Seeing spin dynamics in atomic gases

The dynamics of internal spin, electronic orbital, and nuclear motion states of atoms and molecules have preoccupied the atomic and molecular physics community for decades. Increasingly, such dynamics are being examined within many-body systems composed of atomic and molecular gases. Our findings sometimes bear close relation to phenomena observed in condensed-matter systems, while on other occasions they represent truly new areas of investigation. I discuss several examples of spin dynamics that occur within spinor Bose-Einstein gases, highlighting the advantages of spin-sensitive imaging for understanding and utilizing such dynamics.Comment: Chapter in upcoming Review Volume entitled "From Atomic to Mesoscale: The Role of Quantum Coherence in Systems of Various Complexities" from World Scientifi

Contraction and stability analysis of steady-states for open quantum systems described by Lindblad differential equations

For discrete-time systems, governed by Kraus maps, the work of D. Petz has characterized the set of universal contraction metrics. In the present paper, we use this characterization to derive a set of quadratic Lyapunov functions for continuous-time systems, governed by Lindblad differential equations, that have a steady-state with full rank. An extremity of this set is given by the Bures metric, for which the quadratic Lyapunov function is obtained by inverting a Sylvester equation. We illustrate the method by providing a strict Lyapunov function for a Lindblad equation designed to stabilize a quantum electrodynamic "cat" state by reservoir engineering. In fact we prove that any Lindblad equation on the Hilbert space of the (truncated) harmonic oscillator, which has a full-rank equilibrium and which has, among its decoherence channels, a channel corresponding to the photon loss operator, globally converges to that equilibrium.Comment: Submitted (10 pages, 1 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

Digital Signal Processing Research Program

Contains table of contents for Section 2, an introduction, reports on twenty-two research projects and a list of publications.Sanders, a Lockheed-Martin Corporation Contract BZ4962U.S. Army Research Laboratory Contract DAAL01-96-2-0001U.S. Navy - Office of Naval Research Grant N00014-93-1-0686National Science Foundation Grant MIP 95-02885U.S. Navy - Office of Naval Research Grant N00014-96-1-0930National Defense Science and Engineering FellowshipU.S. Air Force - Office of Scientific Research Grant F49620-96-1-0072U.S. Navy - Office of Naval Research Grant N00014-95-1-0362National Science Foundation Graduate Research FellowshipAT&T Bell Laboratories Graduate Research FellowshipU.S. Army Research Laboratory Contract DAAL01-96-2-0002National Science Foundation Graduate FellowshipU.S. Army Research Laboratory/Advanced Sensors Federated Lab Program Contract DAAL01-96-2-000