Simulation of 1D Topological Phases in Driven Quantum Dot Arrays

Edge State, Localization Length, and Critical Exponent from Survival Probability in Topological Waveguides

Edge states in topological phase transitions have been observed in various platforms. To date, verification of the edge states and the associated topological invariant are mostly studied, and yet a quantitative measurement of topological phase transitions is still lacking. Here, we show the direct measurement of edge states and their localization lengths from survival probability. We employ photonic waveguide arrays to demonstrate the topological phase transitions based on the Su-Schrieffer-Heeger model. By measuring the survival probability at the lattice boundary, we show that in the long-time limit, the survival probability is P=(1-e^{-2/ξ_{loc}})^{2}, where ξ_{loc} is the localization length. This length derived from the survival probability is compared with the distance from the transition point, yielding a critical exponent of ν=0.94±0.04 at the phase boundary. Our experiment provides an alternative route to characterizing topological phase transitions and extracting their key physical quantities.

Topology detection in cavity QED

We explore the physics of topological lattice models immersed in c-QED architectures for arbitrary coupling strength with the photon field. We propose the use of the cavity transmission as a topological marker and study its behaviour. For this, we develop an approach combining the input-output formalism with a Mean-Field plus fluctuations description of the setup. We illustrate our results with the specific case of a fermionic Su-Schrieffer-Heeger (SSH) chain coupled to a single-mode cavity. Our findings confirm that the cavity can indeed act as a quantum sensor for topological phases, where the initial state preparation plays a crucial role. Additionally, we discuss the persistence of topological features when the coupling strength increases, in terms of an effective Hamiltonian, and calculate the entanglement entropy. Our approach can be applied to other fermionic systems, opening a route to the characterization of their topological properties in terms of experimental observables.

Out of equilibrium chiral higher order topological insulator on a-flux square lattice

One of the hallmarks of bulk topology is the existence of robust boundary localized states. For instance, a conventionalddimensional topological system hostsd- 1 dimensional surface modes, which are protected by non-spatial symmetries. Recently, this idea has been extended to higher order topological phases with boundary modes that are localized in lower dimensions such as in the corners or in one dimensional hinges of the system. In this work, we demonstrate that a higher order topological phase can be engineered in a nonequilibrium state when the time-independent model does not possess any symmetry protected topological states. The higher order topology is protected by an emerging chiral symmetry, which is generated through the Floquet driving. Using both the exact numerical method and an effective high-frequency Hamiltonian obtained from the Brillouin-Wigner (BW) perturbation theory, we verify the emerging topological phase on aπ-flux square lattice. We show that the localized corner modes in our model are robust against a chiral symmetry preserving perturbation and can be classified as 'extrinsic' higher order topological phase. Finally, we identify a two dimensional topological invariant from the winding number of the corresponding sublattice symmetric one dimensional model. The latter model belongs to class AIII of ten-fold symmetry classification of topological matter.

Quantum Phases of Three-Dimensional Chiral Topological Insulators on a Spin Quantum Simulator

The detection of topological phases of matter has become a central issue in recent years. Conventionally, the realization of a specific topological phase in condensed matter physics relies on probing the underlying surface band dispersion or quantum transport signature of a real material, which may be imperfect or even absent. On the other hand, quantum simulation offers an alternative approach to directly measure the topological invariant on a universal quantum computer. However, experimentally demonstrating high-dimensional topological phases remains a challenge due to the technical limitations of current experimental platforms. Here, we investigate the three-dimensional topological insulators in the AIII (chiral unitary) symmetry class, which yet lack experimental realization. Using the nuclear magnetic resonance system, we experimentally demonstrate their topological properties, where a dynamical quenching approach is adopted and the dynamical bulk-boundary correspondence in the momentum space is observed. As a result, the topological invariants are measured with high precision on the band-inversion surface, exhibiting robustness to the decoherence effect. Our Letter paves the way toward the quantum simulation of topological phases of matter in higher dimensions and more complex systems through controllable quantum phases transitions.

Topological spintronics in a polyacetylene molecule device

Using the Su-Schrieffer-Heeger Hamiltonian and exploiting the Green's function method in the framework of the Landauer-Büttiker formalism, the topological and spin dependent electron transport properties of a trans polyacetylene molecule are studied. It is found that molecules with the intracell single carbon-carbon bonding and the even number of monomers in their chains have two edge states and possess topological properties though their Hamiltonians do not respect the chiral symmetry. A perpendicular exchange magnetic field and two perpendicular and transverse electric fields are used to induce and manipulate the quantum spin dependent electron transport properties. The exchange field induces the spin polarization in different electron energy regions which are expanded by stronger exchange fields. Therefore this proposed device works as a perfect spin filter. The spin polarization can be manipulated by applying the perpendicular electric field and remains robust against the transverse electric field variations.

Floquet Engineering Topological Many-Body Localized Systems

We show how second-order Floquet engineering can be employed to realize systems in which many-body localization coexists with topological properties in a driven system. This allows one to implement and dynamically control a symmetry protected topologically ordered qubit even at high energies, overcoming the roadblock that the respective states cannot be prepared as ground states of nearest-neighbor Hamiltonians. Floquet engineering-the idea that a periodically driven nonequilibrium system can effectively emulate the physics of a different Hamiltonian-is exploited to approximate an effective three-body interaction among spins in one dimension, using time-dependent two-body interactions only. In the effective system, emulated topology and disorder coexist, which provides an intriguing insight into the interplay of many-body localization that defies our standard understanding of thermodynamics and into the topological phases of matter, which are of fundamental and technological importance. We demonstrate explicitly how combining Floquet engineering, topology, and many-body localization allows one to harvest the advantages (time-dependent control, topological protection, and reduction of heating, respectively) of each of these subfields while protecting them from their disadvantages (heating, static control parameters, and strong disorder).

Refocusing in Situ Electron Microscopy: Moving beyond Visualization of Nanoparticle Self-Assembly To Gain Practical Insights into Advanced Material Fabrication

Despite incredible progress in preparing extended nanoparticle superlattices by self-assembly, theoretically predicted collective properties of extended nanoparticle superlattices are rarely correlated to observations due to the presence of defects. Enhanced fundamental understanding of the kinetics involved in nanoparticle superlattice self-assembly, specifically defect formation and annealing kinetics and mechanisms, is needed to prepare defect-free nanoparticle superlattices. In situ transmission electron microscopy (TEM) enables direct visualization of nanoparticle self-assembly phenomena in real time and at atomic spatial resolution; however, effective translation of in situ TEM data into new predictive models and material synthesis design rules remains a persistent challenge. Recent work by Ondry et al. in this issue of ACS Nano utilized atomic resolution in situ TEM to establish defect removal kinetics in epitaxially attached CdSe nanocrystal pairs, revealing a set of practical guidelines for minimizing defect formation in extended nanoparticle solids. Motivated by this work, in this Perspective, I explore and discuss the most effective and impactful uses of in situ TEM for nanoscience research and the associated technical barriers for performing in situ TEM measurements that are meaningful to bulk-scale self-assembly experiments.