Universal quantum fluctuations of a cavity mode driven by a Josephson junction

We analyze the quantum dynamics of a superconducting cavity coupled to a voltage biased Josephson junction. The cavity is strongly excited at resonances where the voltage energy lost by a Cooper pair traversing the circuit is a multiple of the cavity photon energy. We find that the resonances are accompanied by substantial squeezing of the quantum fluctuations of the cavity over a broad range of parameters and are able to identify regimes where the fluctuations in the system take on universal values.Comment: 5 pages, 4 figure

Dissipation due to tunneling two-level systems in gold nanomechanical resonators

We present measurements of the dissipation and frequency shift in nanomechanical gold resonators at temperatures down to 10 mK. The resonators were fabricated as doubly-clamped beams above a GaAs substrate and actuated magnetomotively. Measurements on beams with frequencies 7.95 MHz and 3.87 MHz revealed that from 30 mK to 500 mK the dissipation increases with temperature as $T^{0.5}$, with saturation occurring at higher temperatures. The relative frequency shift of the resonators increases logarithmically with temperature up to at least 400 mK. Similarities with the behavior of bulk amorphous solids suggest that the dissipation in our resonators is dominated by two-level systems

Changes with Time in the Availability of Soil Applied Zinc to Navy Beans and in the Chemical Extraction of Zinc from Soils

The effect of the incubation of zinc (Zn) applied to the soil on Zn uptake and the Zn concentrations in chemical extractants was studied. In a glasshouse experiment using a Zn-deficient gravelly sandy loam, the effect of recently applied Zn was compared with that of Zn incubated with the soil for 15 days at 40°C on growth and Zn uptake by navy beans (Phaseolus vulgaris cv. Gallaroy). At the second harvest (33 days after sowing), the dry weight of shoots of recently applied Zn was consistently higher than that of incubated Zn, except at the highest rate of 1 µg Zn g-1 soil, where yields were similar. Comparisons of the slope of the linear regressions of Zn uptake as a function of rate of application showed that incubated Zn was approximately 80% as effective as recently applied Zn. A laboratory experiment measured the decrease in Zn concentration in HCl, EDTA, DTPA, and dilute CaCl2 with incubation for up to 8 days at 40°C in four contrasting soils from Western Australia and Queensland. An addition of 2.5 µg Zn g-1 soil increased the concentration of Zn in all extractants at all times of incubation compared with the untreated soil. The recovery of the added Zn was generally highest with HCl and lowest with 0.002 M CaCl2 and decreased exponentially in all extractants with increasing time of incubation in all soils. The order of the rate of decrease in Zn concentration for all extractants was krasnozem \u3e gravelly sandy loam \u3e sand \u3e sandy clay loam. The model, Y = CtB, where C and B are constants, was used to describe the relationship between the recovery of added Zn and time of incubation

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

Nonlinear modal coupling in a high-stress doubly-clamped nanomechanical resonator

We present results from a study of the nonlinear intermodal coupling between different flexural vibrational modes of a single high-stress, doubly-clamped silicon nitride nanomechanical beam. The measurements were carried out at 100 mK and the beam was actuated using the magnetomotive technique. We observed the nonlinear behavior of the modes individually and also measured the coupling between them by driving the beam at multiple frequencies. We demonstrate that the different modes of the resonator are coupled to each other by the displacement induced tension in the beam, which also leads to the well known Duffing nonlinearity in doubly-clamped beams.Comment: 15 pages, 7 figure

Measuring mechanical motion with a single spin

We study theoretically the measurement of a mechanical oscillator using a single two level system as a detector. In a recent experiment, we used a single electronic spin associated with a nitrogen vacancy center in diamond to probe the thermal motion of a magnetized cantilever at room temperature {Kolkowitz et al., Science 335, 1603 (2012)}. Here, we present a detailed analysis of the sensitivity limits of this technique, as well as the possibility to measure the zero point motion of the oscillator. Further, we discuss the issue of measurement backaction in sequential measurements and find that although backaction heating can occur, it does not prohibit the detection of zero point motion. Throughout the paper we focus on the experimental implementation of a nitrogen vacancy center coupled to a magnetic cantilever; however, our results are applicable to a wide class of spin-oscillator systems. Implications for preparation of nonclassical states of a mechanical oscillator are also discussed.Comment: 17 pages, 6 figure