Synthetic Landau levels for photons (1511.07381v2)

Abstract: Synthetic photonic materials are an emerging platform for exploring the interface between microscopic quantum dynamics and macroscopic material properties[1-5]. Photons experiencing a Lorentz force develop handedness, providing opportunities to study quantum Hall physics and topological quantum science[6-8]. Here we present an experimental realization of a magnetic field for continuum photons. We trap optical photons in a multimode ring resonator to make a two-dimensional gas of massive bosons, and then employ a non-planar geometry to induce an image rotation on each round-trip[9]. This results in photonic Coriolis/Lorentz and centrifugal forces and so realizes the Fock-Darwin Hamiltonian for photons in a magnetic field and harmonic trap[10]. Using spatial- and energy-resolved spectroscopy, we track the resulting photonic eigenstates as radial trapping is reduced, finally observing a photonic Landau level at degeneracy. To circumvent the challenge of trap instability at the centrifugal limit[10,11], we constrain the photons to move on a cone. Spectroscopic probes demonstrate flat space (zero curvature) away from the cone tip. At the cone tip, we observe that spatial curvature increases the local density of states, and we measure fractional state number excess consistent with the Wen-Zee theory, providing an experimental test of this theory of electrons in both a magnetic field and curved space[12-15]. This work opens the door to exploration of the interplay of geometry and topology, and in conjunction with Rydberg electromagnetically induced transparency, enables studies of photonic fractional quantum Hall fluids[16,17] and direct detection of anyons[18-19].

Synthetic Landau Levels for Photons: An Experimental Realization

The paper "Synthetic Landau Levels for Photons" presents a detailed paper on the creation of synthetic magnetic fields for photons and their subsequent manifestation in a form analogous to electronic Landau levels, within a specially constructed optical resonator. The research provides a comprehensive experimental and theoretical framework that facilitates the exploration of non-trivial geometric and topological effects in photonic systems, paving the way for further investigations into quantum Hall physics.

Experimental Framework

The authors leverage a non-planar multimode ring resonator to impose a synthetic magnetic field on photons, effectively simulating the dynamics of massive bosons subjected to Lorentz forces. The essential design of the resonator exploits the analogy between the transverse properties of light in a near-degenerate cavity and those of massive, trapped particles in a two-dimensional (2D) space. By fine-tuning mirror arrangements and optical path length, photonic eigenstates are manipulated to exhibit discrete rotational symmetry akin to Landau levels in electronic systems. The coupling of such geometric modifications induces Coriolis and Lorentz-type forces on trapped photons, thereby implementing the Fock-Darwin Hamiltonian.

Results

Key findings of the paper include:

• Mode Detection: Through spatial- and energy-resolved spectroscopy, the authors identify photonic eigenstates and their evolution as the harmonic trapping is progressively reduced. At the centrifugal limit, they observe the formation of degenerate Landau levels for photons, characterized by unique ring-shaped modes associated with angular momentum winding.
• Curvature and Density of States: The researchers crucially explore the effects of spatial curvature on these synthetic Landau levels. Upon confining photon movement to a conical surface, they observe a fractional increase in the local density of states at the cone tip, consistent with predictions from the Wen-Zee theory. Such findings provide experimental verification of theoretical expectations about electronic behavior in curved space with threaded magnetic fields.
• Mode Stability and Disorder: The experiment reveals that, despite the presence of local disorder due to mirror imperfections, the topology-induced protection ensures mode stability and lifetime, critical for advancing towards investigations involving stronger correlations, such as anyonic braiding statistics.

Implications

This paper profoundly impacts both theoretical and practical domains. The realization of synthetic Landau levels in photonic systems represents a new frontier in quantum simulators, facilitating controlled studies on quantum Hall effects in non-electronic substrates. The successful application of complex topology and geometry to photon dynamics opens avenues for the development of systems exhibiting fractional quantum Hall behavior, potentially leading to novel devices for quantum information processing and topological quantum computing. Furthermore, the compatibility with Rydberg-mediated photon-photon interactions positions this work as a precursor to exploring strongly correlated states of light.

Future Prospects

The paper suggests several directions for future research, including refined exploration into fractional quantum Hall regimes and measuring fractional state accumulation in excited Landau levels. Given the robustness of the synthetic constructs, extending this framework to analyze Hall viscosity or deeper geometric-topological interplay in photonic fluids presents exciting possibilities. This research community can anticipate further advancements in synthetic quantum materials, particularly with the integration of more sophisticated interaction schemes to manifest photonic analogs of electronic quantum phenomena.