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

Cavity Induced Interfacing of Atoms and Light

This chapter introduces cavity-based light-matter quantum interfaces, with a single atom or ion in strong coupling to a high-finesse optical cavity. We discuss the deterministic generation of indistinguishable single photons from these systems; the atom-photon entanglement intractably linked to this process; and the information encoding using spatio-temporal modes within these photons. Furthermore, we show how to establish a time-reversal of the aforementioned emission process to use a coupled atom-cavity system as a quantum memory. Along the line, we also discuss the performance and characterisation of cavity photons in elementary linear-optics arrangements with single beam splitters for quantum-homodyne measurements.Comment: to appear as a book chapter in a compilation "Engineering the Atom-Photon Interaction" published by Springer in 2015, edited by A. Predojevic and M. W. Mitchel

Feedback Network Models for Quantum Transport

Quantum feedback networks have been introduced in quantum optics as a set of rules for constructing arbitrary networks of quantum mechanical systems connected by uni-directional quantum optical fields, and has allowed for a system theoretic approach to open quantum optics systems. Our aim here is to establish a network theory for quantum transport systems where typically the mediating fields between systems are bi-directional. Mathematically this leads us to study quantum feedback networks where fields arrive at ports in input-output pairs, which is then just a specially case of the uni-directional theory. However, it is conceptually important to develop this theory in the context of quantum transport theory, and the resulting theory extends traditional approaches which tends to view the components in quantum transport as scatterers for the various fields, in the process allows us to consider emission and absorption of field quanta by these components. The quantum feedback network theory is applicable to both Bose and Fermi fields, moreover it applies to nonlinear dynamics for the component systems. In this first paper on the subject, we advance the general theory, but study the case of linear passive quantum components in some detail.Comment: 15 pages, 17 figure

Feedback control of quantum state reduction

Feedback control of quantum mechanical systems must take into account the probabilistic nature of quantum measurement. We formulate quantum feedback control as a problem of stochastic nonlinear control by considering separately a quantum filtering problem and a state feedback control problem for the filter. We explore the use of stochastic Lyapunov techniques for the design of feedback controllers for quantum spin systems and demonstrate the possibility of stabilizing one outcome of a quantum measurement with unit probability

Large collective Lamb shift of two distant superconducting artificial atoms

Virtual photons can mediate interaction between atoms, resulting in an energy shift known as a collective Lamb shift. Observing the collective Lamb shift is challenging, since it can be obscured by radiative decay and direct atom-atom interactions. Here, we place two superconducting qubits in a transmission line terminated by a mirror, which suppresses decay. We measure a collective Lamb shift reaching 0.8% of the qubit transition frequency and exceeding the transition linewidth. We also show that the qubits can interact via the transmission line even if one of them does not decay into it.Comment: 7+5 pages, 4+2 figure