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      A Bose-Einstein Condensate on a Synthetic Hall Cylinder

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          Abstract

          The geometry of a physical space is a key ingredient underlying many exotic quantum phenomena. However, accessing physical spaces with non-trivial geometries and many associated unique phenomena are often impeded by experimental constraints. Here, we realize a Bose-Einstein condensate (BEC) on a synthetic cylindrical surface subject to a net radial synthetic magnetic flux, topologically equivalent to a two-dimensional (2D) Hall ribbon with two edges connected. This cylindrical surface comprises a real spatial dimension and a curved synthetic dimension formed by cyclically-coupled spin states. The BEC on such a Hall cylinder has counterintuitive properties unattainable by its counterparts in 2D planes. It develops a crystalline order with a nonsymmorphic symmetry and the period of its density modulation halves the lattice spacing. Bloch oscillations of the BEC in the momentum space double the period of the band structure, analogous to traveling on a Mobius strip. Our work opens the door to engineering synthetic curved spaces and observing intriguing quantum phenomena inherent to the topology of spaces.

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          Synthetic Landau levels for photons

          Synthetic photonic materials are an emerging platform for exploring the interface between microscopic quantum dynamics and macroscopic material properties[1-7]. Making photons experience a Lorentz force imbues them with handedness, providing unique opportunities for studying quantum Hall physics and topological quantum science[8-10]. Here we present the first experimental realization of a magnetic field for continuum photons. We trap optical photons in a ring resonator to make a 2D quantum gas and employ a non-planar geometry to induce an image rotation on each round-trip[11]. 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[12]. Using spatial- and energy-resolved spectroscopy, we track the 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[12-14], we constrain the photons to move on a cone. Spectroscopic probes demonstrate flat space 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 effective theory, providing the first experimental test of this theory of electrons in both a magnetic field and curved space[15-18]. 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[19,20] and direct detection of anyons[21,22].
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            Author and article information

            Journal
            06 September 2018
            Article
            1809.02122
            b907d0b2-efad-4918-a472-9cbcc21a746e

            http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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            Custom metadata
            cond-mat.quant-gas quant-ph

            Quantum physics & Field theory,Quantum gases & Cold atoms
            Quantum physics & Field theory, Quantum gases & Cold atoms

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