Synthetic Landau levels for photons

Abstract

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 spatialand 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].The Lorentz force on a charged particle moving in a magnetic field leads to the unique topological features of quantum Hall systems, including precisely quantized Hall conductance, topologically protected edge transport, and, in the presence of interactions, the predicted anyonic and non-abelian braiding statistics that form the basis of topological quantum computing [20]. To controllably explore the emergence of these phenomena, efforts have recently focused on realizing synthetic materials in artificial magnetic fields, and in particular, upon implementations for cold atoms and photons. Successful photonic implementations have employed lattices with engineered tunneling [6,[21][22][23][24]. However, it is desirable to realize artificial magnetic fields in the simpler case of a continuum (lattice-free) material [7,25,26], where strong interactions are more easily accessible and the theory maps more directly to fractional quantum Hall systems. In this work, we develop a new approach and demonstrate the first continuum synthetic magnetic field for light.To achieve photonic Landau levels we harness the powerful analogy between photons in a near-degenerate multimode cavity and massive, trapped 2d particles [27,28]. Owing to mirror curvature, the transverse dynamics of a running wave resonator are equivalent to those of a 2D quantum h...

Chiral quantum optics

“…We emphasize that chiral coupling of emitters to waveguides is distinct from the physics of chiral edge channels, which were observed in recent seminal experiments in condensed-matter [9] and photonic systems [10][11][12][13][14]. Chiral edge channels emerge as manifestations of topology in 2D materials leading to a topological protection of the wave transport through the channel towards backscattering from disorder.…”

Generation and spectroscopic signatures of a fractional quantum Hall liquid of photons in an incoherently pumped optical cavity

“…Even though our theory is focused on the non-planar ring cavity configuration, where Landau levels for photons and Rydberg-EIT photon blockade have been recently observed [7,10], the ideas presented here are fully general and may be extended to other optical configurations combining a synthetic magnetic field for photons and strong photonphoton interactions.…”

“…We consider an optical set-up inspired by the recent experiment [7], namely a non-planar ring cavity. Assuming that the free spectral range of the cavity is larger than all other energy scales of the photon fluid, we can assume that photons only occupy a single running-wave longitudinal mode of the ring cavity and their motion is confined to the two-dimensional xy transverse plane.…”

“…Mott insulators. While previous works in the quantum Hall framework [15] concentrate on spatially homogeneous geometries with no boundaries, we here introduce an external potential profile [19,20] as a way to control the number of particles in the Laughlin state and suppress its excitation in stateof-the-art configurations [7]. For a given lateral confinement, the incompressibility of the Laughlin state puts a bound on the maximum number of particles that the frequency-dependent incoherent pump can inject into the cavity before the Laughlin gap pushes the transition offresonance.…”

Tunable-Range, Photon-Mediated Atomic Interactions in Multimode Cavity QED

“…Though BECs were employed in the latter two experiments, the number of modes was insufficient to mediate short-range interactions. In addition to the experimental platform described in this paper, prospects are bright also for the future observation of the self-organization of atoms coupled to photonic bandgap waveguides [33] and for creating and exploring topological states with Rydberg atoms coupled to multimode twisted ring cavities [3,34].…”