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

Local rigidity of hyperbolic manifolds with geodesic boundary

Let W be a compact hyperbolic n-manifold with totally geodesic boundary. We prove that if n>3 then the holonomy representation of pi_1 (W) into the isometry group of hyperbolic n-space is infinitesimally rigid.Comment: 30 page

Design of nanophotonic circuits for autonomous subsystem quantum error correction

We reapply our approach to designing nanophotonic quantum memories to formulate an optical network that autonomously protects a single logical qubit against arbitrary single-qubit errors. Emulating the 9 qubit Bacon-Shor subsystem code, the network replaces the traditionally discrete syndrome measurement and correction steps by continuous, time-independent optical interactions and coherent feedback of unitarily processed optical fields.Comment: 12 pages, 4 figure

Triangulations and volume form on moduli spaces of flat surfaces

In this paper, we are interested in flat metric structures with conical singularities on surfaces which are obtained by deforming translation surface structures. The moduli space of such flat metric structures can be viewed as some deformation of the moduli space of translation surfaces. Using geodesic triangulations, we define a volume form on this moduli space, and show that, in the well-known cases, this volume form agrees with usual ones, up to a multiplicative constant.Comment: 42 page

The dressed atom as binary phase modulator: towards attojoule/edge optical phase-shift keying

Nanophotonic technologies offer great promise for ultra-low power optical signal processing, but relatively few nonlinear-optical phenomena have yet been explored as bases for robust digital modulation/switching~\cite{Yang07,Fara08,Liu10,Noza10}. Here we show that a single two-level system (TLS) coupled strongly to an optical resonator can impart binary phase modulation on a saturating probe beam. Our experiment relies on spontaneous emission to induce occasional transitions between positive and negative phase shifts---with each such edge corresponding to a dissipated energy of just one photon ($\approx 0.23$ aJ)---but an optical control beam could be used to trigger additional phase switching at signalling rates above this background. Although our ability to demonstrate controlled switching in our atom-based experiment is limited, we discuss prospects for exploiting analogous physics in a nanophotonic device incorporating a quantum dot as the TLS to realize deterministic binary phase modulation with control power in the aJ/edge regime.Comment: 7 pages, 4 figure

Upgrading the Local Ergodic Theorem for planar semi-dispersing billiards

The Local Ergodic Theorem (also known as the `Fundamental Theorem') gives sufficient conditions under which a phase point has an open neighborhood that belongs (mod 0) to one ergodic component. This theorem is a key ingredient of many proofs of ergodicity for billiards and, more generally, for smooth hyperbolic maps with singularities. However the proof of that theorem relies upon a delicate assumption (Chernov-Sinai Ansatz), which is difficult to check for some physically relevant models, including gases of hard balls. Here we give a proof of the Local Ergodic Theorem for two dimensional billiards without using the Ansatz.Comment: 17 pages, 2 figure

Recurrence in generic staircases

The straight-line flow on almost every staircase and on almost every square tiled staircase is recurrent. For almost every square tiled staircase the set of periodic orbits is dense in the phase space

Escape orbits and Ergodicity in Infinite Step Billiards

In a previous paper we defined a class of non-compact polygonal billiards, the infinite step billiards: to a given decreasing sequence of non-negative numbers $\{p_{n}$, there corresponds a table \Bi := \bigcup_{n\in\N} [n,n+1] \times [0,p_{n}]. In this article, first we generalize the main result of the previous paper to a wider class of examples. That is, a.s. there is a unique escape orbit which belongs to the alpha and omega-limit of every other trajectory. Then, following a recent work of Troubetzkoy, we prove that generically these systems are ergodic for almost all initial velocities, and the entropy with respect to a wide class of ergodic measures is zero.Comment: 27 pages, 8 figure