Single-photon Optomechanics

Optomechanics experiments are rapidly approaching the regime where the radiation pressure of a single photon displaces the mechanical oscillator by more than its zero-point uncertainty. We show that in this limit the power spectrum has multiple sidebands and that the cavity response has several resonances in the resolved-sideband limit. Using master-equation simulations, we also study the crossover from the weak-coupling many-photon to the single-photon strong-coupling regime. Finally, we find non-Gaussian steady-states of the mechanical oscillator when multi-photon transitions are resonant. Our study provides the tools to detect and take advantage of this novel regime of optomechanics.Comment: 4 pages, 4 figure

Cannon-Thurston maps for pared manifolds of bounded geometry

Let Nh ∈, H(M, P) be a hyperbolic structure of bounded geometry on a pared manifold such that each component of ∂0M = ∂M - P is incompressible. We show that the limit set of Nh is locally connected by constructing a natural Cannon-Thurston map. This provides a unified treatment, an alternate proof and a generalization of results due to Cannon and Thurston, Minsky, Bowditch, Klarreich and the author

Signatures of superfluidity for Feshbach-resonant Fermi gases

We consider atomic Fermi gases where Feshbach resonances can be used to continuously tune the system from weak to strong interaction regime, allowing to scan the whole BCS-BEC crossover. We show how a probing field transferring atoms out of the superfluid can be used to detect the onset of the superfluid transition in the high-$T_c$ and BCS regimes. The number of transferred atoms, as a function of the energy given by the probing field, peaks at the gap energy. The shape of the peak is asymmetric due to the single particle excitation gap. Since the excitation gap includes also a pseudogap contribution, the asymmetry alone is not a signature of superfluidity. Incoherent nature of the non-condensed pairs leads to broadening of the peak. The pseudogap and therefore the broadening decay below the critical temperature, causing a drastic increase in the asymmetry. This provides a signature of the transition.Comment: Revised version, accepted to Phys. Rev. Letters. Figures changed, explanations adde

On discreteness of commensurators

We begin by showing that commensurators of Zariski dense subgroups of isometry groups of symmetric spaces of non-compact type are discrete provided that the limit set on the Furstenberg boundary is not invariant under the action of a (virtual) simple factor. In particular for rank one or simple Lie groups, Zariski dense subgroups with non-empty domain of discontinuity have discrete commensurators. This generalizes a Theorem of Greenberg for Kleinian groups. We then prove that for all finitely generated, Zariski dense, infinite covolume discrete subgroups of Isom(H3), commensurators are discrete. Together these prove discreteness of commensurators for all known examples of finitely presented, Zariski dense, infinite covolume discrete subgroups of Isom(X) for X an irreducible symmetric space of non-compact type

The four-year experience of first-generation students at a small independent university : engagement, student learning, and satisfaction.

This dissertation explored the four-year college experience of first-generation and continuing-generation students at a small private institution. Using Astin\u27s I-E-O model (1970), the following variables in the student experience were considered: precollege student characteristics (input); engagement in academic experiences, cocurricular activities, campus relationships (environment); and satisfaction, learning (outcome). The sample consisted of seniors participating in the National Survey of Student Engagement (NSSE) and/or a direct measure of general education learning, the ETS Measure of Academic Proficiency and Progress. Results of the analysis of learning indicated no difference in first-generation and continuing-generation students\u27 measures (n = 342). One exception was found in a subsequent model built which excluded students who did not submit a FAFSA (less financially needy students); first-generation status was a positive predictor of learning (ß=.25). No precollege characteristics (input) or engagement variables (environment) were associated with learning (outcome), other than aptitude ACT composite (ß =.66, n = 39). Regarding satisfaction, no significant difference existed in senior measures between first-generation and continuing-generation students after controlling for aptitude (p \u3c .05). When considering the environmental variables which influence satisfaction, campus relationships were strong positive predictors of satisfaction (n = 175). These environment variables were calculated from NSSE Pike scalelets, four of which were significant (p \u3c .05): quality of campus relationships/interpersonal environment (ß =.59); varied education experience (ß = -.18); support for student success (ß =.17); and higher order thinking skills (ß =.14). No precollege characteristics significantly influenced satisfaction. In comparing the overall college experience, the difference in the student groups was limited to only a few variables, none of which influenced learning or satisfaction. First-generation students rated lower the quality of their campus relationships and the support they received for success (p \u3c .05). First-generation students typically worked more hours for pay, commuted to campus, and had greater financial need. The results of this single institution study did not support previous literature showing first-generation students high-risk, a characteristic which can influence retention, satisfaction, and learning. The most significant finding from this project was the positive influence of campus relationships on seniors\u27 satisfaction, regardless of parents\u27 education level

Mapping class groups and interpolating complexes: rank

Abstract. A family of interpolating graphs C(S, ξ) of complexity ξ is constructed for a surface S and -2 ≤ ξ ≤ ξ(S). For ξ = -2,-1, ξ (S) -1 these specialize to graphs quasi-isometric to the marking graph, the pants graph and the curve graph respectively. We generalize the notion of a hierarchy and Theorems of Brock-Farb and Behrstock-Minsky to show that the rank of C(S, ξ) is rξ, the largest number of disjoint copies of subsurfaces of complexity greater than ξ that may be embedded in S. The interpolating graphs C(S, ξ) interpolate between the pants graph and the curve graph

Influence of pure-dephasing by phonons on exciton-photon interfaces: Quantum microscopic theory

We have developed a full quantum microscopic theory to analyze the time evolution of transversal and longitudinal components of an exciton-single photon system coupled to bulk acoustic phonons. These components are subjected to two decay processes. One is radiative relaxation and the other is pure-dephasing due to exciton-phonon interaction. The former results in a decay with an exponent linear to time, while the latter causes a faster initial decay than the radiative decay. We analyzed the dependence of the components on the duration of the input one-photon pulse, temperature, and radiative relaxation rates. Such a quantitative analysis is important for the developments of atom-photon interfaces which enable coherent transfer of quantum information between photons and atomic systems. We found that, for a GaAs spherical quantum dot in which the exciton interacts with bulk phonons, the maximal probability of the excited state can be increased up to 75 %. This probability can be considered as the efficiency for quantum information transfer from photon to exciton.Comment: 9pages, 5figure