The Theory of Matrices. By F R. Gantmacher. Two volumes, pp. 374 and 276. 1959. (Translated from the Russian by K. A. Hirsch; Chelsea Publishing Company, New York)

Microwave photonics with superconducting quantum circuits

In the past 20 years, impressive progress has been made both experimentally and theoretically in superconducting quantum circuits, which provide a platform for manipulating microwave photons. This emerging field of superconducting quantum microwave circuits has been driven by many new interesting phenomena in microwave photonics and quantum information processing. For instance, the interaction between superconducting quantum circuits and single microwave photons can reach the regimes of strong, ultra-strong, and even deep-strong coupling. Many higher-order effects, unusual and less familiar in traditional cavity quantum electrodynamics with natural atoms, have been experimentally observed, e.g., giant Kerr effects, multi-photon processes, and single-atom induced bistability of microwave photons. These developments may lead to improved understanding of the counterintuitive properties of quantum mechanics, and speed up applications ranging from microwave photonics to superconducting quantum information processing. In this article, we review experimental and theoretical progress in microwave photonics with superconducting quantum circuits. We hope that this global review can provide a useful roadmap for this rapidly developing field.

Reciprocity is a fundamental principle in optics, requiring that the response of a transmission channel is symmetric when source and observation points are interchanged. It is of major significance because it poses fundamental constraints on the way we process optical signals. Non-reciprocal devices, which break this symmetry, have become fundamental in photonic systems. Today they require magnetic materials that are bulky, costly and cannot be integrated. This is in stark contrast with most photonic devices, including sources, modulators, switches, waveguides, interconnects and antennas, which may be realized at the nanoscale. Here, we review recent progress and opportunities offered by temporal modulation to break reciprocity, revealing its potential for compact, low-energy, integrated non-reciprocal devices, and discuss the future of this exciting research field. The progress on non-reciprocal photonic devices enabled by temporal modulation is reviewed.

Non-reciprocal photonics based on time modulation

A system theory criterion for positive real matrices

Fabrication techniques indicate that it is easier to obtain earthed capacitors than unearthed ones in integrated circuits. To take advantage of these techniques, a method to earth all capacitors, by replacing them with earthed gyrator-capacitor combinations, is described here.

Grounding of capacitors in integrated circuits

A direct-coupled gyrator circuit which can be easily realised in integrated-circuit form is described. Since the gyrator action extends to d.c., it is practicable to realise d.c. transformers by cascading two such gyrators.

Direct-coupled gyrator suitable for integrated circuits and time variation

http://ieeexplore.ieee.org/iel5/5/31077/01446251.pdf

On reciprocity and time-variable networks

The paper deals with the synthesis of passive networks and relies on general systems theory and control concepts. The network-synthesis problem is first interpreted in state-variable terminology, solved as a control problem and the solution is then translated back into network-theory terms. After a review of state-space formulations, an algebraic theory of synthesis is developed, beginning with a minimal state-space realisation, perhaps obtained through control-theory procedures, from which a synthesis of rational positive-real impedance matrices is obtained through a transformation on the state. The method rests upon an appropriate basis change, in the state-space, obtained by factoring the Pmatrix of the control-theory positive real lemma. The minimum number of resistors and reactive elements is used. The paper also serves as a review of the ‘state-of-the-art’ for formal nport synthesis; the results lead to new methods of attacking open problems, as well as to methods of analysis and synthesis via digital computers.

Impedance synthesis via state-space techniques

Using constant transformations and matrix embeddings it is shown how to find all constant realizations of an arbitrary rational transfer function matrix. Explicit means of calculating the transformations are given and the theory is applied to finding essentially all equivalent networks.

R.W. Newcomb

Papers

Grounding of capacitors in integrated circuits

Direct-coupled gyrator suitable for integrated circuits and time variation

On reciprocity and time-variable networks

Impedance synthesis via state-space techniques

Equivalence of linear time-invariant dynamical systems