Mesoscopic Mechanical Resonators as Quantum Non-Inertial Reference Frames

An atom attached to a micrometer-scale wire that is vibrating at a frequency of 100 MHz and with displacement amplitude 1 nm experiences an acceleration magnitude 10^9 ms^-2, approaching the surface gravity of a neutron star. As one application of such extreme non-inertial forces in a mesoscopic setting, we consider a model two-path atom interferometer with one path consisting of the 100 MHz vibrating wire atom guide. The vibrating wire guide serves as a non-inertial reference frame and induces an in principle measurable phase shift in the wave function of an atom traversing the wire frame. We furthermore consider the effect on the two-path atom wave interference when the vibrating wire is modeled as a quantum object, hence functioning as a quantum non-inertial reference frame. We outline a possible realization of the vibrating wire, atom interferometer using a superfluid helium quantum interference setup.Comment: Published versio

Quantum analysis of a nonlinear microwave cavity-embedded dc SQUID displacement detector

We carry out a quantum analysis of a dc SQUID mechanical displacement detector, comprising a SQUID with mechanically compliant loop segment, which is embedded in a microwave transmission line resonator. The SQUID is approximated as a nonlinear, current dependent inductance, inducing an external flux tunable, nonlinear Duffing self-interaction term in the microwave resonator mode equation. Motion of the compliant SQUID loop segment is transduced inductively through changes in the external flux threading SQUID loop, giving a ponderomotive, radiation pressure type coupling between the microwave and mechanical resonator modes. Expressions are derived for the detector signal response and noise, and it is found that a soft-spring Duffing self-interaction enables a closer approach to the displacement detection standard quantum limit, as well as cooling closer to the ground state

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

The Effect of Surface Roughness on the Universal Thermal Conductance

We explain the reduction of the thermal conductance below the predicted universal value observed by Schwab et al. in terms of the scattering of thermal phonons off surface roughness using a scalar model for the elastic waves. Our analysis shows that the thermal conductance depends on two roughness parameters: the roughness amplitude $\delta$ and the correlation length $a$. At sufficiently low temperatures the conductance decrease from the universal value quadratically with temperature at a rate proportional to $\delta ^{2}a$. Values of $\delta$ equal to 0.22 and $a$ equal to about 0.75 of the width of the conduction pathway give a good fit to the data.Comment: 10 pages, 5 figures. Ref. added, typo correcte

Combining research and design: A mixed methods approach aimed at understanding and optimising inpatient medication storage systems

BACKGROUND: Almost every patient admitted to hospital will receive medication during their stay. Medication errors are an important cause of patient morbidity and mortality, as well as an economic burden for healthcare institutions. Research suggests that current methods of storing medication on hospital wards are not fit for purpose, contributing to inefficiency and error. AIM: To improve medication storage in inpatient areas, by exploring variation and challenges related to medication storage and designing a prototype solution. METHODS: Set in four hospitals in an English teaching hospital trust, the study used a mixed methods approach comprising a quantitative descriptive survey of storage facilities and practices followed by mixed methods observations of medication rounds and interviews with patients, nurses and pharmacy staff. Quantitative data were presented descriptively and qualitative data analysed thematically and using a human-centered design approach. RESULTS: We identified wide variation in medication storage facilities and practices across 77 wards. Observations and staff interviews in six wards revealed five problem areas: poor management of multiple storage facilities; lack of visibility and organisation of medication within trolleys; inadequate size of storage; lack of ownership and knowledge of standard practice; and use of key locks. Patients were largely satisfied with receiving their medication. Systematic and consistent physical organisation of medication in medication trolleys, and integrating and implementing principles of best practice, were identified as areas for intervention. DISCUSSION AND CONCLUSION: Variation in medication storage facilities and practices existed both across the organization and on individual wards. Multiple challenges were identified in how medication was stored, which if addressed may improve the efficiency and safety of medication administration and in turn, staff and patient experience. The use of design principles alongside a research approach resulted in a rapid, iterative process for developing and refining potential solutions to improve inpatient medication storage

Phonon-mediated thermal conductance of mesoscopic wires with rough edges

We present an analysis of acoustic phonon propagation through long, free-standing, insulating wires with rough surfaces. Due to a crossover from ballistic propagation of the lowest-frequency phonon mode at $\omega <\omega _{1}=\pi c/W$ to a diffusive (or even localized) behavior upon the increase of phonon frequency, followed by re-entrance into the quasi-ballistic regime, the heat conductance of a wire acquires an intermediate tendency to saturate within the temperature range $T\sim \hbar \omega_{1}/k_{B}$.Comment: 4 pages, 3 figures included; minor changes and corrections, figures 1 and 2 replaced by better versions; to appear in PRB Brief Report

Noise properties of two single electron transistors coupled by a nanomechanical resonator

We analyze the noise properties of two single electron transistors (SETs) coupled via a shared voltage gate consisting of a nanomechanical resonator. Working in the regime where the resonator can be treated as a classical system, we find that the SETs act on the resonator like two independent heat baths. The coupling to the resonator generates positive correlations in the currents flowing through each of the SETs as well as between the two currents. In the regime where the dynamics of the resonator is dominated by the back-action of the SETs, these positive correlations can lead to parametrically large enhancements of the low frequency current noise. These noise properties can be understood in terms of the effects on the SET currents of fluctuations in the state of a resonator in thermal equilibrium which persist for times of order the resonator damping time.Comment: Accepted for publication in Phys. Rev.

Graphical Evolution of Spin Network States

The evolution of spin network states in loop quantum gravity can be described by introducing a time variable, defined by the surfaces of constant value of an auxiliary scalar field. We regulate the Hamiltonian, generating such an evolution, and evaluate its action both on edges and on vertices of the spin network states. The analytical computations are carried out completely to yield a finite, diffeomorphism invariant result. We use techniques from the recoupling theory of colored graphs with trivalent vertices to evaluate the graphical part of the Hamiltonian action. We show that the action on edges is equivalent to a diffeomorphism transformation, while the action on vertices adds new edges and re-routes the loops through the vertices.Comment: 24 pages, 21 PostScript figures, uses epsfig.sty, Minor corrections in the final formula in the main body of the paper and in the formula for the Tetrahedral net in the Appendi

Closed-Flux Solutions to the Constraints for Plane Gravity Waves

The metric for plane gravitational waves is quantized within the Hamiltonian framework, using a Dirac constraint quantization and the self-dual field variables proposed by Ashtekar. The z axis (direction of travel of the waves) is taken to be the entire real line rather than the torus (manifold coordinatized by (z,t) is RxR rather than $S_1$ x R). Solutions to the constraints proposed in a previous paper involve open-ended flux lines running along the entire z axis, rather than closed loops of flux; consequently, these solutions are annihilated by the Gauss constraint at interior points of the z axis, but not at the two boundary points. The solutions studied in the present paper are based on closed flux loops and satisfy the Gauss constraint for all z.Comment: 18 pages; LaTe