Strong Optomechanical Squeezing of Light

We create squeezed light by exploiting the quantum nature of the mechanical interaction between laser light and a membrane mechanical resonator embedded in an optical cavity. The radiation pressure shot noise (fluctuating optical force from quantum laser amplitude noise) induces resonator motion well above that of thermally driven motion. This motion imprints a phase shift on the laser light, hence correlating the amplitude and phase noise, a consequence of which is optical squeezing. We experimentally demonstrate strong and continuous optomechanical squeezing of 1.7 +/- 0.2 dB below the shot noise level. The peak level of squeezing measured near the mechanical resonance is well described by a model whose parameters are independently calibrated and that includes thermal motion of the membrane with no other classical noise sources.Comment: 12 pages, 8 figure

The Kelvin Formula for Thermopower

Thermoelectrics are important in physics, engineering, and material science due to their useful applications and inherent theoretical difficulty, especially in strongly correlated materials. Here we reexamine the framework for calculating the thermopower, inspired by ideas of Lord Kelvin from 1854. We find an approximate but concise expression, which we term as the Kelvin formula for the the Seebeck coefficient. According to this formula, the Seebeck coefficient is given as the particle number $N$ derivative of the entropy $\Sigma$, at constant volume $V$ and temperature $T$, $S_{\text{Kelvin}}=\frac{1}{q_e}\{\frac{\partial {\Sigma}}{\partial N} \}_{V,T}$. This formula is shown to be competitive compared to other approximations in various contexts including strongly correlated systems. We finally connect to a recent thermopower calculation for non-Abelian fractional quantum Hall states, where we point out that the Kelvin formula is exact.Comment: 6 pages, 2 figure

Measurement and Compensation of Horizontal Crabbing at the Cornell Electron Storage Ring Test Accelerator

In storage rings, horizontal dispersion in the rf cavities introduces horizontal-longitudinal (xz) coupling, contributing to beam tilt in the xz plane. This coupling can be characterized by a "crabbing" dispersion term {\zeta}a that appears in the normal mode decomposition of the 1-turn transfer matrix. {\zeta}a is proportional to the rf cavity voltage and the horizontal dispersion in the cavity. We report experiments at the Cornell Electron Storage Ring Test Accelerator (CesrTA) where xz coupling was explored using three lattices with distinct crabbing properties. We characterize the xz coupling for each case by measuring the horizontal projection of the beam with a beam size monitor. The three lattice configurations correspond to a) 16 mrad xz tilt at the beam size monitor source point, b) compensation of the {\zeta}a introduced by one of two pairs of RF cavities with the second, and c) zero dispersion in RF cavities, eliminating {\zeta}a entirely. Additionally, intrabeam scattering (IBS) is evident in our measurements of beam size vs. rf voltage.Comment: 5 figures, 10 page

Finite temperature properties of the triangular lattice t-J model, applications to Nax_xCoO2_2

We present a finite temperature ($T$) study of the t-J model on the two-dimensional triangular lattice for the negative hopping $t$, as relevant for the electron-doped Na$_x$CoO$_2$ (NCO). To understand several aspects of this system, we study the $T$-dependent chemical potential, specific heat, magnetic susceptibility, and the dynamic Hall-coefficient across the entire doping range. We show systematically, how this simplest model for strongly correlated electrons describes a crossover as function of doping ($x$) from a Pauli-like weakly spin-correlated metal close to the band-limit (density $n=2$) to the Curie-Weiss metallic phase ($1.5<n<1.75$) with pronounced anti-ferromagnetic (AFM) correlations at low temperatures and Curie-Weiss type behavior in the high-temperature regime. Upon further reduction of the doping, a new energy scale, dominated by spin-interactions ($J$) emerges (apparent both in specific heat and susceptibility) and we identify an effective interaction $J_{eff}(x)$, valid across the entire doping range. This is distinct from Anderson's formula, as we choose here $t<0$, hence the opposite sign of the usual Nagaoka-ferromagnetic situation. This expression includes the subtle effect of weak kinetic AFM - as encountered in the infinitely correlated situation ($U=\infty$). By explicit computation of the Kubo-formulae, we address the question of practical relevance of the high-frequency expression for the Hall coefficient $R_H^*$. We hope to clarify some open questions concerning the applicability of the t-J model to real experimental situations through this study

Improving broadband displacement detection with quantum correlations

Interferometers enable ultrasensitive measurement in a wide array of applications from gravitational wave searches to force microscopes. The role of quantum mechanics in the metrological limits of interferometers has a rich history, and a large number of techniques to surpass conventional limits have been proposed. In a typical measurement configuration, the tradeoff between the probe's shot noise (imprecision) and its quantum backaction results in what is known as the standard quantum limit (SQL). In this work we investigate how quantum correlations accessed by modifying the readout of the interferometer can access physics beyond the SQL and improve displacement sensitivity. Specifically, we use an optical cavity to probe the motion of a silicon nitride membrane off mechanical resonance, as one would do in a broadband displacement or force measurement, and observe sensitivity better than the SQL dictates for our quantum efficiency. Our measurement illustrates the core idea behind a technique known as \textit{variational readout}, in which the optical readout quadrature is changed as a function of frequency to improve broadband displacement detection. And more generally our result is a salient example of how correlations can aid sensing in the presence of backaction.Comment: 17 pages, 5 figure

Trehalose Is A Chemical Attractant In The Establishment Of Coral Symbiosis

Coral reefs have evolved with a crucial symbiosis between photosynthetic dinoflagellates (genus Symbiodinium) and their cnidarian hosts (Scleractinians). Most coral larvae take up Symbiodinium from their environment; however, the earliest steps in this process have been elusive. Here we demonstrate that the disaccharide trehalose may be an important signal from the symbiont to potential larval hosts. Symbiodinium freshly isolated from Fungia scutaria corals constantly released trehalose (but not sucrose, maltose or glucose) into seawater, and released glycerol only in the presence of coral tissue. Spawning Fungia adults increased symbiont number in their immediate area by excreting pellets of Symbiodinium, and when these naturally discharged Symbiodinium were cultured, they also released trehalose. In Y-maze experiments, coral larvae demonstrated chemoattractant and feeding behaviors only towards a chamber with trehalose or glycerol. Concomitantly, coral larvae and adult tissue, but not symbionts, had significant trehalase enzymatic activities, suggesting the capacity to utilize trehalose. Trehalase activity was developmentally regulated in F. scutaria larvae, rising as the time for symbiont uptake occurs. Consistent with the enzymatic assays, gene finding demonstrated the presence of a trehalase enzyme in the genome of a related coral, Acropora digitifera, and a likely trehalase in the transcriptome of F. scutaria. Taken together, these data suggest that adult F. scutaria seed the reef with Symbiodinium during spawning and the exuded Symbiodinium release trehalose into the environment, which acts as a chemoattractant for F. scutaria larvae and as an initiator of feeding behavior- the first stages toward establishing the coral-Symbiodinium relationship. Because trehalose is a fixed carbon compound, this cue would accurately demonstrate to the cnidarian larvae the photosynthetic ability of the potential symbiont in the ambient environment. To our knowledge, this is the first report of a chemical cue attracting the motile coral larvae to the symbiont