Engineering spin-orbit coupling for photons and polaritons in microstructures

One of the most fundamental properties of electromagnetism and special relativity is the coupling between the spin of an electron and its orbital motion. This is at the origin of the fine structure in atoms, the spin Hall effect in semiconductors, and underlies many intriguing properties of topological insulators, in particular their chiral edge states. Configurations where neutral particles experience an effective spin-orbit coupling have been recently proposed and realized using ultracold atoms and photons. Here we use coupled micropillars etched out of a semiconductor microcavity to engineer a spin-orbit Hamiltonian for photons and polaritons in a microstructure. The coupling between the spin and orbital momentum arises from the polarisation dependent confinement and tunnelling of photons between micropillars arranged in the form of a hexagonal photonic molecule. Dramatic consequences of the spin-orbit coupling are experimentally observed in these structures in the wavefunction of polariton condensates, whose helical shape is directly visible in the spatially resolved polarisation patterns of the emitted light. The strong optical nonlinearity of polariton systems suggests exciting perspectives for using quantum fluids of polaritons11 for quantum simulation of the interplay between interactions and spin-orbit coupling.Comment: main text: pages 1-11 (4 figures); supplementary material: pages 12-28 (9 figures

State-recycling and time-resolved imaging in topological photonic lattices

Photonic lattices - arrays of optical waveguides - are powerful platforms for simulating a range of phenomena, including topological phases. While probing dynamics is possible in these systems, by reinterpreting the propagation direction as "time," accessing long timescales constitutes a severe experimental challenge. Here, we overcome this limitation by placing the photonic lattice in a cavity, which allows the optical state to evolve through the lattice multiple times. The accompanying detection method, which exploits a multi-pixel single-photon detector array, offers quasi-real time-resolved measurements after each round trip. We apply the state-recycling scheme to intriguing photonic lattices emulating Dirac fermions and Floquet topological phases. In this new platform, we also realise a synthetic pulsed electric field, which can be used to drive transport within photonic lattices. This work opens a new route towards the detection of long timescale effects in engineered photonic lattices and the realization of hybrid analogue-digital simulators.Comment: Comments are welcom

Universal High-Frequency Behavior of Periodically Driven Systems: from Dynamical Stabilization to Floquet Engineering

We give a general overview of the high-frequency regime in periodically driven systems and identify three distinct classes of driving protocols in which the infinite-frequency Floquet Hamiltonian is not equal to the time-averaged Hamiltonian. These classes cover systems, such as the Kapitza pendulum, the Harper-Hofstadter model of neutral atoms in a magnetic field, the Haldane Floquet Chern insulator and others. In all setups considered, we discuss both the infinite-frequency limit and the leading finite-frequency corrections to the Floquet Hamiltonian. We provide a short overview of Floquet theory focusing on the gauge structure associated with the choice of stroboscopic frame and the differences between stroboscopic and non-stroboscopic dynamics. In the latter case one has to work with dressed operators representing observables and a dressed density matrix. We also comment on the application of Floquet Theory to systems described by static Hamiltonians with well-separated energy scales and, in particular, discuss parallels between the inverse-frequency expansion and the Schrieffer-Wolff transformation extending the latter to driven systems.Comment: 84 pages, 25 figures, 4 appendice