Extracting the quantum metric tensor through periodic driving

Abstract

We propose a generic protocol to experimentally measure the quantum metric tensor, a fundamental geometric property of quantum states. Our method is based on the observation that the excitation rate of a quantum state directly relates to components of the quantum metric upon applying a proper time-periodic modulation. We discuss the applicability of this scheme to generic two-level systems, where the Hamiltonian's parameters can be externally tuned, and also to the context of Bloch bands associated with lattice systems. As an illustration, we extract the quantum metric of the multi-band Hofstadter model. Moreover, we demonstrate how this method can be used to directly probe the spread functional, a quantity which sets the lower bound on the spread of Wannier functions and signals phase transitions. Our proposal offers a universal probe for quantum geometry, which could be readily applied in a wide range of physical settings, ranging from circuit-QED systems to ultracold atomic gases.

6 + 1 pages, 3 figures

References in corpus (20)

• Topological Photonics
• Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms
• Topological Bands for Ultracold Atoms
• Fidelity, dynamic structure factor, and susceptibility in critical phenomena
• Quantum critical scaling of the geometric tensors
• Band geometry, Berry curvature and superfluid weight
• An Aharonov-Bohm interferometer for determining Bloch band topology
• Artificial gauge fields in materials and engineered systems
• Observation of topological transitions in interacting quantum circuits
• The insulator/Chern-insulator transition in the Haldane model
• Dichroic f-sum rule and the orbital magnetization of crystals
• Position-Momentum Duality and Fractional Quantum Hall Effect in Chern Insulators
• Abelian and Non-Abelian Quantum Geometric Tensor
• Interaction dependent heating and atom loss in a periodically driven optical lattice
• Orbital magnetism of coupled bands models
• Steady-state Hall response and quantum geometry of driven-dissipative lattices
• Quantum metric contribution to the pair mass in spin-orbit coupled Fermi superfluids
• Quantized Rabi Oscillations and Circular Dichroism in Quantum Hall Systems
• High-precision multiband spectroscopy of ultracold fermions in a nonseparable optical lattice
• Geometrical effects in orbital magnetic susceptibility

Cited by in corpus (87)

• Measuring quantized circular dichroism in ultracold topological matter
• Experimental Measurement of the Quantum Metric Tensor and Related Topological Phase Transition with a Superconducting Qubit
• Relations between topology and the quantum metric for Chern insulators
• Consequences of Time-reversal-symmetry Breaking in the Light-Matter Interaction: Berry Curvature, Quantum Metric and Diabatic Motion
• Experimental measurement of the quantum geometric tensor using coupled qubits in diamond
• Kähler geometry and Chern insulators: Relations between topology and the quantum metric
• Microwave Spectroscopy Reveals the Quantum Geometric Tensor of Topological Josephson Matter
• Semi-classical wave packet dynamics in non-uniform electric fields
• Experimental Observation of Tensor Monopoles with a Superconducting Qudit
• Revealing tensor monopoles through quantum-metric measurements
• Quantum Fisher information measurement and verification of the quantum Cramér-Rao bound in a solid-state qubit
• Berry Curvature and Quantum Metric in $N$-band systems -- an Eigenprojector Approach
• Contrasting lattice geometry dependent versus independent quantities: ramifications for Berry curvature, energy gaps, and dynamics
• The quantum geometric origin of capacitance in insulators
• Experimental estimation of the quantum Fisher information from randomized measurements
• Quantum Metric Induced Phases in Moiré Materials
• Measurement of Topological Order based on Metric-Curvature Correspondence
• Second Chern Number and Non-Abelian Berry Phase in Topological Superconducting Systems
• Nontrivial Quantum Geometry and the Strength of Electron-Phonon Coupling
• Relating the topology of Dirac Hamiltonians to quantum geometry: When the quantum metric dictates Chern numbers and winding numbers
• Nontrivial quantum geometry of degenerate flat bands
• Ground-state quantum geometry in superconductor-quantum dot chains
• Probing localization and quantum geometry by spectroscopy
• Circular dichroism as a probe for topology in three-dimensional semimetals
• Mapping quantum geometry and quantum phase transitions to real space by a fidelity marker
• Optical manifestations and bounds of topological Euler class
• Dynamical quantum phase transitions in a spinor Bose-Einstein condensate and criticality enhanced quantum sensing
• Transconductance quantization in a topological Josephson tunnel junction circuit
• Floquet-engineering of nodal rings and nodal spheres and their characterization using the quantum metric
• Optimal Generators for Quantum Sensing
• Quantum metric of non-Hermitian Su-Schrieffer-Heeger systems
• Chiral quantum optics in the bulk of photonic quantum Hall systems
• Dual Haldane sphere and quantized band geometry in chiral multifold fermions
• Direct measurement of quantum Fisher information
• Signatures of two- and three-dimensional semimetals from circular dichroism
• Revealing Chern number from quantum metric
• Quantum geometric tensor and quantum phase transitions in the Lipkin-Meshkov-Glick model
• Quantum Fluctuation of the Quantum Geometric Tensor and its Manifestation as Intrinsic Hall Signatures in Time-Reversal Invariant Systems
• From Classical to Quantum Information Geometry: A Guide for Physicists
• Superfluid weight in the isolated band limit within the generalized random phase approximation
• Extracting non-Abelian quantum metric tensor and its related Chern numbers
• Interplay of Band Geometry and Topology in Ideal Chern Insulators in Presence of External Electromagnetic Fields
• Nested-sphere description of the N-level Chern number and the generalized Bloch hypersphere
• Topological properties of a non-Hermitian quasi-1D chain with a flat band
• Local geometry and quantum geometric tensor of mixed states
• Classical analog of the quantum metric tensor
• Quantum optics measurement scheme for quantum geometry and topological invariants
• Drude weight and the many-body quantum metric in one-dimensional Bose systems
• Quantum geometry of singlet superconductors
• Tensor monopoles and negative magnetoresistance effect in optical lattices
• Dielectric and optical markers originating from quantum geometry
• Optical absorption measurement of spin Berry curvature and spin Chern marker
• Band geometry from position-momentum duality at topological band crossings
• Corner Charge Fluctuation as an Observable for Quantum Geometry and Entanglement in Two-dimensional Insulators
• Geometry of the parameter space of a quantum system: Classical point of view
• Intrinsic gyrotropic magnetic current from Zeeman quantum geometry
• Interferometric geometry from symmetry-broken Uhlmann gauge group with applications to topological phase transitions
• Quantum multiparameter estimation enhanced by a topological phase transition
• Polaron spectra and edge singularities for correlated flat bands
• Sj$\ddot{\text{o}}$qvist quantum geometric tensor of finite-temperature mixed states
• Geometry and speed of evolution for a spin-s system with long-range zz-type Ising interaction
• Classical description of the parameter space geometry in the Dicke and Lipkin-Meshkov-Glick models
• Fubini-Study metric and topological properties of flat band electronic states: the case of an atomic chain with $s-p$ orbitals
• Information geometry of quantum critical submanifolds: relevant, marginal and irrelevant operators
• Geometrical Rabi oscillations and Landau-Zener transitions in non-Abelian systems
• A synthetic monopole source of Kalb-Ramond field in diamond
• Localization anisotropy and complex geometry in two-dimensional insulators
• Quantum geometric bounds in spinful systems with trivial band topology
• Hallmarks of tunneling dynamics with broken reflective symmetry
• Quantum geometrical effects in non-Hermitian systems
• Time-dependent quantum geometric tensor and some applications
• Photoprotected spin Hall effect on graphene with substrate induced Rashba spin-orbit coupling
• Generalized quantum geometric tensor for excited states using the path integral approach
• Geometric semimetals and their simulation in synthetic matter
• Quantum Metric-induced Oscillations in Flat Bands
• Circular Dichroism on the Edge of Quantum Hall Systems: From Many-Body Chern Number to Anisotropy Measurements
• Direct measurement of the quantum geometric tensor in pseudo-Hermitian systems
• Real space quantum metric of solids
• Band topology of pseudo-Hermitian phases through tensor Berry connections and quantum metric
• Singular connection approach to topological phases and resonant optical responses
• Measuring distance between quantum states on a quantum computer
• Exceptional flat bands in bipartite non-Hermitian lattices
• Quantum geometric tensor in systems with fractional band dispersion
• Theory of Berry Singularity Markers: Diagnosing Topological Phase Transitions via Lock-In Tomography
• Revisiting flat band superconductivity: dependence on minimal quantum metric and band touchings
• Evolution of quantum geometric tensor of 1D periodic systems after a quench
• Topological dynamics of adiabatic cat states