Feedback cooling of a cantilever's fundamental mode below 5 mK

We cool the fundamental mechanical mode of an ultrasoft silicon cantilever from a base temperature of 2.2 K to 2.9 +/- 0.3 mK using active optomechanical feedback. The lowest observed mode temperature is consistent with limits determined by the properties of the cantilever and by the measurement noise. For high feedback gain, the driven cantilever motion is found to suppress or "squash" the optical interferometer intensity noise below the shot noise level.Comment: 4 pages, 6 figure

Nuclear spin relaxation induced by a mechanical resonator

We report on measurements of the spin lifetime of nuclear spins strongly coupled to a micromechanical cantilever as used in magnetic resonance force microscopy. We find that the rotating-frame correlation time of the statistical nuclear polarization is set by the magneto-mechanical noise originating from the thermal motion of the cantilever. Evidence is based on the effect of three parameters: (1) the magnetic field gradient (the coupling strength), (2) the Rabi frequency of the spins (the transition energy), and (3) the temperature of the low-frequency mechanical modes. Experimental results are compared to relaxation rates calculated from the spectral density of the magneto-mechanical noise.Comment: 4 pages, 4 figure

Dynamical Properties of a Growing Surface on a Random Substrate

The dynamics of the discrete Gaussian model for the surface of a crystal deposited on a disordered substrate is investigated by Monte Carlo simulations. The mobility of the growing surface was studied as a function of a small driving force $F$ and temperature $T$. A continuous transition is found from high-temperature phase characterized by linear response to a low-temperature phase with nonlinear, temperature dependent response. In the simulated regime of driving force the numerical results are in general agreement with recent dynamic renormalization group predictions.Comment: 10 pages, latex, 3 figures, to appear in Phys. Rev. E (RC

Soliton Staircases and Standing Strain Waves in Confined Colloidal Crystals

We show by computer simulation of a two-dimensional crystal confined by corrugated walls that confinement can be used to impose a controllable mesoscopic superstructure of predominantly mechanical elastic character. Due to an interplay of the particle density of the system and the width D of the confining channel, "soliton staircases" can be created along both parallel confining boundaries, that give rise to standing strain waves in the entire crystal. The periodicity of these waves is of the same order as D. This mechanism should be useful for structure formation in the self-assembly of various nanoscopic materials.Comment: 22 pages, 5 figure

Symmetric-Asymmetric transition in mixtures of Bose-Einstein condensates

We propose a new kind of quantum phase transition in phase separated mixtures of Bose-Einstein condensates. In this transition, the distribution of the two components changes from a symmetric to an asymmetric shape. We discuss the nature of the phase transition, the role of interface tension and the phase diagram. The symmetric to asymmetric transition is the simplest quantum phase transition that one can imagine. Careful study of this problem should provide us new insight into this burgeoning field of discovery.Comment: 6 pages, 3 eps figure

Fractional Quantum Hall States in Narrow Channels

A model system is considered where two dimensional electrons are confined by a harmonic potential in one direction, and are free in the other direction. Ground state in strong magnetic fields is investigated through numerical diagonalization of the Hamiltonian. It is shown that the fractional quantum Hall states are realized even in the presence of the external potential under suitable conditions, and a phase diagram is obtained.Comment: 8 pages, 2 figures (not included

Wigner crystallization and metal-insulator transition of two-dimensional holes in GaAs/AlGaAs at B=0

We report the transport properties of a low disorder two-dimensional hole system (2DHS) in the GaAs/AlGaAs heterostructure, which has an unprecedentedly high peak mobility of $7\times 10^5cm^2/Vs$, with hole density of $4.8\times 10^9 cm^{-2}<p<3.72\times 10^{10}cm^{-2}$ in the temperature range of $50mK<T<1.3K$. From their T, p, and electric field dependences, we find that the metal-insulator transition in zero magnetic field in this exceptionally clean 2DHS occurs at $r_s=35.1\pm0.9$, which is in good agreement with the critical $r_s$ for Wigner crystallization ${r_s}^c=37\pm 5$, predicted by Tanatar and Ceperley for an ideally clean 2D system.Comment: 4 pages, 4 Postscript figure

Melting of the classical bilayer Wigner crystal: influence of the lattice symmetry

The melting transition of the five different lattices of a bilayer crystal is studied using the Monte-Carlo technique. We found the surprising result that the square lattice has a substantial larger melting temperature as compared to the other lattice structures, which is a consequence of the specific topology of the temperature induced defects. A new melting criterion is formulated which we show to be universal for bilayers as well as for single layer crystals.Comment: 4 pages, 5 figures (postscript files). Accepted in Physical Review Letter

A Bias-Aware EnKF Estimator for Aerodynamic Flows

Ensemble methods can integrate measurement data and CFD-based models to estimate the state of fluid systems in a robust and cost-efficient way. However, discretization errors can render numerical solutions a biased representation of reality. Left unaccounted for, biased forecast and observation models can lead to poor estimator performance. In this work, we propose a low-rank representation for the bias whose dynamics is represented by a colorednoise process. System state and bias parameters are simultaneously corrected on-line with the Ensemble Kalman Filter (EnKF) algorithm. The proposed methodology is demonstrated to achieve a 70% error reduction for the problem of estimating the state of the two-dimensional low-Re flow past a flat plate at high angle of attack using an ensemble of coarse-mesh simulations and pressure measurements at the surface of the body, compared to a bias-blind estimator. Strategies to determine the bias statistics and to deal with nonlinear observation functions in the context of ensemble methods are discussed