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Synthetic Gauge Fields in Quantum Optics

Periodic Reporting for period 1 - SynOptic (Synthetic Gauge Fields in Quantum Optics)

Reporting period: 2015-10-01 to 2017-09-30

Controlling the flow of light lies at the heart of many current and emerging technologies. For example, we use photonics everyday to image the world around us and to transmit information over long distances in optical fibers. There are also ongoing efforts to develop photonic processing units to be included in faster and more energy-efficient all-optical computer chips and/or integrated with standard semiconductor technology. In the longer-term, the quantum properties of light may even be exploited for quantum communication and computing.

Along with these developments in optical sciences, research in quantum condensed matter physics has dramatically advanced our understanding of “topological states of matter”, as recognized by the 2016 Physics Nobel Prize. In these systems, electrons can flow along one-way surface channels that are unaffected by disorder and dirt in the sample. This exotic physics arises from the interplay of the electrical charge of the electron and “gauge fields”, such as magnetic fields.

Now, a fast-growing research area is uniting these two strands to engineer topological photonic states to enhance quantum optical technologies, for example, by providing robust one-way waveguides for light. However, photons do not carry an electrical charge and so do not respond in the same way as electrons to magnetic fields. Instead, innovative approaches are needed to engineer the effects of the magnetic field synthetically.

In this Fellowship, our objective was to theoretically propose ways to implement synthetic magnetic fields or “spin-orbit couplings” for light, and to understand how such effects can be explored in cutting-edge experiments. This is important as optical set-ups can be used to engineer new types of topological systems, allowing us to study the fundamentals of topological physics, as well as to make progress towards applications in robust optical components or, in the long-term, even fault-free topological quantum computing.
Our project was divided into several key themes based on developing synthetic gauge fields for systems including photonic resonator lattices, classical pendula and optical fiber loops. Throughout, we built on local and international collaborations, and benefited from a strong synergy with other research lines active at the host institution on institutional funds or on other projects.

Firstly, we explored new effects arising from synthetic gauge fields in two-dimensional photonic resonator lattices. In this direction, we explored how strain can lead to a controllable pseudo-magnetic field in honeycomb lattices that simulate the motion of electrons in a strained sheet of graphene. We showed, in particular, how strain can be used to control the propagation of light at the edge of such lattices. We then explored how recent experiments on synthetic gauge fields for square resonator lattices would be affected by additional energy shifts mimicking a harmonic trapping potential. As we had previously shown, the eigenstates of such a model can be interpreted as unusual momentum-space Landau levels on a torus. We then proposed an optical experiment to probe this physics, and expanded the analogy of momentum-space magnetism to explore a “momentum-space quantum Hall effect”.

Secondly, we investigated new ways to implement synthetic gauge fields and energy bands with non-trivial geometrical properties in classical set-ups. In an experimental collaboration with the group of Peschel (Jena), we showed that the Berry curvature, a geometrical property of an energy band, can be mapped out from the motion of a wave-packet in an “optical mesh lattice” of two coupled optical fiber loops. This provided both the first direct observation of Berry curvature effects in an optical system, as well as a proof-of-principle demonstration that wave-packet dynamics provide a high-resolution tool for probing geometric properties. Separately, we theoretically proposed how to engineer a synthetic magnetic field for classical pendula by driving the pendula quickly in time. We also collaborated with the group of Pugno (Trento) to demonstrate experimentally that a synthetic spin-orbit coupling for pendula can be engineered by pre-tensioning the springs connecting six pendula in a hexagon.

Finally, we focused on the emerging topic of synthetic dimensions and higher-dimensional topological physics. “Synthetic dimensions” are a general idea in which internal states are coupled and reinterpreted as lattice sites along an extra spatial dimension. A significant advantage of this is that the external coupling can imprint an artificial magnetic field even for neutral particles. We collaborated with Zilberberg (Zurich) and Goldman (Brussels) to propose how synthetic dimensions could be extended into integrated photonics by coupling the modes of a silicon ring resonator. We showed how this could be used, in principle, to create an on-chip optical isolator or to realise a four-dimensional topological system experimentally. We also demonstrated theoretically how certain classes of observables, such as those probed in photonics, can have crucially different behavior to properties measured in solid-state experiments. Synthetic dimensions have therefore opened up many interesting questions by providing new ways to engineer synthetic gauge fields for photons and by making higher-dimensional topological physics accessible in the lab.

All these results have been disseminated through theoretical or joint theoretical-experimental peer-reviewed publications and are freely available to the whole community on the arXiv repository. We have also presented our work at international conferences and universities, and organized a three-day international workshop on Topological Photonics, held in Trento in April 2016 (“TopoDays 2016”). We have talked about our research to school students, popularized our work in an online article and highlighted out activities on a project
Our project has made important contributions to the state-of-the-art including: understanding how to control light propagation in strained honeycomb lattices; proposing photonics experiments to probe analogue momentum-space magnetic fields; experimentally mapping out geometrical properties of optical states; showing how to engineer synthetic gauge fields for classical 2028oscillators; proposing how to implement a synthetic dimension for integrated photonics; and demonstrating how 4D quantum Hall physics can be probed for photons. Throughout we paid particular attention to current experiments, and many of our theoretical ideas were directly implemented in collaborations. Our results in this sense have made a fundamental contribution towards bringing the field of topological photonics to a full scientific maturity.

In the future, our project can have a societal impact by deepening our understanding of quantum physics and by feeding through in the long-term to photonics technologies. Our project has opened up several promising research lines, including the possibilities of harnessing topological protection in an on-chip optical isolator and of exploiting geometrical and, in the future, topological effects in fiber-optics networks. From a more speculative perspective, exploiting synthetic dimensions to realize effectively high-dimensional systems could be a promising ingredient in the direction of realizing a fault-free topological quantum computing device.
Our experimental collaboration mapping out the geometrical properties of optical states