Kuramoto model with coupling through an external medium

Synchronization of coupled oscillators is often described using the Kuramoto model. Here we study a generalization of the Kuramoto model where oscillators communicate with each other through an external medium. This generalized model exhibits interesting new phenomena such as bistability between synchronization and incoherence and a qualitatively new form of synchronization where the external medium exhibits small-amplitude oscillations. We conclude by discussing the relationship of the model to other variations of the Kuramoto model including the Kuramoto model with a bimodal frequency distribution and the Millennium Bridge problem.Comment: 9 pages, 3 figure

Comment on "Evidence for Quantized Displacement in Macroscopic Nanomechanical Oscillators"

In a recent Letter, Gaidarzhy et al. [1] claim to have observed evidence for "quantized displacements" of a high-order mode of a nanomechanical oscillator. We contend that the methods employed by the authors are unsuitable in principle to observe such states for any harmonic mode

Ion trap transducers for quantum electromechanical oscillators

An enduring challenge for contemporary physics is to experimentally observe and control quantum behavior in macroscopic systems. We show that a single trapped atomic ion could be used to probe the quantum nature of a mesoscopic mechanical oscillator precooled to 4K, and furthermore, to cool the oscillator with high efficiency to its quantum ground state. The proposed experiment could be performed using currently available technology.Comment: 4 pages, 2 figure

Exciton lifetime in InAs/GaAs quantum dot molecules

The exciton lifetimes $T_1$ in arrays of InAs/GaAs vertically coupled quantum dot pairs have been measured by time-resolved photoluminescence. A considerable reduction of $T_1$ by up to a factor of $\sim$ 2 has been observed as compared to a quantum dots reference, reflecting the inter-dot coherence. Increase of the molecular coupling strength leads to a systematic decrease of $T_1$ with decreasing barrier width, as for wide barriers a fraction of structures shows reduced coupling while for narrow barriers all molecules appear to be well coupled. The coherent excitons in the molecules gain the oscillator strength of the excitons in the two separate quantum dots halving the exciton lifetime. This superradiance effect contributes to the previously observed increase of the homogeneous exciton linewidth, but is weaker than the reduction of $T_2$. This shows that as compared to the quantum dots reference pure dephasing becomes increasingly important for the molecules

A high-reflectivity high-Q micromechanical Bragg-mirror

We report on the fabrication and characterization of a micromechanical oscillator consisting only of a free-standing dielectric Bragg mirror with high optical reflectivity and high mechanical quality. The fabrication technique is a hybrid approach involving laser ablation and dry etching. The mirror has a reflectivity of 99.6%, a mass of 400ng, and a mechanical quality factor Q of approximately 10^4. Using this micromirror in a Fabry Perot cavity, a finesse of 500 has been achieved. This is an important step towards designing tunable high-Q high-finesse cavities on chip.Comment: 3 pages, 2 figure

Enhancement of Cavity Cooling of a Micromechanical Mirror Using Parametric Interactions

It is shown that an optical parametric amplifier inside a cavity can considerably improve the cooling of the micromechanical mirror by radiation pressure. The micromechanical mirror can be cooled from room temperature 300 K to sub-Kelvin temperatures, which is much lower than what is achievable in the absence of the parametric amplifier. Further if in case of a precooled mirror one can reach millikelvin temperatures starting with about 1 K. Our work demonstrates the fundamental dependence of radiation pressure effects on photon statistics.Comment: 14 pages, 7 figure

Self-cooling of a micro-mirror by radiation pressure

We demonstrate passive feedback cooling of a mechanical resonator based on radiation pressure forces and assisted by photothermal forces in a high-finesse optical cavity. The resonator is a free-standing high-reflectance micro-mirror (of mass m=400ng and mechanical quality factor Q=10^4) that is used as back-mirror in a detuned Fabry-Perot cavity of optical finesse F=500. We observe an increased damping in the dynamics of the mechanical oscillator by a factor of 30 and a corresponding cooling of the oscillator modes below 10 K starting from room temperature. This effect is an important ingredient for recently proposed schemes to prepare quantum entanglement of macroscopic mechanical oscillators.Comment: 11 pages, 9 figures, minor correction

Statistical mechanics of transcription-factor binding site discovery using Hidden Markov Models

Hidden Markov Models (HMMs) are a commonly used tool for inference of transcription factor (TF) binding sites from DNA sequence data. We exploit the mathematical equivalence between HMMs for TF binding and the "inverse" statistical mechanics of hard rods in a one-dimensional disordered potential to investigate learning in HMMs. We derive analytic expressions for the Fisher information, a commonly employed measure of confidence in learned parameters, in the biologically relevant limit where the density of binding sites is low. We then use techniques from statistical mechanics to derive a scaling principle relating the specificity (binding energy) of a TF to the minimum amount of training data necessary to learn it.Comment: 25 pages, 2 figures, 1 table V2 - typos fixed and new references adde

Steady-state spin densities and currents

This article reviews steady-state spin densities and spin currents in materials with strong spin-orbit interactions. These phenomena are intimately related to spin precession due to spin-orbit coupling which has no equivalent in the steady state of charge distributions. The focus will be initially on effects originating from the band structure. In this case spin densities arise in an electric field because a component of each spin is conserved during precession. Spin currents arise because a component of each spin is continually precessing. These two phenomena are due to independent contributions to the steady-state density matrix, and scattering between the conserved and precessing spin distributions has important consequences for spin dynamics and spin-related effects in general. In the latter part of the article extrinsic effects such as skew scattering and side jump will be discussed, and it will be shown that these effects are also modified considerably by spin precession. Theoretical and experimental progress in all areas will be reviewed