Dynamical instabilities of a resonator driven by a superconducting single-electron transistor

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.Comment: 23 pages, 6 Figures, Accepted for NJ

Dynamics of a nanomechanical resonator coupled to a superconducting single-electron transistor

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

Entanglement and decoherence of a micromechanical resonator via coupling to a Cooper box

We analyse the quantum dynamics of a micromechanical resonator capacitively coupled to a Cooper box. With appropriate quantum state control of the Cooper box, the resonator can be driven into a superposition of spatially separated states. The Cooper box can also be used to probe the environmentally-induced decoherence of the resonator superposition state.Comment: 4 pages, 3 figure

Peculiar Features of the Interaction Potential between Hydrogen and Antihydrogen at Intermediate Separations

We evaluate the interaction potential between a hydrogen and an antihydrogen using the second-order perturbation theory within the framework of the four-body system in a separable two-body basis. We find that the H-Hbar interaction potential possesses the peculiar features of a shallow local minimum located around interatomic separations of r ~ 6 a.u. and a barrier rising at r~5 a.u. Additional theoretical and experimental investigations on the nature of these peculiar features will be of great interest.Comment: 13 pages, 6 figure

Quantum master equation descriptions of a nanomechanical resonator coupled to a single-electron transistor

We analyse the quantum dynamics of a nanomechanical resonator coupled to a normal-state single-electron transistor (SET). Starting from a microscopic description of the system, we derive a master equation for the SET island charge and resonator which is valid in the limit of weak electro-mechanical coupling. Using this master equation we show that, apart from brief transients, the resonator always behaves like a damped harmonic oscillator with a shifted frequency and relaxes into a thermal-like steady state. Although the behaviour remains qualitatively the same, we find that the magnitude of the resonator damping rate and frequency shift depend very sensitively on the relative magnitudes of the resonator period and the electron tunnelling time. Maximum damping occurs when the electrical and mechanical time-scales are the same, but the frequency shift is greatest when the resonator moves much more slowly than the island charge. We then derive reduced master equations which describe just the resonator dynamics. By making slightly different approximations, we obtain two different reduced master equations for the resonator. Apart from minor differences, the two reduced master equations give rise to a consistent picture of the resonator dynamics which matches that obtained from the master equation including the SET island charge.Comment: 22 pages, 4 figure

Current noise of a superconducting single electron transistor coupled to a resonator

We analyze the current and zero-frequency current noise properties of a superconducting single electron resonator (SSET) coupled to a resonator, focusing on the regime where the SSET is operated in the vicinity of the Josephson quasiparticle resonance. We consider a range of coupling strengths and resonator frequencies to reflect the fact that in practice the system can be tuned to quite a high degree with the resonator formed either by a nanomechanical oscillator or a superconducting stripline fabricated in close proximity to the SSET. For very weak couplings the SSET acts on the resonator like an effective thermal bath. In this regime the current characteristics of the SSET are only weakly modified by the resonator. Using a mean field approach, we show that the current noise is nevertheless very sensitive to the correlations between the resonator and the SSET charge. For stronger couplings, the SSET can drive the resonator into limit cycle states where self-sustained oscillation occurs and we find that regions of well-defined bistability exist. Dynamical transitions into and out of the limit cycle state are marked by strong fluctuations in the resonator energy, but these fluctuations are suppressed within the limit cycle state. We find that the current noise of the SSET is strongly influenced by the fluctuations in the resonator energy and hence should provide a useful indicator of the resonator's dynamics.Comment: Reduced quality figures for arXiv version; v2 minor correction

Distribution and abundance of fish and crayfish in a Waikato stream in relation to basin area

The aim of this study was to relate the longitudinal distribution of fish and crayfish to increasing basin area and physical site characteristics in the Mangaotama Stream, Waikato region, North Island, New Zealand. Fish and crayfish were captured with two-pass removal electroshocking at 11 sites located in hill-country with pasture, native forest, and mixed land uses within the 21.6 km2 basin. Number of fish species and lineal biomass of fish increased with increasing basin area, but barriers to upstream fish migration also influenced fish distribution; only climbing and non-migratory species were present above a series of small waterfalls. Fish biomass increased in direct proportion to stream width, suggesting that fish used much of the available channel, and stream width was closely related to basin area. Conversely, the abundance of crayfish was related to the amount of edge habitat, and therefore crayfish did not increase in abundance as basin area increased. Densities of all fish species combined ranged from 17 to 459 fish 100 m-2, and biomass ranged from 14 to 206 g m-2. Eels dominated the fish assemblages, comprising 85-100% of the total biomass; longfinned eels the majority of the biomass at most sites. Despite the open access of the lower sites to introduced brown trout, native species dominated all the fish communities sampled

How hosts control worms

No abstract available

Quantum dynamics of a Josephson junction driven cavity mode system in the presence of voltage bias noise

We give a semiclassical analysis of the average photon number as well as photon number variance (Fano factor F) for a Josephson junction (JJ) embedded microwave cavity system, where the JJ is subject to a fluctuating (i.e., noisy) bias voltage with finite dc average. Through the ac Josephson effect, the dc voltage bias drives the effectively nonlinear microwave cavity mode into an amplitude squeezed state (F <1), as has been established previously [Armour et al., Phys. Rev. Lett. 111, 247001 (2013)], but bias noise acts to degrade this squeezing. We find that the sensitivity of the Fano factor to bias voltage noise depends qualitatively on which stable fixed point regime the system is in for the corresponding classical nonlinear steady-state dynamics. Furthermore, we show that the impact of voltage bias noise is most significant when the cavity is excited to states with large average photon number