Effective Theory of Non-Adiabatic Quantum Evolution Based on the Quantum Geometric Tensor

Abstract

We study the role of the quantum geometric tensor (QGT) in the evolution of quantum systems. We show that all its components play an important role on the extra phase acquired by a spinor and on the trajectory of an accelerated wavepacket in any realistic finite-duration experiment. While the adiabatic phase is determined by the Berry curvature (the imaginary part of the tensor), the non-adiabaticity is determined by the quantum metric (the real part of the tensor) and allows to determine corrections in the regimes where Landau-Zener approach is inapplicable. The particular case of a planar microcavity in the strong coupling regime allows to extract the QGT components by direct light polarization measurements and to check their effects on the quantum evolution.

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Cited by in corpus (48)

• Direct measurement of the quantum geometric tensor in a two-dimensional continuous medium
• Nonadiabatic Landau-Zener-Stückelberg-Majorana transitions, dynamics, and interference
• 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
• Extracting the quantum metric tensor through periodic driving
• Experimental measurement of the quantum geometric tensor using coupled qubits in diamond
• Kähler geometry and Chern insulators: Relations between topology and the quantum metric
• Semi-classical wave packet dynamics in non-uniform electric fields
• Experimental measurement of the divergent quantum metric of an exceptional point
• Quantum metric and wavepackets at exceptional points in non-Hermitian systems
• Relating the topology of Dirac Hamiltonians to quantum geometry: When the quantum metric dictates Chern numbers and winding numbers
• Non-Abelian Bloch oscillations in higher-order topological insulators
• Ground-state quantum geometry in superconductor-quantum dot chains
• Longitudinal and anomalous Hall conductivity of a general two-band model
• Floquet-engineering of nodal rings and nodal spheres and their characterization using the quantum metric
• Direct measurement of quantum Fisher information
• Generalized Quantum Geometric Tensor in a Non-Hermitian Exciton-Polariton System
• Revealing Chern number from quantum metric
• Direct optical probe of magnon topology in two-dimensional quantum magnets
• Quantum Fluctuation of the Quantum Geometric Tensor and its Manifestation as Intrinsic Hall Signatures in Time-Reversal Invariant Systems
• Instantaneous response and quantum geometry of insulators
• Universal semiclassical equations based on the quantum metric
• Interplay of Band Geometry and Topology in Ideal Chern Insulators in Presence of External Electromagnetic Fields
• Polariton Hall Effect in Transition-Metal Dichalcogenides
• Extracting non-Abelian quantum metric tensor and its related Chern numbers
• Local geometry and quantum geometric tensor of mixed states
• Photonic band structure design using persistent homology
• Quantum metric on the Brillouin Zone in correlated electron systems and its relation to topology for Chern insulators
• Non-Abelian quantum geometric tensor in degenerate topological semimetals
• Quantum metric dependent anomalous velocity in systems subject to complex electric fields
• Wannier Topology and Quadrupole Moments for a generalized Benalcazar-Bernevig-Hughes Model
• Sj$\ddot{\text{o}}$qvist quantum geometric tensor of finite-temperature mixed states
• Geometrical Rabi oscillations and Landau-Zener transitions in non-Abelian systems
• Localization anisotropy and complex geometry in two-dimensional insulators
• Manifestation of the Berry connection in chiral lattice systems
• Quantum geometry in many-body systems with precursors of criticality
• Geometric semimetals and their simulation in synthetic matter
• Hallmarks of tunneling dynamics with broken reflective symmetry
• Orbital anomalous Hall effect in the few-layer Weyl semimetal TaIrTe4
• Quantum geometrical effects in non-Hermitian systems
• Nontrivial band geometry in an optically active system
• Quantum geometric tensors from sub-bundle geometry
• Band topology of pseudo-Hermitian phases through tensor Berry connections and quantum metric
• Microcavity polaritons for topological photonics
• Spin-polarized scanning tunneling microscopy measurement scheme for determining the quantum geometric tensor
• Compact and programmable large-scale optical processor in free space
• Topological dynamics of adiabatic cat states
• Evolution of quantum geometric tensor of 1D periodic systems after a quench