Steady-state Hall response and quantum geometry of driven-dissipative lattices

Abstract

We study the effects of the quantum geometric tensor, i.e., the Berry curvature and the Fubini-Study metric, on the steady state of driven-dissipative bosonic lattices. We show that the quantum-Hall-type response of the steady-state wave function in the presence of an external potential gradient depends on all the components of the quantum geometric tensor. Looking at this steady-state Hall response, one can map out the full quantum geometric tensor of a sufficiently flat band in momentum space using a driving field localized in momentum space. We use the two-dimensional Lieb lattice as an example and numerically demonstrate how to measure the quantum geometric tensor.

6 + 5 pages, 2 figures

References in corpus (9)

• Topological Photonics
• Observation of phononic helical edge states in a mechanical 'topological insulator'
• Fidelity, dynamic structure factor, and susceptibility in critical phenomena
• Quantum critical scaling of the geometric tensors
• Band geometry, Berry curvature and superfluid weight
• Position-Momentum Duality and Fractional Quantum Hall Effect in Chern Insulators
• Abelian and Non-Abelian Quantum Geometric Tensor
• Orbital magnetism of coupled bands models
• Spin Gauge Fields: from Berry Phase to Topological Spin Transport and Hall Effects

Cited by in corpus (17)

• Experimental Measurement of the Quantum Metric Tensor and Related Topological Phase Transition with a Superconducting Qubit
• Measurements of the quantum geometric tensor in solids
• The quantum geometric origin of capacitance in insulators
• Floquet-engineering of nodal rings and nodal spheres and their characterization using the quantum metric
• Extracting non-Abelian quantum metric tensor and its related Chern numbers
• Local geometry and quantum geometric tensor of mixed states
• Quantized Hall drift in a frequency-encoded photonic Chern insulator
• Non-Abelian quantum geometric tensor in degenerate topological semimetals
• Quantum metric dependent anomalous velocity in systems subject to complex electric fields
• Sj$\ddot{\text{o}}$qvist quantum geometric tensor of finite-temperature mixed states
• Quantum geometry of bosonic Bogoliubov quasiparticles
• Classical description of the parameter space geometry in the Dicke and Lipkin-Meshkov-Glick models
• Generalized quantum geometric tensor for excited states using the path integral approach
• Quantum geometrical effects in non-Hermitian systems
• Band topology of pseudo-Hermitian phases through tensor Berry connections and quantum metric
• Minimal Hamiltonian deformations as bulk probes of effective non-Hermiticity in Dirac materials
• Evolution of quantum geometric tensor of 1D periodic systems after a quench