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

Tunable coupling to a mechanical oscillator circuit using a coherent feedback network

We demonstrate a fully cryogenic microwave feedback network composed of modular superconducting devices connected by transmission lines and designed to control a mechanical oscillator coupled to one of the devices. The network features an electromechanical device and a tunable controller that coherently receives, processes and feeds back continuous microwave signals that modify the dynamics and readout of the mechanical state. While previous electromechanical systems represent some compromise between efficient control and efficient readout of the mechanical state, as set by the electromagnetic decay rate, the tunable controller produces a closed-loop network that can be dynamically and continuously tuned between both extremes much faster than the mechanical response time. We demonstrate that the microwave decay rate may be modulated by at least a factor of 10 at a rate greater than $10^4$ times the mechanical response rate. The system is easy to build and suggests that some useful functions may arise most naturally at the network-level of modular, quantum electromagnetic devices.Comment: 11 pages, 6 figures, final published versio

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

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

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

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

Geometry, topology and dynamics of geodesic flows on noncompact polygonal surfaces

We establish the background for the study of geodesics on noncompact polygonal surfaces. For illustration, we study the recurrence of geodesics on $Z$-periodic polygonal surfaces. We prove, in particular, that almost all geodesics on a topologically typical $Z$-periodic surface with boundary are recurrent.Comment: 34 pages, 13 figures. To be published in V. V. Kozlov's Festschrif

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

Ergodicity of certain cocycles over certain interval exchanges

We show that for odd-valued piecewise-constant skew products over a certain two parameter family of interval exchanges, the skew product is ergodic for a full-measure choice of parameters