A fully quantum mechanical theory of diode mixers which includes quantization of the external circuit is presented. We find that Tucker's theory for SIS mixer conversion efficiencies is correct, but that his expression for the measurement noise must be augmented by an amount corresponding to half a photon at every frequency to which the mixer responds. Noise in high quality SIS mixers is shown to be accurately described by the conceptually simpler photodiode mixer noise theory. The radiation coupling efficiency term, η, which appears in photodiode theory turns out to be the coupling efficiency between the signal source admittance and the admittance which the SIS presents to the LO. Our theory reduces to Caves' quantum linear amplifier formalism, and therefore predicts measurement noises bounded by the quantum lower limit ofhv/k_{B}. Predictions of performance versus frequency for SIS's are made. We predict that NbN SIS's will behave as nearly ideal photodiodes for frequencies as high as 3000 GHz.
A fully quantum mechanical theory of diode mixers which includes quantization of the external circuit is presented. We find that Tucker's theory for SIS mixer conversion efficiencies is correct, but that his expression for the measurement noise must be augmented by an amount corresponding to half a photon at every frequency to which the mixer responds. Noise in high quality SIS mixers is shown to be accurately described by the conceptually simpler photodiode mixer noise theory. The radiation coupling efficiency term, η, which appears in photodiode theory turns out to be the coupling efficiency between the signal source admittance and the admittance which the SIS presents to the LO. Our theory reduces to Caves' quantum linear amplifier formalism, and therefore predicts measurement noises bounded by the quantum lower limit ofhv/k_{B}. Predictions of performance versus frequency for SIS's are made. We predict that NbN SIS's will behave as nearly ideal photodiodes for frequencies as high as 3000 GHz.
Heterodyne receivers based on superconductor-insulator-superconductor (SIS) tunnel diodes are the most sensitive available for near-millimeter wavelengths. Since the late seventies, receivers based on SISs have been used for millimeter band observations at radio observatories around the world. The work described here was carried out with the elusive goal in mind of developing ideal SIS receivers for radioastronomy. This thesis describes one researcher's path towards this goal. In the first chapter, a basic description of SIS diodes, their interaction with radiation, and heterodyne detection are given. The important detailed results of J. R. Tucker's tunnel diode heterodyne theory are described, since subsequent chapters rely on Tucker's work quite heavily. Throughout this introductory chapter, extremely simple (by comparison with the algebraic theoretical results) physical models are used to describe superconductivity, SISs, photon-assisted tunneling, and heterodyne detection. It is the author's experience that these physical models can be used to derive correct theoretical results, long before these results are proved rigorously. The second chapter presents a fully quantum mechanical theory of heterodyne detection with diodes. This theory was developed because Tucker's theory for tunnel diodes predicts a greater mixer sensitivity than is possible considering Heisenberg's uncertainty principle for radiation. Tucker does not quantize the radiation incident on the SIS, although his treatment of the isolated tunnel diode is completely quantum mechanical. In chapter 2, the quantization of radiation is carried out for heterodyne diode detectors. The formalism is shown to obey quantum limits on sensitivity. Finally, an ideal SIS mixer is shown to have noise properties identical to those of optical mixers based on ideal photodiodes. In possession of an apparently complete theory for SIS mixers, the third chapter presents a sampling of numerical results from that theory. Four different non-ideal tunnel diodes are used for these calculations so that a quantitative feel for the importance of diode quality can be achieved. The effects of dc and LO bias, signal and image source admittance, frequency of operation, and junction quality are all explored. This information will be useful for the proper engineering of SIS mixers. Finally, the fully optimized performance of the four tunnel diodes is presented as frequency is varied. It is shown that reasonably good quality lead-alloy SISs should behave like photodiodes up to frequencies as high as 1500 GHz. Finally, chapter 4 presents a prototype open-structure SIS mixer. Measurements in the laboratory show this mixer to be quite sensitive for signal frequencies from 115 to 761 GHz. Unlike all other SIS receivers, in which the diode is mounted across a waveguide, this mixer relies on the bowtie-on-quartz antenna structure, which has been investigated by D. B. Rutledge and his students. This difference is essential to the multi-octave spectral coverage of this mixer. It is probable that waveguide designs will never achieve good results above 500 GHz, and as of now, there are no SIS-waveguide mixers which operate well above 300 GHz. Tests at the Owens Valley Radio Observatory verify the suitablility of this mixer for radioastronomy, but these tests have been limited to frequencies of 260 GHz and lower.
A quantum-statistical analysis of the signal and noise performance of the quasiparticle (SIS) heterodyne mixers is presented. In contrast with the earlier theories, the quantum properties of the signal source have been taken into consistent consideration. In the quantum range of sensitivity the noise properties of the mixer can be characterized by the noise parameter ΘNintroduced earlier for the parametric amplifiers. Using the conventional 3-port model of the mixer circuit and the microscopic theory of the superconducting tunnel junctions we have obtained a general expression for ΘNand evaluated it numerically for various quasiparticle current step widths, dc bias voltages, local oscillator powers, signal frequencies ωs, signal source admittances Ysand operation temperatures T. In a reasonable range of these parameters,\Theta_{N}^{DSB}has turned out to be less than the so-called quantum limith\omega_{s}/2. On the contrary, in the single sideband mode of the mixer performance, ΘNis always larger thanh\omega_{s}/2. The difference between the two modes of operation is discussed from the point of view of the quantum theory of measurements.
Heterodyne mixers for millimeter wavelengths which have conversion gain and noise comparable to the quantum limit can be made using the non-linearity of the quasi-particle I-V curve of SIS or SIN tunnel junctions. When the voltage range of the non-linearity becomes small compared with hω/e, classical device theory breaks down and photon assisted tunneling theory must be used to understand mixer performance. In this paper we describe detailed computer simulations of SIS and SIN quasiparticle mixers. Predictions for conversion efficiency and noise are given for both devices as a function of operating frequency, bias voltage, RF source conductance and local oscillator power. A novel type of SIN harmonic mixer is proposed for which gain is also predicted.
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.
The dominant source of noise in an SIS mixer is the noise in the photon-induced current. We have made accurate measurements of noise induced in SIS junctions by 95 GHz photons. The noise is measured at 1.5 GHz using a low-noise cryogenic measurement system. The measured photon-induced noise is compared to the noise predicted by Tucker's theory augmented by a vacuum/thermal noise term. For small to moderate rf powers, at which SIS mixers are operated, the measured noise is nearly perfectly predicted by this theory for all the devices measured. Measurements of series arrays of SIS junctions also agree with this theory showing that the noise of each SIS junction in the array is independent. At large rf powers, the measured noise was higher than the predicted noise, in devices with smaller capacitance. We also measured the noise in single junctions and arrays with no rf radiation. These measurements agreed very well with the predicted shot noise for most bias conditions.>
It is noted that it is possible to operate a mixer as a phase-sensitive linear amplifier by pumping with two local oscillators (LOs) separated in frequency by twice the IF (intermediate frequency) and symmetrically located about the signal frequency. In principle a phase-sensitive amplifier can detect a signal without adding any noise. The authors present a formalism developed to describe two-LO mixers, and extend the quantum mixer theory to calculate expressions for the gain and noise of a two-LO mixer. The full quantum mechanical formulation used here enables an analysis of the mixer noise for general input states, for example, a squeezed state. It is demonstrated that a two-LO mixer is phase-sensitive. The results are pertinent to the design of phase-sensitive heterodyne receivers with SIS (superconductor-insulator-superconductor) quasiparticle mixers.>