Quantum Simulations with Photons and Polaritons, 1st ed. 2017 Merging Quantum Optics with Condensed Matter Physics Quantum Science and Technology Series

This book reviews progress towards quantum simulators based on photonic and hybrid light-matter systems, covering theoretical proposals and recent experimental work.  Quantum simulators are specially designed quantum computers. Their main aim is to simulate and understand complex and inaccessible quantum many-body phenomena found or predicted in condensed matter physics, materials science and exotic quantum field theories. Applications will include the engineering of smart materials, robust optical or electronic circuits, deciphering quantum chemistry and even the design of drugs.

Technological developments in the fields of interfacing light and matter, especially in many-body quantum optics, have motivated recent proposals for quantum simulators based on strongly correlated photons and polaritons generated in hybrid light-matter systems. The latter have complementary strengths to cold atom and ion based simulators and they can probe for example out of equilibrium phenomena in a natural driven-dissipative setting. This book covers some of the most important works in this area reviewing the proposal for Mott transitions and Luttinger liquid physics with light,  to simulating interacting relativistic theories, topological insulators and gauge field physics. The stage of the field now is at a point where on top of the numerous theory proposals; experiments are also reported.

Connecting to the theory proposals presented in the chapters, the main experimental quantum technology platforms developed from groups worldwide to realize photonic and polaritonic simulators in the laboratory are also discussed. These include coupled microwave resonator arrays in superconducting circuits, semiconductor based polariton systems,  and integrated quantum photonic chips.

Introduction; Dimitris G. Angelakis

1 Strongly correlated polaritons in nonlinear cavity arrays; Andrea Tomadin, Davide Rossini, Rosario Fazio.

1.1 Introduction. 1.2 Modelling of nonlinear cavity-arrays. 1.3 Equilibrium phase diagram of cavity-array models. 1.4 Nonequilibrium dynamics of cavity-array models. References.

2 Phase diagram and excitations of the Jaynes-Cummings-Hubbard model; Sebastian Schmidt and Gianni Blatter.

2.1 Introduction. 2.2 Degenerate perturbation theory. 2.3 Greens function approach. 2.4 Slave-boson approach. 2.5 Critical exponents. 2.6 Relation to the Dicke model. 2.7 Acknowledgement. References.

3 Out-of-equilibrium physics in driven dissipative photonic resonator arrays; Changsuk Noh, Stephen R. Clark, Dieter Jaksch, Dimitris G. Angelakis.

3.1 Introduction. 3.2 Modelling CRAs. 3.3 Computing the properties of CRAs. 3.4 Non-equilibrium many-body phases of photons in CRAs. 3.5 Summary and outlook. References.

4 Topological physics with photons; Mohammad Hafezi and Jacob Taylor.

4.1 Introduction. 4.2 Gauge field and topological features in noninteracting photonic system. 4.3 Interacting photons and many-body regime. 4.4 Outlook. References.

5 Exciton-Polariton Quantum Simulators; Na Young Kim and Yoshihisa Yamamoto.

5.1 Introduction. 5.2 Hardware of Exciton-Polariton Quantum Simulators. 5.3 Software of Exciton-Polariton Analog Quantum Simulators. 5.4 Exciton-Polaritons in Two-Dimensional Lattices. 5.5 Outlook. References.

6.1 Introduction. 6.2 Nanophotonic platforms:  light propagation and confinement. 6.3 Strongly correlated photons on chip. 6.4 Conclusions and outlook. References.

7 Quantum simulations with circuit quantum electrodynamics; Guillermo Romero, Enrique Solano, and Lucas Lamata.

7.1 Introduction. 7.2 Circuit Network Theory. 7.3 Circuit Quantum Electrodynamics. 7.4 Analog Quantum Simulations with Superconducting Circuits. 7.5 Digital Quantum Simulations with Superconducting Circuits. 7.6 Conclusion. References.

8 Dirac Dynamics  in  Waveguide  Arrays: From Zitterbewegung to  Photonic Topological Insulators; F. Dreisow, M. C. Rechtsman, J. M. Zeuner,  Y. Plotnik, R. Keil, S. Nolte, M. Segev, and A. Szameit.

Glossary.

The first title to address the growing field of photonic quantum simulators

Contains contributions from all leading groups working in the field reviewing many different approaches

Describes theoretical proposals and ongoing experimental work

Includes supplementary material: sn.pub/extras