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

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

Real elements in the mapping class group of T2T^2

We present a complete classification of elements in the mapping class group of the torus which have a representative that can be written as a product of two orientation reversing involutions. Our interest in such decompositions is motivated by features of the monodromy maps of real fibrations. We employ the property that the mapping class group of the torus is identifiable with $SL(2,\Z)$ as well as that the quotient group $PSL(2,\Z)$ is the symmetry group of the {\em Farey tessellation} of the Poincar\'e disk.Comment: 15 pages, 11 figure

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

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

Cosmological Time in (2+1) - Gravity

We consider maximal globally hyperbolic flat (2+1) spacetimes with compact space S of genus g>1. For any spacetime M of this type, the length of time that the events have been in existence is M defines a global time, called the cosmological time CT of M, which reveals deep intrinsic properties of spacetime. In particular, the past/future asymptotic states of the cosmological time recover and decouple the linear and the translational parts of the ISO(2,1)-valued holonomy of the flat spacetime. The initial singularity can be interpreted as an isometric action of the fundamental group of S on a suitable real tree. The initial singularity faithfully manifests itself as a lack of smoothness of the embedding of the CT level surfaces into the spacetime M. The cosmological time determines a real analytic curve in the Teichmuller space of Riemann surfaces of genus g, which connects an interior point (associated to the linear part of the holonomy) with a point on Thurston's natural boundary (associated to the initial singularity).Comment: Totally new version with strongly improved exposition. Clarifying examples and figures have been included. 21 pages, Latex, 9 figure

Letter from W[illia]m G. Kerckhoff to W[illia]m H. Knight, 1899 Apr 28.

[ COPY ]WM.G. KERCKHOFF,T. P. LUKENS, CHARLES SILENT.JOHN F. FRANCIS,M. L. GRAFF,ADOLPH PETSCH,ABBOT KINNEY.Forest and water Assoriationof Lus Angeles county.[Los Angeles Branch of the Forest and Water Society of Southern California.]WM.G.KERCKHOFF. president,254 S. Los Angeles St.,T.P.LUKENS, Vice-pres.,pasadena.WM.H.KNIGHT, Secretary,27Bryson block.Lus Angeles, Cal. April 28, 1899.To the HonorableSECRETARY OF THE INTERIOR,Washington, D. C.Dear Sir:The Forest and Water Association of Los Angeles County desires most respectfully to call your attention to the following facts: The conservation of our mountain forests is a work of the most vital importance to the people of Southern California. In noother locality of the United States is the welfare of its people so dependent on the protection of its forests, and the preservation of its water sheds.During the past three years a very large proportion of our forest reservations has been devastated and denuded by forest fires and the herding of sheep and other stock upon them, and the damage and loss to Southern California from these causes has been incalculable.We are now approaching the dry season of another year, in a succession of years with a very limited rainfall, and as yet with nosteps taken, so far as we have learned, to provide a force of men at all adequate to properly care for these reservations during the coming dry season; and it is imperative that some suitable action be taken at once in the line of caring for these reservations in a manner commensurate with the great importance of the work.We would, most respectfully yet most urgently, request that you grant us, at the earliest possible time, adequate aid for properly caring for these reservations, and would suggest:1. That the herding of sheep or other stock upon the reservations, or the passage of stock over them, (which is often used as a pretense in order to get an opportunity to use them for pasture) be absolutely prohibited.2. Large portions of the Sierra Madre Range are very rugged and precipitous, being almost inaccessible except by the use of trails, the construction of which should be provided for so that fires may be readily combatted.,br\u3e3. The forest reservations are largely used for the purpose of camping in the summer time, and many of the forest fires are to tributable to the06195 Forest and \u27water Assariation. No. 2.careless use of camp fires. We recommend a system of permits to be granted at the entrances to these reserves, under such regulations as will not make it a hardship upon the people desiring to camp, but which at the same time will keep out irresponsible parties and check the careless use of fire.4. In addition to the force required in other forest reservations of Southern California, we estimate that the San Gabriel Reservation, which is mainly within this County, will require at least two companies of soldiers.5. When civilians are selected for patrolmen, we suggest that they be taken from the mountaineers who are familiar with these localities.6. We also urge the importance of replanting the denuded portions of our mountains as rapidly as possible to such varieties of trees as are known to be best adapted to the conditions and requirements. If permitted to remain bare for any length of time, the rain will gully the steep slopes and wash away the little remaining soil, carrying debris to cover the rich valley lands, and there will be no water for irrigation.A Forestry School has been organized under the auspices of the University of Southern California for the purpose of furnishing educated foresters to the Government. Associations, general and local, for the protection of our forest reservations, are being organized all over Southern California. These embrace our most prominent citizens who are giving it much careful thought and attention, and who are desirous of aiding and upholding the Government in every way possible. We believe that these organizations, if permitted, could furnish the Department with many valuable suggestions. In this connection we tender to the Government the aid and assistance of our Association.Very respectfully,WM. G. KERCKHOFF, President.WM. H. KNIGHTSecretary