Topological properties of matter are one of hot topics in condensed matter physics. Recently, these concepts are extended to non-equilibrium systems, especially periodically driven systems. Here we study such non-equilibrium topological quantum phenomena in cold atomic systems in twodimensional optical lattices. First we show results on non-interacting atoms, and then focus on interaction effects on the non-equilibrium topological phases based on time-dependent Schrieffer-Wolfftype perturbation theory.
Topological properties of matter are one of hot topics in condensed matter physics. Recently, these concepts are extended to non-equilibrium systems, especially periodically driven systems. Here we study such non-equilibrium topological quantum phenomena in cold atomic systems in twodimensional optical lattices. First we show results on non-interacting atoms, and then focus on interaction effects on the non-equilibrium topological phases based on time-dependent Schrieffer-Wolfftype perturbation theory.
Recently, concepts of topological phases of matter are extended to nonequilibrium systems, especially periodically driven systems. In this paper, we construct an example which shows nonequilibrium topological phase transitions using ultracold fermions in optical lattices. We show that the Rabi oscillation has the possibility to induce nonequilibrium topological phases which are classified into time-reversal-invariant topological insulators for a two-orbital model of alkaline-earth-metal atoms. Furthermore, we study the nonequilibrium topological phases using time-dependent Schrieffer--Wolff-type perturbation theory, and we obtain an analytical expression to describe the topological phase transitions from a high-frequency limit of external driving fields.
This is an introductory review of the physics of topological quantum matter with cold atoms. Topological quantum phases, originally discovered and investigated in condensed matter physics, have recently been explored in a range of different systems, which produced both fascinating physics findings and exciting opportunities for applications. Among the physical systems that have been considered to realize and probe these intriguing phases, ultracold atoms become promising platforms due to their high flexibility and controllability. Quantum simulation of topological phases with cold atomic gases is a rapidly evolving field, and recent theoretical and experimental developments reveal that some toy models originally proposed in condensed matter physics have been realized with this artificial quantum system. The purpose of this article is to introduce these developments. The article begins with a tutorial review of topological invariants and the methods to control parameters in the Hamiltonians of neutral atoms. Next, topological quantum phases in optical lattices are introduced in some detail, especially several celebrated models, such as the Su–Schrieffer–Heeger model, the Hofstadter–Harper model, the Haldane model and the Kane–Mele model. The theoretical proposals and experimental implementations of these models are discussed. Notably, many of these models cannot be directly realized in conventional solid-state experiments. The newly developed methods for probing the intrinsic properties of the topological phases in cold-atom systems are also reviewed. Finally, some topological phases with cold atoms in the continuum and in the presence of interactions are discussed, and an outlook on future work is given.
Mathematical tools and concepts initially developed to study topological properties of geometrical objects have allowed for better understanding and interpretation of a number of phenomena in condensed matter physics, from the quantum Hall effect to topological insulators. It would be interesting to realize analogs of these phenomena with light scattered by cold atoms because atomic systems are simpler and allow for better control than complex solid-state compounds in which electrons interact with each other and with phonons, and where disorder is omnipresent. At the same time, mastering topological photonics of cold atoms may lead to interesting applications in quantum information science, for example. We study the opening of topological band gaps in two-dimensional honeycomb lattices of two-level atoms [1], the impact of disorder on their properties [2], as well as the constructive role that disorder can play by inducing a topologically nontrivial phase known as “topological Anderson insulator” [2,3]. Modifying the structure of the atomic lattice in an appropriate way allows for constructing a synthetic spin degree of freedom and thus for exploring the physics of spinful particles, such as the quantum spin Hall effect, for example. The analogy between topological phenomena in solid-state physics and in optics of cold atoms is not complete: atomic systems exhibit a number of new features due to the vector nature of light and to the differences in the impact of disorder on their properties.1. P. Wulles and S.E. Skipetrov, Topological photonic band gaps in honeycomb atomic arrays, arXiv:2308.134232. S.E. Skipetrov and P. Wulles, Topological transitions and Anderson localization of light in disordered atomic arrays, Phys. Rev. A 105, 043514 (2022)3. S.E. Skipetrov and P. Wulles, Photonic topological Anderson insulator in a two-dimensional atomic lattice, Comptes Rendus. Physique 24(S3), 39–54 (2023)
Topological matter is a popular topic in both condensed matter and cold-atom research. In the past decades, a variety of models have been identified with fascinating topological features. Some, but not all, of the models can be found in materials. As a fully controllable system, cold atoms trapped in optical lattices provide an ideal platform to simulate and realize these topological models. Here we present a proposal for synthesizing topological models in cold atoms based on a one-dimensional spin-dependent optical lattice potential. In our system, features such as staggered tunneling, staggered Zeeman field, nearest-neighbor interaction, beyond-near-neighbor tunneling, etc. can be readily realized. They underlie the emergence of various topological phases. Our proposal can be realized with current technology and hence has potential applications in quantum simulation of topological matter.
Topological phases of matter are understood to be characterized by particular configurations of entanglement encoded within the ground states of many-body quantum systems. In this thesis, we discuss how novel phenomena associated with topological phases can arise in systems that are driven out of equilibrium or coupled to their surroundings, which are not described by ground state physics. Firstly, we consider systems undergoing unitary time evolution due to some external driving. We show how the entanglement features of the time-dependent wavefunction can be topologically characterized, and demonstrate that these topological properties are reflected in the dynamics of various quantities usually associated with topological phases in equilibrium. We introduce a new non-equilibrium topological classification scheme which can be used to predict whether or not the topological features of a given system will be preserved under time evolution. In brief, this classification captures the fact that certain symmetries (namely antiunitary symmetries) are inevitably broken once the system is driven out of equilibrium; thus any topological phenomena protected by such symmetries cannot be expected to persist in non-equilibrium scenarios. Secondly, we investigate how topologically non-trivial systems are affected by dissipative effects, i.e.~coupling to an external environment. We demonstrate that system-environment interactions facilitate processes in the system that effectively break any antiunitary symmetries, regardless of the symmetries of the microscopic Hamiltonian. Accordingly, those phases that were shown to be unstable against time-dependent driving are also fragile against coupling to an environment. To illustrate the consequences of this fragility, we consider the effects of dissipation on the coherence properties of topological bound states, as well as the conductance properties of chiral and helical topological edge modes. We find that the decoherence rate of the former and the deviation from quantized conductivity of the latter are (not) exponentially suppressed in the inverse temperature when the phase in question is protected by unitary (antiunitary) symmetries. These results regarding open systems can be connected to the same non-equilibrium classification developed in the context of isolated systems undergoing unitary dynamics. Our findings highlight a distinction between topological phases that are either robust or fragile against non-equilibrium effects and/or system-environment coupling. The ramifications for the use of such systems in quantum technologies are discussed.
The topology of quantum materials is the frontier research in condensed matter physics. In contrast with the conventional classification of materials by using the local symmetry breaking criterion, the states of quantum systems are classified according to the topology of wave functions. The potential applications of topological states may lead the traditional microelectronics to break through and accelerate the significant improvement in topological electronics. Most of the recent studies focus on the topological states of quantum systems under equilibrium conditions without external perturbations. The topological states of quantum systems far from the equilibrium under time-periodic driving have attracted wide attention. Here we first introduce the framework of Floquet engineering under the frame of the Floquet theorem. The nonequilibrium topological states of massless and massive Dirac fermions are discussed including the mechanism of phase transition. Light field driven electronic transition term in the quantum material gains extra time-dependent phase. Thereby the manipulation of effective transition term of the electron is realized to regulate the non-equilibrium topological states. We also mention how the photoinduced coherent phonon affects the nonequilibrium topological states of quantum systems from the perspective of atom manufacturing. Furthermore, research outlook on the nonequilibrium topological states is given. This review provides some clues to the design of physical properties and transport behaviors of quantum materials out of equilibrium.