The shape of hyperbolic Dehn surgery space

In this paper we develop a new theory of infinitesimal harmonic deformations for compact hyperbolic 3-manifolds with ``tubular boundary''. In particular, this applies to complements of tubes of radius at least R_0 = \arctanh(1/\sqrt{3}) \approx 0.65848 around the singular set of hyperbolic cone manifolds, removing the previous restrictions on cone angles. We then apply this to obtain a new quantitative version of Thurston's hyperbolic Dehn surgery theorem, showing that all generalized Dehn surgery coefficients outside a disc of ``uniform'' size yield hyperbolic structures. Here the size of a surgery coefficient is measured using the Euclidean metric on a horospherical cross section to a cusp in the complete hyperbolic metric, rescaled to have area 1. We also obtain good estimates on the change in geometry (e.g. volumes and core geodesic lengths) during hyperbolic Dehn filling. This new harmonic deformation theory has also been used by Bromberg and his coworkers in their proofs of the Bers Density Conjecture for Kleinian groups.Comment: 46 pages, 3 figure

The SLH framework for modeling quantum input-output networks

Many emerging quantum technologies demand precise engineering and control over networks consisting of quantum mechanical degrees of freedom connected by propagating electromagnetic fields, or quantum input-output networks. Here we review recent progress in theory and experiment related to such quantum input-output networks, with a focus on the SLH framework, a powerful modeling framework for networked quantum systems that is naturally endowed with properties such as modularity and hierarchy. We begin by explaining the physical approximations required to represent any individual node of a network, eg. atoms in cavity or a mechanical oscillator, and its coupling to quantum fields by an operator triple $(S,L,H)$. Then we explain how these nodes can be composed into a network with arbitrary connectivity, including coherent feedback channels, using algebraic rules, and how to derive the dynamics of network components and output fields. The second part of the review discusses several extensions to the basic SLH framework that expand its modeling capabilities, and the prospects for modeling integrated implementations of quantum input-output networks. In addition to summarizing major results and recent literature, we discuss the potential applications and limitations of the SLH framework and quantum input-output networks, with the intention of providing context to a reader unfamiliar with the field.Comment: 60 pages, 14 figures. We are still interested in receiving correction

Remnants of semiclassical bistability in the few-photon regime of cavity QED

Broadband homodyne detection of the light transmitted by a Fabry-Perot cavity containing a strongly-coupled $^{133}$Cs atom is used to probe the dynamic optical response in a regime where semiclassical theory predicts bistability but strong quantum corrections should apply. While quantum fluctuations destabilize true equilibrium bistability, our observations confirm the existence of metastable states with finite lifetimes and a hysteretic response is apparent when the optical drive is modulated on comparable timescales. Our experiment elucidates remnant semiclassical behavior in the attojoule ($\sim10$ photon) regime of single-atom cavity QED, of potential significance for ultra-low power photonic signal processing.Comment: 14 pages, 7 figure

A superconducting microwave multivibrator produced by coherent feedback

We investigate a coherent nonlinear feedback circuit constructed from pre-existing superconducting microwave devices. The network exhibits emergent bistable and astable states, and we demonstrate its operation as a latch and the frequency locking of its oscillations. While the network is tedious to model by hand, our observations agree quite well with the semiclassical dynamical model produced by a new software package [N. Tezak et al., arXiv:1111.3081v1] that systematically interpreted an idealized schematic of the system as a quantum optic feedback network.Comment: 9 double-spaced pages, 5 figures and supplement. To appear in Phys. Rev. Let

Single-sideband modulator for frequency domain multiplexing of superconducting qubit readout

We introduce and experimentally characterize a superconducting single-sideband modulator compatible with cryogenic microwave circuits, and propose its use for frequency domain multiplexing of superconducting qubit readout. The monolithic single-quadrature modulators that comprise the device are formed with purely reactive elements (capacitors and Josephson junction inductors) and require no microwave-frequency control tones. Microwave signals in the 4 to 8 GHz band, with power up to -85 dBm, are converted up or down in frequency by as much as 120 MHz. Spurious harmonics in the device can be suppressed by up to 25 dB for select probe and modulation frequencies.Comment: 5 page main text, 6 page supplementary informatio

The extended mapping class group is generated by three symmetries

We prove that the extended mapping class group is generated by three orientation reversing involutions.Comment: A version of the article which appeared in C. R. Acad. Sc