Quantum Simulation with Interacting Photons (1605.00383v2)

Abstract: Enhancing optical nonlinearities so that they become appreciable on the single photon level and lead to nonclassical light fields has been a central objective in quantum optics for many years. After this has been achieved in individual micro-cavities representing an effectively zero-dimensional volume, this line of research has shifted its focus towards engineering devices where such strong optical nonlinearities simultaneously occur in extended volumes of multiple nodes of a network. Recent technological progress in several experimental platforms now opens the possibility to employ the systems of strongly interacting photons these give rise to as quantum simulators. Here we review the recent development and current status of this research direction for theory and experiment. Addressing both, optical photons interacting with atoms and microwave photons in networks of superconducting circuits, we focus on analogue quantum simulations in scenarios where effective photon-photon interactions exceed dissipative processes in the considered platforms.

Overview of Quantum Simulation with Interacting Photons

The paper by Michael J. Hartmann, titled "Quantum Simulation with Interacting Photons," provides an extensive examination of the use of interacting photons in quantum simulations, specifically focusing on the substantial technological and theoretical advancements in the field over recent years. This area of research is pivotal in quantum optics, aiming to engineer systems where strong optical nonlinearities enable significant interactions between individual photons. The paper extensively covers both analogue quantum simulations involving optical photons interacting with atoms in networks, as well as those with microwave photons in superconducting circuits.

Scientific Context and Motivation

Quantum simulations are highly valuable for studying complex quantum many-body systems that are beyond the reach of classical computational methods. A core challenge in this domain involves managing the exponentially growing dimensionality of the Hilbert space as the number of quantum particles increases. By utilizing quantum systems to simulate other quantum systems, researchers hope to gain insights into otherwise intractable problems in many-body physics. The focus of Hartmann’s paper is on leveraging interacting photons as quantum simulators capable of unravelling complex phenomena inherent in quantum many-body physics.

Interacting Photons in Quantum Simulations

Optical Photons and Nonlinear Media

Initially, the review discusses quantum simulations using optical photons that interact with atomic media. A significant breakthrough in this area is the engineering of strong optical nonlinearities at the single-photon level within individual micro-cavities. The attention has then shifted to systems where these nonlinearities occur concurrently across extended networks of cavities. The research is particularly interesting because of its potential applications in simulating many-body models like the Bose-Hubbard and Jaynes-Cummings-Hubbard models.

The review presents the Bose-Hubbard model with dark state polaritons as a framework where effective on-site interactions between excitations are realized. Additionally, systems utilizing exciton-polaritons, which are quasiparticles arising from strong coupling of photons and electronic excitations in semiconductors, are explored as another mechanism for simulating many-body environments.

Furthermore, the paper explores the Jaynes-Cummings-Hubbard model, which describes coupled atom-cavity systems, highlighting its relevance in simulating spin models and other complex quantum systems.

Microwave Photons in Superconducting Circuits

In parallel, substantial progress has been made with superconducting circuits where microwave photons are involved. These circuits, via Josephson junctions and transmon qubits, have allowed for the exploration of strong photon-photon interactions and the realization of phenomena analogous to those found in cavity QED, but with enhanced ease of manipulation at microwave frequencies. The paper of Bose-Hubbard models and Jaynes-Cummings-Hubbard models within these systems is noteworthy, given their potential scalability and quantum coherence properties.

The paper mentions non-local interactions achieved in these systems, emphasizing their capability to emulate cross-Kerr interactions, which are significant in the paper of quantum technologies.

Future Prospects and Implications

The reviewed research has implications for advancing both theoretical understanding and practical applications of quantum simulation. By demonstrating the feasibility of simulating highly correlated quantum systems, the paper suggests possible pathways for future discoveries in quantum computation and the development of new materials.

The use of interacting photons as quantum simulators addresses potential breakthroughs in quantum technologies, including the realization of novel quantum phases and the investigation of topological effects. Hartmann's synthesis points toward a future where such systems could drastically enhance our capability to simulate and manipulate complex quantum phenomena, providing a foundational step towards scalable quantum computing and other quantum technologies.

In conclusion, Hartmann’s review presents a comprehensive overview of the state-of-the-art in using interacting photons for quantum simulation, outlining significant advances and pointing towards future directions in both experimental and theoretical domains. The focus on both optical and microwave regimes opens multiple avenues for continued research and potential applications in various quantum technology fields.