We investigate the behavior of a quantum resonator coupled to a superconducting single-electron transistor tuned to the Josephson quasiparticle resonance and show that the dynamics is similar in many ways to that found in a micromaser. Coupling to the SSET can drive the resonator into non-classical states of self-sustained oscillation via either continuous or discontinuous transitions. Increasing the coupling further leads to a sequence of transitions and regions of multistability.PACS numbers: 85.85.+j, 85.35.Gv, 74.78.Na Systems where a mesoscopic conductor such as a single-electron transistor is coupled to a nanomechanical resonator have been studied intensively because the current through the conductor can be extremely sensitive to the motion of the resonator and hence may be used to monitor its position with almost quantum-limited precision [1,2,3,4]. Furthermore, where either the coupling between the electrons and the resonator is non-linear [5] or the electronic transport occurs via a resonance [4], dynamic instabilities in the resonator can occur leading to self-sustained oscillations. The way a nanomechanical resonator can be driven into states of finite amplitude oscillation by successive interactions with a current of electrons in a conductor parallels the behavior of quantum optical systems, such as the micromaser, in which an electromagnetic cavity is pumped by interactions with a steady stream of individual two-level atoms [6]. This contrasts with a standard laser (a nanomechanical version of which was envisioned in [7]) where an oscillator interacts simultaneously with many two-level systems.In a superconducting single-electron transistor (SSET) transport can occur via resonant processes involving both coherent motion of Cooper pairs and incoherent quasiparticle tunneling, the simplest of which is the Josephson quasiparticle (JQP) resonance [8]. In the vicinity of a JQP resonance, the dynamics of a resonator coupled linearly to the SSET is very sensitive to the bias point [3,4,9]. For bias points on one side of the resonance, the SSET acts on the resonator like a thermal bath and its current can monitor the position of the resonator with exquisite sensitivity. In contrast, biasing on the opposite side of the JQP resonance can drive the resonator into states of self-sustained oscillation [4].In this Letter we explore the quantum dynamics of a resonator coupled to a SSET and show that it is analogous to that of a micromaser. Less noisy than a laser, a micromaser [6,10] can generate number-squeezed states of the cavity and exhibits not a single threshold transition, but a series of transitions between different dynamical states. Although the SSET-resonator system and micromaser differ in the details of the interactions between their respective sub-components, we find a num- ber of important similarities in their dynamics, many of which first arise when the resonator is sufficiently fast to match the time-scale of the electrical transport. Previous theoretical studies of this system have concentrat...

We present an analysis of the dynamics of a nanomechanical resonator coupled to a superconducting single electron transistor (SSET) in the vicinity of the Josephson quasiparticle (JQP) and double Josephson quasiparticle (DJQP) resonances. For weak coupling and wide separation of dynamical timescales, we find that for either superconducting resonance the dynamics of the resonator is given by a Fokker-Planck equation, i.e., the SSET behaves effectively as an equilibrium heat bath, characterised by an effective temperature, which also damps the resonator and renormalizes its frequency. Depending on the gate and drain-source voltage bias points with respect to the superconducting resonance, the SSET can also give rise to an instability in the mechanical resonator marked by negative damping and temperature within the appropriate Fokker-Planck equation. Furthermore, sufficiently close to a resonance, we find that the Fokker-Planck description breaks down. We also point out that there is a close analogy between coupling a nanomechanical resonator to a SSET in the vicinity of the JQP resonance and Doppler cooling of atoms by means of lasers.

We investigate the dynamical instabilities of a resonator coupled to a superconducting single-electron transistor (SSET) tuned to the Josephson quasiparticle (JQP) resonance. Starting from the quantum master equation of the system, we use a standard semiclassical approximation to derive a closed set of mean field equations which describe the average dynamics of the resonator and SSET charge. Using amplitude and phase coordinates for the resonator and assuming that the amplitude changes much more slowly than the phase, we explore the instabilities which arise in the resonator dynamics as a function of coupling to the SSET, detuning from the JQP resonance and the resonator frequency. We find that the locations (in parameter space) and sizes of the limit cycle states predicted by the mean field equations agree well with numerical solutions of the full master equation for sufficiently weak SSET-resonator coupling. The mean field equations also give a good qualitative description of the set of dynamical transitions in the resonator state that occur as the coupling is progressively increased.

The recent emergence of near-term climate prediction, wherein climate models are initialized with the contemporaneous state of the Earth system and integrated up to 10 years into the future, has prompted the development of three different multiannual forecasting techniques of North Atlantic hurricane frequency. Descriptions of these three different approaches, as well as their respective skill, are available in the peer-reviewed literature, but because these various studies are sufficiently different in their details (e.g., period covered, metric used to compute the skill, measure of hurricane activity), it is nearly impossible to compare them. Using the latest decadal reforecasts currently available, we present a direct comparison of these three multiannual forecasting techniques with a combination of simple statistical models, with the hope of offering a perspective on the current state-of-the-art research in this field and the skill level currently reached by these forecasts. Using both deterministic and probabilistic approaches, we show that these forecast systems have a significant level of skill and can improve on simple alternatives, such as climatological and persistence forecasts.

The Intergovernmental Panel on Climate Change's (IPCC) ''very likely'' statement that anthropogenic emissions are affecting climate is based on a statistical detection and attribution methodology that strongly depends on the characterization of internal climate variability. In this paper, the authors test the robustness of this statement in the case of global mean surface air temperature, under different representations of such variability. The contributions of the different natural and anthropogenic forcings to the global mean surface air temperature response are computed using a box diffusion model. Representations of internal climate variability are explored using simple stochastic models that nevertheless span a representative range of plausible temporal autocorrelation structures, including the short-memory first-order autoregressive [AR(1)] process and the long-memory fractionally differencing process. The authors find that, independently of the representation chosen, the greenhouse gas signal remains statistically significant under the detection model employed in this paper. The results support the robustness of the IPCC detection and attribution statement for global mean temperature change under different characterizations of internal variability, but they also suggest that a wider variety of robustness tests, other than simple comparisons of residual variance, should be performed when dealing with other climate variables and/or different spatial scales.