Feng Mei

Topological phase transitions and Thouless pumping of light in photonic waveguide arrays

Photonic waveguide arrays provide an excellent platform for simulating conventional topological systems, and they can also be employed for the study of novel topological phases in photonics systems. However, a direct measurement of bulk topological invariants remains a great challenge. Here we study topological features of generalized commensurate Aubry-Andre-Harper (AAH) photonic waveguide arrays and construct a topological phase diagram by calculating all bulk Chern numbers, and then explore the bulk-edge correspondence by analyzing the topological edge states and their winding numbers. In contrast to incommensurate AAH models, diagonal and off-diagonal commensurate AAH models are not topologically equivalent. In particular, there appear nontrivial topological phases with large Chern numbers and topological phase transitions. By implementing Thouless pumping of light in photonic waveguide arrays, we propose a simple scheme to measure the bulk Chern numbers.

Topological invariant and cotranslational symmetry in strongly interacting multi-magnon systems

It is still an outstanding challenge to characterize and understand the topological features of strongly interacting states such as bound-states in interacting quantum systems. Here, by introducing a cotranslational symmetry in an interacting multi-particle quantum system, we systematically develop a method to define a Chern invariant, which is a generalization of the well-known Thouless-Kohmoto-Nightingale-den Nijs invariant, for identifying strongly interacting topological states. As an example, we study the topological multi-magnon states in a generalized Heisenberg XXZ model, which can be realized by the currently available experiment techniques of cold atoms [Phys. Rev. Lett. \textbf{111}, 185301 (2013); Phys. Rev. Lett. \textbf{111}, 185302 (2013)]. Through calculating the two-magnon excitation spectrum and the defined Chern number, we explore the emergence of topological edge bound-states and give their topological phase diagram. We also analytically derive an effective single-particle Hofstadter superlattice model for a better understanding of the topological bound-states. Our results not only provide a new approach to defining a topological invariant for interacting multi-particle systems, but also give insights into the characterization and understanding of strongly interacting topological states.

Witnessing topological Weyl semimetal phase in a minimal circuit-QED lattice

We present a feasible protocol to mimic topological Weyl semimetal phase in a small one-dimensional circuit-QED lattice. By modulating the photon hopping rates and on-site photon frequencies in parametric spaces, we demonstrate that the momentum space of this one-dimensional lattice model can be artificially mapped to three dimensions accompanied by the emergence of topological Weyl semimetal phase. Furthermore, via a lattice-based cavity input-output process, we show that all the essential topological features of Weyl semimetal phase, including the topological charge associated with each Weyl point and the open Fermi arcs, can be unambiguously detected in a circuit with four dissipative resonators by measuring the reflection spectra. These remarkable features may open a new prospect in using well-controlled small quantum lattices to mimic and study topological phases.

Topological magnon bound states in periodically modulated Heisenberg XXZ chains

Strongly interacting topological states in multi-particle quantum systems pose great challenges to both theory and experiment. Recently, bound states of elementary spin waves (magnons) in quantum magnets have been experimentally observed in quantum Heisenberg chains comprising ultracold Bose atoms in optical lattices. Here, we explore a strongly interacting topological state called topological magnon bound-state in the quantum Heisenberg chain under cotranslational symmetry. We find that the cotranslational symmetry is the key to the definition of a topological invariant for multi-particle quantum states, which enables us to characterize the topological features of multi-magnon excitations. We calculate energy spectra, density distributions, correlations and Chern numbers of the two-magnon bound-states and show the existence of topological protected edge bound-states. Our study not only opens a new prospect to pursue topological magnon bound-states, but also gives insights into the characterization and understanding of strongly interacting topological states.

Simulation and measurement of the fractional particle number in one-dimensional optical lattices

We propose a scheme to mimic and directly measure the fractional particle number in a generalized Su-Schrieffer-Heeger model with ultracold fermions in one-dimensional optical lattices. We show that the fractional particle number in this model can be simulated in the momentum-time parameter space in terms of Berry curvature without a spatial domain wall. In this simulation, a hopping modulation is adiabatically tuned to form a kink-type configuration and the induced current plays the role of an analogous soliton distributing in the time domain, such that the mimicked fractional particle number is expressed by the particle transport. Two feasible experimental setups of optical lattices for realizing the required Su-Schrieffer-Heeger Hamiltonian with tunable parameters and time-varying hopping modulation are presented. We also show practical methods for measuring the particle transport in the proposed cold atom systems by numerically calculating the shift of the Wannier center and the center of mass of an atomic cloud.

Topologically Protected Quantum State Transfer via Edge States in Superconducting Circuits

Robust quantum state transfer (QST) is an indispensable ingredient in scalable quantum information processing. Here we present an experimentally feasible mechanism for realizing robust QST via topologically protected edge states in superconducting qubit chains. Using superconducting Xmon qubits with tunable couplings, we construct generalized Su-Schrieffer-Heeger models and analytically derive the wave functions of topological edge states. We find that such edge states can be employed as a quantum channel to realize robust QST between remote qubits. With a numerical simulation, we show that both single-qubit states and two-qubit entangled states can be robustly transferred in the presence of sizable imperfections in the qubit couplings. The transfer fidelity demonstrates a wide plateau at the value of unity in the imperfection magnitude. This approach is general and can be implemented in a variety of quantum computing platforms.

Superfluid–Mott-insulator quantum phase transition of light in a two-mode cavity array with ultrastrong coupling

In this paper we construct a new type of cavity array, in each cavity of which multiple two-level atoms interact with two independent photon modes. This system can be totally governed by a two-mode Dicke-lattice model, which includes all of the counter-rotating terms and therefore works well in the ultrastrong coupling regime achieved in recent experiments. Attributed to its special atom-photon coupling scheme, this model supports a global conserved excitation and a continuous

Synthetic spin-orbit coupling and topological polaritons in Janeys-Cummings lattices

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Robust quantum state transfer via topological edge states in superconducting qubit chains

symmetry, rather than the discrete

Topology-dependent quantum dynamics and entanglement-dependent topological pumping in superconducting qubit chains

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