Quantum Friction of Micromechanical Resonators at Low Temperatures

Dissipation of micro- and nano-scale mechanical structures is dominated by quantum-mechanical tunneling of two-level defects intrinsically present in the system. We find that at high frequencies--usually, for smaller, micron-scale structures--a novel mechanism of phonon pumping of two-level defects gives rise to weakly temperature-dependent internal friction, $Q^{-1}$, concomitant to the effects observed in recent experiments. Due to their size, comparable to or shorter than the emitted phonon wavelength, these structures suffer from superradiance-enhanced dissipation by the collective relaxation of a large number of two-level defects contained within the wavelength.Comment: To apear in Phys. Rev. Let

Spin-1/2 Heisenberg-Antiferromagnet on the Kagome Lattice: High Temperature Expansion and Exact Diagonalisation Studies

For the spin-$\frac{1}{2}$ Heisenberg antiferromagnet on the Kagom\'e lattice we calculate the high temperature series for the specific heat and the structure factor. A comparison of the series with exact diagonalisation studies shows that the specific heat has further structure at lower temperature in addition to a high temperature peak at $T\approx 2/3$. At $T=0.25$ the structure factor agrees quite well with results for the ground state of a finite cluster with 36 sites. At this temperature the structure factor is less than two times its $T=\infty$ value and depends only weakly on the wavevector $\bf q$, indicating the absence of magnetic order and a correlation length of less than one lattice spacing. The uniform susceptibility has a maximum at $T\approx 1/6$ and vanishes exponentially for lower temperatures.Comment: 15 pages + 5 figures, revtex, 26.04.9

Landau levels in the case of two degenerate coupled bands: kagome lattice tight-binding spectrum

The spectrum of charged particles hopping on a kagome lattice in a uniform transverse magnetic field shows an unusual set of Landau levels at low field. They are unusual in two respects: the lowest Landau levels are paramagnetic so their energies decrease linearly with increasing field magnitude, and the spacings between the levels are not equal. These features are shown to follow from the degeneracy of the energy bands in zero magnetic field. We give a general discussion of Landau levels in the case of two degenerate bands, and show how the kagome lattice tight-binding model includes one special case of this more general problem. We also discuss the consequences of this for the behavior of the critical temperature of a kagome grid superconducting wire network, which is the experimental system that originally motivated this work.Comment: 18 pages, 8 figure

Quantum Interference on the Kagom\'e Lattice

We study quantum interference effects due to electron motion on the Kagom\'e lattice in a perpendicular magnetic field. These effects arise from the interference between phase factors associated with different electron closed-paths. From these we compute, analytically and numerically, the superconducting-normal phase boundary for Kagom\'e superconducting wire networks and Josephson junction arrays. We use an analytical approach to analyze the relationship between the interference and the complex structure present in the phase boundary, including the origin of the overall and fine structure. Our results are obtained by exactly summing over one thousand billion billions ($\sim 10^{21}$) closed paths, each one weighted by its corresponding phase factor representing the net flux enclosed by each path. We expect our computed mean-field phase diagrams to compare well with several proposed experiments.Comment: 9 pages, Revtex, 3 figures upon reques

Possible chiral phase transition in two-dimensional solid 3^3He

We study a spin system with two- and four-spin exchange interactions on the triangular lattice, which is a possible model for the nuclear magnetism of solid $^3$He layers. It is found that a novel spin structure with scalar chiral order appears if the four-spin interaction is dominant. Ground-state properties are studied using the spin-wave approximation. A phase transition concerning the scalar chirality occurs at a finite temperature, even though the dimensionality of the system is two and the interaction has isotropic spin symmetry. Critical properties of this transition are studied with Monte Carlo simulations in the classical limit.Comment: 4 pages, Revtex, 4 figures, to appear in Phys.Rev.Let

Quantum Noise Limits for Nonlinear, Phase-Invariant Amplifiers

Any quantum device that amplifies coherent states of a field while preserving their phase generates noise. A nonlinear, phase-invariant amplifier may generate less noise, over a range of input field strengths, than any linear amplifier with the same amplification. We present explicit examples of such nonlinear amplifiers, and derive lower bounds on the noise generated by a nonlinear, phase-invariant quantum amplifier.Comment: RevTeX, 6 pages + 4 figures (included in file; hard copy sent on request

Imaginary Squashing Mode Spectroscopy of Helium Three B

We have made precision measurements of the frequency of a collective mode of the superfluid 3He-B order parameter, the J=2- imaginary squashing mode. Measurements were performed at multiple pressures using interference of transverse sound in an acoustic cavity. Transverse waves propagate in the vicinity of this order parameter mode owing to off-resonant coupling. At the crossing of the sound mode and the order parameter mode, the sound wave is strongly attenuated. We use both velocity and attenuation measurements to determine precise values of the mode frequency with a resolution between 0.1% and 0.25%.Comment: 6 pages, 4 figures, submitted to proceedings of Quantum Fluids and Solids (QFS) Conference 2006; revised 9/26/0

Anomaly in the stability limit of liquid helium 3

We propose that the liquid-gas spinodal line of helium 3 reaches a minimum at 0.4 K. This feature is supported by our cavitation measurements. We also show that it is consistent with extrapolations of sound velocity measurements. Speedy [J. Phys. Chem. 86, 3002 (1982)] previously proposed this peculiar behavior for the spinodal of water and related it to a change in sign of the expansion coefficient alpha, i. e. a line of density maxima. Helium 3 exhibits such a line at positive pressure. We consider its extrapolation to negative pressure. Our discussion raises fundamental questions about the sign of alpha in a Fermi liquid along its spinodal.Comment: 5 pages, 3 figure

Elastic Wave Transmission at an Abrupt Junction in a Thin Plate, with Application to Heat Transport and Vibrations in Mesoscopic Systems

The transmission coefficient for vibrational waves crossing an abrupt junction between two thin elastic plates of different widths is calculated. These calculations are relevant to ballistic phonon thermal transport at low temperatures in mesoscopic systems and the Q for vibrations in mesoscopic oscillators. Complete results are calculated in a simple scalar model of the elastic waves, and results for long wavelength modes are calculated using the full elasticity theory calculation. We suggest that thin plate elasticty theory provide a useful and tractable approximation to the full three dimensional geometry.Comment: 35 pages, including 12 figure

Evidence for a Self-Bound Liquid State and the Commensurate-Incommensurate Coexistence in 2D 3^3He on Graphite

We made heat-capacity measurements of two dimensional (2D) $^3$He adsorbed on graphite preplated with monolayer $^4$He in a wide temperature range (0.1 $\leq T \leq$ 80 mK) at densities higher than that for the 4/7 phase (= 6.8 nm$^{-2}$). In the density range of 6.8 $\leq \rho \leq$ 8.1 nm$^{-2}$, the 4/7 phase is stable against additional $^3$He atoms up to 20% and they are promoted into the third layer. We found evidence that such promoted atoms form a self-bound 2D Fermi liquid with an approximate density of 1 nm$^{-2}$ from the measured density dependence of the $\gamma$-coefficient of heat capacity. We also show evidence for the first-order transition between the commensurate 4/7 phase and the ferromagnetic incommensurate phase in the second layer in the density range of 8.1 $\leq \rho \leq$ 9.5 nm$^{-2}$.Comment: 6 pages, 4 figure