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Journal Article
Synthetic Landau levels for photons
2016
Overview
It is an long-standing goal to produce a photonic quantum Hall effect, analogous to the well-known quantum Hall effect for electrons; now an artificial magnetic field for a continuum of photons has been produced, making it possible to observe photonic Landau levels in a photonic quantum Hall material.
A magnetic field for light
Employing topological effects in the design of optical devices and materials offers exciting new directions in applications and fundamental research. It is an outstanding goal to produce a photonic quantum Hall effect, with topologically protected photonic edge states, analogous to the well-known quantum Hall effect for electrons. In previous topological photonic approaches, photons were restricted to lattices of waveguides. To realize an artificial magnetic field for a continuum of photons, Nathan Schine
et al
. make a carefully designed trap for photons, using four mirrors so that photons are subject to a Coriolis force equivalent to a Lorentz force as if produced by a magnetic field. The approach made it possible to observe photonic Landau levels in a photonic quantum Hall material.
Synthetic photonic materials are an emerging platform for exploring the interface between microscopic quantum dynamics and macroscopic material properties
1
,
2
,
3
,
4
,
5
. Photons experiencing a Lorentz force develop handedness, providing opportunities to study quantum Hall physics and topological quantum science
6
,
7
,
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
,
13
,
14
,
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
.
