Measuring Hopf links and Hopf invariants in a quenched topological Raman lattice

Abstract

In a recent experimental work [Z. Wu et al., Science 354, 83 (2016)], the PKU-USTC group realized a two-dimensional two-band quantum anomalous Hall model on a square Raman lattice. By quenching the atom-laser detuning of such a Raman lattice, the time-dependent Bloch vectors for each quasimomentum points define a Hopf mapping from quasimomentum-time space $(k_x,k_y,t)\in T^3$ to the Bloch sphere $S^2$. The Hopf links between the preimages of any two Bloch vectors on $S^2$ can be measured experimentally through Bloch state tomography using spin-resolved time-of-flight measurement together with suitable radio-frequency manipulations. The dynamical Hopf invariants, which are quasimomentum-time integrations of Chern-Simons densities, can also be extracted experimentally through certain quench processes. As the Hopf invariant equals the Chern number of the post-quench Hamiltonian, the measurements of Hopf links and Hopf invariants provide an alternative way of understanding the topological phase diagram of the equilibrium system.

arXiv comment7 pages, 6 figures. Some references are added

References in corpus (34)

• Many-Body Physics with Ultracold Gases
• Quantum Simulation
• Experimental realisation of the topological Haldane model
• Artificial gauge potentials for neutral atoms
• Realization of the Hofstadter Hamiltonian with ultracold atoms in optical lattices
• Light-induced gauge fields for ultracold atoms
• Realizing the Harper Hamiltonian with Laser-Assisted Tunneling in Optical Lattices
• Observation of a Many-Body Dynamical Phase Transition with a 53-Qubit Quantum Simulator
• Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms
• Spin-Orbit Coupled Degenerate Fermi Gases
• Spin-Injection Spectroscopy of a Spin-Orbit Coupled Fermi Gas
• Topological quantization of the spin Hall effect in two-dimensional paramagnetic semiconductors
• Realization of Two-Dimensional Spin-orbit Coupling for Bose-Einstein Condensates
• Experimental reconstruction of the Berry curvature in a topological Bloch band
• Observation of a dynamical topological phase transition
• Seeing topological order in time-of-flight measurements
• Observation of Bose-Einstein Condensation in a Strong Synthetic Magnetic Field
• Topological surface states in three-dimensional magnetic insulators
• Uncover Topology by Quantum Quench Dynamics
• Quantum Quenches in Chern Insulators
• Measuring Topological Number of a Chern-Insulator from Quench Dynamics
• Floquet Topological States in Shaking Optical Lattices
• Dynamical classification of topological quantum phases
• Tomography of band insulators from quench dynamics
• Dynamical Buildup of a Quantized Hall Response from Non-Topological States
• Detecting Topological Phases in Cold Atoms
• Persistent Hall response in a quantum quench
• Hall Response and Edge Current Dynamics in Chern Insulators out of Equilibrium
• Non-equilibrium Fractional Hall Response After a Topological Quench
• Topology and entanglement in quench dynamics
• Observation of topological links associated with Hopf insulators in a solid-state quantum simulator
• Phase vortices of the quenched Haldane Model
• Topological quantum quench dynamics carrying arbitrary Hopf and second-Chern numbers
• Detection of Chern numbers and entanglement in topological two-species systems through subsystem winding numbers

Cited by in corpus (18)

• Topological Euler class as a dynamical observable in optical lattices
• Topological carbon materials: a new perspective
• Dynamical detection of topological charges
• Observing topological charges and dynamical bulk-surface correspondence with ultracold atoms
• Topological Invariants for Quantum Quench Dynamics from Unitary Evolution
• Extracting the Quantum Geometric Tensor of an Optical Raman Lattice by Bloch State Tomography
• Characterizing topological phases by quantum quenches: A general theory
• Non-Bloch quench dynamics
• Preparing Atomic Topological Quantum Matter by Adiabatic Nonunitary Dynamics
• Nested-sphere description of the N-level Chern number and the generalized Bloch hypersphere
• Linking invariant for the quench dynamics of a two-dimensional two-band Chern insulator
• Three-dimensional $\mathcal{P}\mathcal{T}$-symmetric topological phases with Pontryagin index
• Emergent topology and symmetry-breaking order in correlated quench dynamics
• Quench dynamics of Hopf insulators
• Quantum quenches in a pseudo-Hermitian Chern insulator
• Scheme to Equilibrate the Quantized Hall Response of Topological Systems from Coherent Dynamics
• Flat Bands in Three-dimensional Lattice Models with Non-trivial Hopf Index
• Quantum oscillation in Hopf-link semimetals