Interaction-induced topologically nontrivial phases have been theoretically predicted and need more experimental verification. Cold atom systems with tunable interaction strength provide a flexible platform for studying these effects. Here, we focus on the experimental signature of topological phase and topological phase transition (TPT). Since the topological Hamiltonian carries the information of the topology of the system, we first establish its relation to the single-particle density matrix (SPDM) for interacting two-band systems, and then design a tomography scheme for the SPDM in cold atom experiments. Thus the Berry curvature of the topological Hamiltonian, the Chern number, and the TPT point can be reconstructed from experimental data.
Topologically ordered phase has emerged as one of most exciting concepts that not only broadens our understanding of phases of matter, but also has been found to have potential application in fault-tolerant quantum computation. The direct measurement of topological properties, however, is still a challenge, especially in interacting quantum system. Here we realize two to four spin one-dimensional Heisenberg chains using nuclear magnetic resonance simulators and observe interaction-induced topological transitions, where Berry curvature in the parameter space of Hamiltonian is probed by means of dynamical response and then the first Chern number is extracted by integrating the curvature over the closed surface. The utilized experimental method provides a powerful means to explore topological phenomena in quantum systems with many-body interactions.
Different topological phases of quantum systems have become areas of increased focus in recent decades. In particular, the question of how to realize and manipulate systems with a nontrivial first Chern number is pursued both experimentally and theoretically. Here we go beyond typical spin-1/2 systems and consider both single and coupled spin-1 systems as a means of realizing higher first Chern numbers and studying the emergence of different topological phases. We show that rich topological phase diagrams can be realized by coupling two spin-1 systems using both numerical and analytical methods. Furthermore, we consider a concrete realization of spin-1 systems using a superconducting circuit. This realization includes nonstandard spin-spin interaction terms that may endanger the topological properties. We argue, however, that the realistic circuit Hamiltonian including all terms should be expected to show the rich phase structure as well. This puts our theoretical predictions within reach of state-of-the-art experimental setups.
We demonstrate that dynamical probes provide direct means of detecting the topological phase transition (TPT) between conventional and topological phases, which would otherwise be difficult to access because of loss or heating processes. We propose to avoid such heating by rapidly quenching in and out of the short-lived topological phase across the transition that supports gapless excitations. Following the quench, the distribution of excitations in the final conventional phase carries signatures of the TPT. We apply this strategy to study the TPT into a Majorana-carrying topological phase predicted in one-dimensional spin-orbit-coupled Fermi gases with attractive interactions. The resulting spin-resolved momentum distribution, computed by self-consistently solving the time-dependent Bogoliubov-de Gennes equations, exhibits Kibble-Zurek scaling and Stückelberg oscillations characteristic of the TPT. We discuss parameter regimes where the TPT is experimentally accessible.
Interactions generically have important effects on topological quantum phases. For a quantum anomalous Hall (QAH) insulator, the presence of interactions can qualitatively change a topological phase diagram, which, however, is typically hard to measure in an experiment. Here we propose a scheme based on quench dynamics to detect the mean-field topological phase diagram of an interacting Chern insulator described by the QAH-Hubbard model, with nontrivial dynamical quantum physics being uncovered. We focus on the dynamical properties of the system at a weak to intermediate Hubbard interaction, which mainly induces a ferromagnetic order under the mean-field level. Remarkably, three characteristic times---
ts,tc, and
t∗---are found in the quench dynamics. The first two (
ts,tc) capture the emergences of dynamical self-consistent particle density and the dynamical topological phase transition, respectively, while the third one (
t∗) gives a linear scaling time on the topological phase boundaries. We show generically that the characteristic times obey
ts>t∗>tc (
t∗<ts<tc) in the repulsive (attractive) interacting regime, when the system is quenched from an initial nearly fully polarized state to the topologically nontrivial regimes. Moreover, the Chern number of the equilibrium phase of postquench interacting Hamiltonian can be determined by any two of the three timescales, providing a dynamical way to determine the equilibrium mean-field topological phases. Experimentally, the measurement of
ts is challenging, while
tc and
t∗ can be directly read out by measuring the spin polarizations of four Dirac points and the time-dependent particle density, respectively, showing the feasibility of the present dynamical scheme. Our work opens a way to detect by quench dynamics the mean-field phase diagram of Chern insulators with interactions.
Chern insulators are band insulators which exhibit a gap in the bulk and gapless excitations in the edge. Detection of Chern insulators is a serious challenge in cold atoms since the Hall transport measurements are technically unrealistic for neutral atoms. By establishing a natural correspondence between the time-reversal invariant topological insulator and the quantum anomalous Hall system, we show for a class of Chern insulators that the topology can be determined by only measuring Bloch eigenstates at highly symmetric points of the Brillouin zone. Furthermore, we introduce two experimental schemes, including the spin-resolved Bloch oscillation, to carry out the measurement. These schemes are highly feasible under realistic experimental conditions. Our results may provide a powerful tool to detect topological phases in cold atoms.
Quantum metrology is deeply connected to quantum geometry, through the fundamental notion of quantum Fisher information. Inspired by advances in topological matter, it was recently suggested that the Berry curvature and Chern numbers of band structures can dictate strict lower bounds on metrological properties, hence establishing a strong connection between topology and quantum metrology. In this work, we provide a first experimental verification of such topological bounds, by performing optimal quantum multi-parameter estimation and achieving the best possible measurement precision. By emulating the band structure of a Chern insulator, we experimentally determine the metrological potential across a topological phase transition, and demonstrate strong enhancement in the topologically non-trivial regime. Our work opens the door to metrological applications empowered by topology, with potential implications for quantum many-body systems.