Coupled Atomic Wires in a Synthetic Magnetic Field

Abstract

We propose and study systems of coupled atomic wires in a perpendicular synthetic magnetic field as a platform to realize exotic phases of quantum matter. This includes (fractional) quantum Hall states in arrays of many wires inspired by the pioneering work [Kane et al. PRL {\bf{88}}, 036401 (2002)], as well as Meissner phases and Vortex phases in double-wires. With one continuous and one discrete spatial dimension, the proposed setup naturally complements recently realized discrete counterparts, i.e. the Harper-Hofstadter model and the two leg flux ladder, respectively. We present both an in-depth theoretical study and a detailed experimental proposal to make the unique properties of the semi-continuous Harper-Hofstadter model accessible with cold atom experiments. For the minimal setup of a double-wire, we explore how a sub-wavelength spacing of the wires can be implemented. This construction increases the relevant energy scales by at least an order of magnitude compared to ordinary optical lattices, thus rendering subtle many-body phenomena such as Lifshitz transitions in Fermi gases observable in an experimentally realistic parameter regime. For arrays of many wires, we discuss the emergence of Chern bands with readily tunable flatness of the dispersion and show how fractional quantum Hall states can be stabilized in such systems. Using for the creation of optical potentials Laguerre-Gauss beams that carry orbital angular momentum, we detail how the coupled atomic wire setups can be realized in non-planar geometries such as cylinders, discs, and tori.

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Cited by in corpus (21)

• Fractional quantum Hall effect in the interacting Hofstadter model via tensor networks
• Coupled-wire constructions: a Luttinger liquid approach to topology
• Bosonic Fractional Quantum Hall States on a Finite Cylinder
• The quantized Hall conductance of a single atomic wire: A proposal based on synthetic dimensions
• Optical Lattice with Torus Topology
• Quantum Many-Body Physics with Ultracold Polar Molecules: Nanostructured Potential Barriers and Interactions
• Emergent periodic and quasiperiodic lattices on surfaces of synthetic Hall tori and synthetic Hall cylinders
• Two-leg ladder Bose Hubbard models with staggered fluxes
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• Synthetic dimensions and topological chiral currents in mesoscopic rings
• Spectrum, Lifshitz transitions and orbital currents in frustrated fermionic ladders with a uniform flux
• Transverse Josephson vortices and localized states in stacked Bose-Einstein condensates
• Microscopic Study of the Coupled-Wire Construction and Plausible Realization in Spin-Dependent Optical Lattices
• Artificial gauge fields in the t-z mapping for optical pulses: spatio-temporal wavepacket control and quantum Hall physics
• Emergence of non-Abelian SU(2) invariance in Abelian frustrated fermionic ladders
• Topological Chiral Edge States in a Synthetic Dimension of Atomic Trap States
• Adiabatic preparation of fractional Chern insulators from an effective thin-torus limit
• Unlocked-relative-phase states in arrays of Bose-Einstein condensates
• The large $|U|$ expansion for a half-filled asymmetric Hubbard model on a triangular ladder in the presence of spin-dependent magnetic flux
• Quantum States and Spectra of Small Cylindrical and Toroidal Lattices
• $p$-band stability of ultracold atom gas in anharmonic optical lattice potential with large energy scales