I study the dynamics of a Josephson junction serving as a threshold detector of fluctuations which is subjected to a general non-equilibrium electronic noise source whose characteristic is to be determined by the junction. This experimental setup was proposed several years ago as a prospective scheme for determining the full counting statistics of an electronic noise source. Despite intensive theoretical as well as experimental research in this direction the promise has not been quite fulfilled yet and I will discuss what the unsolved issues are. First, I review a general theory for the calculation of the exponential part of the non-equilibrium switching rates of the junction and compare its predictions with previous results found in different limiting cases by several authors. I identify several possible weak points in the previous studies and I report a new analytical result for the linear correction to the rate due to the third cumulant of a non-Gaussian noise source in the limit of a very weak junction damping. The various analytical predictions are then compared with the results of the numerical method developed. Finally, I analyze the status of the experimental data thus far made publicly available with respect to the theoretical predictions and discuss briefly the suitability of the present experimental schemes as regards their potential for measuring the whole of the full counting statistics for non-Gaussian noise sources as well as their relation to the available theories.
I study the dynamics of a Josephson junction serving as a threshold detector of fluctuations which is subjected to a general non-equilibrium electronic noise source whose characteristic is to be determined by the junction. This experimental setup was proposed several years ago as a prospective scheme for determining the full counting statistics of an electronic noise source. Despite intensive theoretical as well as experimental research in this direction the promise has not been quite fulfilled yet and I will discuss what the unsolved issues are. First, I review a general theory for the calculation of the exponential part of the non-equilibrium switching rates of the junction and compare its predictions with previous results found in different limiting cases by several authors. I identify several possible weak points in the previous studies and I report a new analytical result for the linear correction to the rate due to the third cumulant of a non-Gaussian noise source in the limit of a very weak junction damping. The various analytical predictions are then compared with the results of the numerical method developed. Finally, I analyze the status of the experimental data thus far made publicly available with respect to the theoretical predictions and discuss briefly the suitability of the present experimental schemes as regards their potential for measuring the whole of the full counting statistics for non-Gaussian noise sources as well as their relation to the available theories.
Motivated by several experimental activities to detect charge noise produced by a mesoscopic conductor with a Josephson junction as on-chip detector, the switching rate out of its zero-voltage state is studied. This process is related to the problem of thermal escape in presence of non-Gaussian fluctuations. In the relevant case of weak higher than second order cumulants, an effective Fokker-Planck equation is derived, which is then used to obtain an explicit expression for the escape rate. Specific results for the rate asymmetry due to the third moment of current noise allow to analyze experimental data and to optimize detection circuits.
Non-Gaussian fluctuations of the electrical current can be detected with a Josephson junction placed on-chip with the noise source. We present preliminary measurements with an NIS junction as a noise source, and a Josephson junction in the thermal escape regime as a noise detector. It is shown that the Josephson junction detects not only the average noise, which manifests itself as an increased effective temperature, but also the noise asymmetry. A theoretical description of the thermal escape of a Josephson junction in presence of noise with a non-zero third cumulant is presented, together with numerical simulations when the noise source is a tunnel junction with Poisson noise. Comparison between experiment and theory is discussed.
We generalize the stochastic path integral formalism by considering Hamiltonian dynamics in the presence of general Markovian noise. Kramers' solution of the activation rate for escape over a barrier is generalized for non-Gaussian driving noise in both the overdamped and underdamped limit. We apply our general results to a Josephson junction detector measuring the electron counting statistics of a mesoscopic conductor. The activation rate dependence on the third current cumulant includes an additional term originating from the backaction of the measurement circuit.
The existence of the third cumulant S3 of voltage fluctuations has demonstrated the non-Gaussian aspect of shot noise in electronic transport. Until now, measurements have been performed at low frequency, \textit{i.e.} in the classical regime ℏω<eV,kBT where voltage fluctuations arise from charge transfer process. We report here the first measurement of S3 at high frequency, in the quantum regime ℏω>eV,kBT. In this regime, experiment cannot be seen as a charge counting statistics problem anymore. It raises central questions of the statistics of quantum noise: 1) the electromagnetic environment of the sample has been proven to strongly influence the measurement, through the possible modulation of the noise of the sample. What happens to this mechanism in the quantum regime? 2) For ℏω>eV, the noise is due to zero point fluctuations and keeps its equilibrium value: S2=Gℏω with G the conductance of the sample. Therefore, S2 is independent of the bias voltage and no photon is emitted by the conductor. Is it possible, as suggested by some theories, that S3=0 in this regime? With regard to these questions, we give theoretical and experimental answers to the environmental effects showing that they involve dynamics of the quantum noise. Using these results, we investigate the question of the third cumulant of quantum noise in the a tunnel junction.
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.
It is well known that the current-biased Josephson junction (CBJJ) can serve as a Josephson threshold detector (JTD) for the sensitive detection of weak microwave signals. Based on the recent work (PRB {\bf 111}, 024501 (2025)) on the detection sensitive limit of the usual equilibrium JTD, here we numerically demonstrate that a non-equilibrium JTD can be alternatively utilized to implement the higher sensitive detection of a weak microwave signal, arriving at its energy quantum limit. In the presence of thermal noise, we numerically simulate the phase dynamics for the CBJJ in the JTD with the different sweep rates of the biased currents, and find that the SCDs of the JTD with and without the microwave signal input show different behaviors. It is demonstrated that, depending on how high the sweep rate of the biased current being applied, the JTD can be operated in either the equilibrium- or the non-equilibrium state. Specifically, under the rapidly non-adiabatic driving, the SCDs of the JTD are obviously insensitive to the thermal noises, which means that the non-equilibrium JTD can possess a higher achievable detection sensitivity, compared with its equilibrium state counterpart. Consequently, the non-equilibrium JTD can be utilized to implement the desired single microwave-photon detection. Also, some of the achievable performance indexes, such as the dynamic range, detection bandwidth, and the photon-number resolvability, etc., of the non-equilibrium JTD have been estimated, when it serves as a wideband microwave single-photon detector.