations
Publisher

Abstract

The properties of an SIS (Superconductor-insulator-superconductor) mixer using a slightly nonideal junction, with finite local oscillator (LO) power, are determined by analytic expansion of the equations of the quantum theory of mixing. The result is that the conversion gain using any reasonably good quality SIS junction is essentially equal to that using a perfect junction. Quite to the contrary, the minimum noise temperature is controlled by the leakage current of the junction: the increase in the minimum added-noise temperature over the quantum limit T/sub Q/=h omega /2k is given by delta T/sub Q/=(h omega /k) square root I/sub 0/I/sub 2//I/sub 1/; this minimum requires that the LO voltage across the junction is V/sub LO/=(64I/sub 0//I/sub 2/) /sup 1/4/h omega /e. (I/sub n/ is the current measured on the unpumped I-V curve of the junction at voltage V/sub 0/+nh omega /e). Therefore, although an SIS mixer using an ideal junction can reach the quantum noise limit only in the limit of zero LO power, even the most nearly ideal junctions require a considerable LO for best sensitivity.

DOI
10.1109/20.133755

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IEEE Transactions on Magnetics•Mar 1, 1991•4 citations
The properties of an SIS (Superconductor-insulator-superconductor) mixer using a slightly nonideal junction, with finite local oscillator (LO) power, are determined by analytic expansion of the equations of the quantum theory of mixing. The result is that the conversion gain using any reasonably good quality SIS junction is essentially equal to that using a perfect junction. Quite to the contrary, the minimum noise temperature is controlled by the leakage current of the junction: the increase in the minimum added-noise temperature over the quantum limit T/sub Q/=h omega /2k is given by delta T/sub Q/=(h omega /k) square root I/sub 0/I/sub 2//I/sub 1/; this minimum requires that the LO voltage across the junction is V/sub LO/=(64I/sub 0//I/sub 2/) /sup 1/4/h omega /e. (I/sub n/ is the current measured on the unpumped I-V curve of the junction at voltage V/sub 0/+nh omega /e). Therefore, although an SIS mixer using an ideal junction can reach the quantum noise limit only in the limit of zero LO power, even the most nearly ideal junctions require a considerable LO for best sensitivity.
Abstract : Theoretical and experimental research has been conducted to elucidate the basic physics behind the properties of superconductor-insulator-superconductor (SIS) tunnel junction receiving devices. The properties of an SIS mixer using a slightly nonideal junction, with finite LO power, were determined by analytic expansion of the equations of the quantum theory of mixing. The resulting equations have a particularly simple form. The minimum noise temperature is controlled by the leakage current of the junction. Even the most nearly ideal junctions made today require a considerable LO for best sensitivity; nevertheless, even a comparatively large leakage current allows mixer noise to be only a small factor above the quantum limit. The saturation properties of SIS mixers subjected to broad-band thermal noise obey the equations derived for monochromatic saturating signals. The Josephson junction tuning inductor was analyzed with the conclusion that such a device is not feasible with present fabrication techniques. Computer calculations using synthetic SIS junction I-V characteristics predicted the performance of an optimized receiver over its entire operating frequency range. Many aspects of the operation of SIS mixers were clarified and unexpected new phenomena were predicted. A 'photon picture' interpretation of the quantum theory of mixing is in the early stages of development. Niobium nitride edge junctions with excellent current-voltage characteristics were fabricated using novel barrier formation processes. The role of surface damage in the quality of NbN edge junction electrical characteristics was investigated and unexpected results were obtained.
Theoretica and experimental research has been conducted to elucidate the basic physics behind the properties of superconductor-insulator-superconductor (SIS) tunnel junction receiving devices. The properties of an SIS mixer using a slightly nonideal junction, with finite LO power, were determined by analytic expansion of the equations of the quantum theory of mixing. The resulting equations have a particularly simple form. The minimum noise temperature is controlled by the leakage current of the junction. Even the most nearly ideal junctions made today require a considerable LO for best sensitivity; nevertheless, even a comparatively large leakage current allows mixer noise to be only a small factor above the quantum limit. The saturation properties of SIS mixers subjected to broad-band thermal noise obey the equations derived for monochromatic saturating signals. The Josephson junction tuning inductor was analyzed with the conclusion that such a device is not feasible with present fabrication techniques. Computer calculations using synthetic SIS junction I-V characteristics predicted the performance of an optimized receiver over its entire operating frequency range. Many aspects of the operation of SIS mixers were clarified and unexpected new phenomena were predicted. A 'photon picture' interpretation of the quantum theory of mixing is in the early stages ofmore » development. Niobium nitride edge junctions with excellent current-voltage characteristics were fabricated using novel barrier formation processes. The role of surface damage in the quality of NbN edge junction electrical characteristics was investigated and unexpected results were obtained.« less
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.
Theoretical research has been conducted to elucidate the basic physics behind the properties of superconductor-insulator-superconductor (SIS) tunnel junction receiving devices. The properties of SIS mixers using nonideal junctions and finite LO power, were determined by analytic expansion of the equations of the quantum theory of mixing, and also by computer simulations of SIS receivers over the entire range of experimental parameters. The result is a new coherent and intuitive picture of SIS mixer behavior. Many of the outstanding mysteries and questions about SIS receivers are resolved, and this contributes greatly to the design and interpretation of SIS mixer experiments. Other calculations show how to achieve sub-quantum noise temperatures in the phase sensitive SIS mixer, an important step towards realization of ultra-low- noise detectors. A simplified model casts doubt on the superlative experimental results reported for the rf-series dc-parallel biased array SIS mixer. Superconductivity; SIS mixer; Submillimeter-wave detection.
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.
Calculations based on the quantum theory of mixing in single-particle tunnel junctions show that there is a fairly simple strategy for optimizing the performance of double-sideband superconductor-insulator-superconductor (SIS) quasiparticle mixers. The best mixer noise temperature is obtained when the signal source is matched to the local oscillator (LO) admittance of the junction. This applies over a very wide range of LO and DC bias conditions. These calculations support the contention that it is the energy dissipation in the device which is important in determining the noise performance, not the small signal admittance or the power gain. This appears to be another demonstration of the Callen and Welton fluctuation-dissipation theorem. which states that it is the dissipation of energy which is responsible for the noise generation in a wide range of devices, and it is this energy dissipation mechanism to which the signal should be coupled to minimize the noise.