Momentum-space Landau levels in driven-dissipative cavity arrays

Abstract

We theoretically study the driven-dissipative Harper-Hofstadter model on a 2D square lattice in the presence of a weak harmonic trap. Without pumping and loss, the eigenstates of this system can be understood, in certain limits, as momentum-space toroidal Landau levels, where the Berry curvature, a geometrical property of an energy band, acts like a momentum-space magnetic field. We show that key features of these eigenstates can be observed in the steady-state of the driven-dissipative system under a monochromatic coherent drive, and present a realistic proposal for an optical experiment using state-of-the-art coupled cavity arrays. We discuss how such spectroscopic measurements may be used to probe effects associated both with the off-diagonal elements of the matrix-valued Berry connection and with the synthetic magnetic gauge.

10 pages, numerical codes available as ancillary files

References in corpus (18)

• Quantum fluids of light
• Dissipationless Quantum Spin Current at Room Temperature
• Observation of phononic helical edge states in a mechanical 'topological insulator'
• Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms
• Observation of chiral edge states with neutral fermions in synthetic Hall ribbons
• Visualizing edge states with an atomic Bose gas in the quantum Hall regime
• Observation of Bose-Einstein Condensation in a Strong Synthetic Magnetic Field
• Hierarchy of Hofstadter states and replica quantum Hall ferromagnetism in graphene superlattices
• Position-Momentum Duality and Fractional Quantum Hall Effect in Chern Insulators
• Spin-orbit coupling and Berry phase with ultracold atoms in 2D optical lattices
• Topological spin transport of relativistic electron
• Spin Gauge Fields: from Berry Phase to Topological Spin Transport and Hall Effects
• Designing Topological Bands in Reciprocal Space
• Exact Solutions of Fractional Chern Insulators: Interacting Particles in the Hofstadter Model at Finite Size
• Gauge matters: Observing the vortex-nucleation transition in a Bose condensate
• Artificial Magnetic Fields in Momentum Space in Spin-Orbit Coupled Systems
• Preparing and probing Chern bands with cold atoms
• Signatures of Bloch-band geometry on excitons: non-hydrogenic spectra in transition metal dichalcogenides

Cited by in corpus (7)

• Topological Photonics
• Topological quantum matter in synthetic dimensions
• Quantum simulations and many-body physics with light
• Floquet topological system based on frequency-modulated classical coupled harmonic oscillators
• Multidimensional dark space and its underlying symmetries: towards dissipation-protected qubits
• Quantum Hall effect in momentum space
• Chiral Wigner crystal phases induced by Berry curvature