No Arabic abstract
The interplay of synchronization and topological band structures with symmetry protected midgap states under the influence of driving and dissipation is largely unexplored. Here we consider a trimer chain of electron shuttles, each consisting of a harmonic oscillator coupled to a quantum dot positioned between two electronic leads. Each shuttle is subject to thermal dissipation and undergoes a bifurcation towards self-oscillation with a stable limit cycle if driven by a bias voltage between the leads. By mechanically coupling the oscillators together, we observe synchronized motion at the ends of the chain, which can be explained using a linear stability analysis. Due to the inversion symmetry of the trimer chain, these synchronized states are topologically protected against local disorder. Furthermore, with current experimental feasibility, the synchronized motion can be observed by measuring the dot occupation of each shuttle. Our results open a new avenue to enhance the robustness of synchronized motion by exploiting topology.
The oscillation of Majorana modes with near zero energy plays a very important role for ascertaining Majorana fermions. The edge states, which also have almost-zero-energy in one-dimensional Su-Schrieffer-Heeger chain (SSHc), have been extensively studied for their topologically protected properties when the on-sites have dissipations induced by independent environments. We here show that common environments shared by each pair of the nearest neighbour sites in the SSHc can result in dissipative couplings between sites, and thus change topologically trivial phase to nontrivial one. The Majorana-like oscillation for the finite-size hybridizations of two non-Hermitian edge states with complex localization lengths can be induced by the dissipative coupling. The controllable topology parameter of the SSHc plays the role of the magnetic field in the nanowire for controlling Majorana oscillation. The measurement for the oscillation is proposed. Our study provides a new way to manipulate edge states and is experimentally feasible within current technology of superconducting quantum circuits.
We report on the observation of a topologically protected edge state at the interface between two topologically distinct domains of the Su-Schrieffer-Heeger model, which we implement in arrays of evanescently coupled dielectric-loaded surface plasmon polariton waveguides. Direct evidence of the topological character of the edge state is obtained through several independent experiments: Its spatial localization at the interface as well as the restriction to one sublattice is confirmed by real-space leakage radiation microscopy. The corresponding momentum-resolved spectrum obtained by Fourier imaging reveals the midgap position of the edge state as predicted by theory.
Describing open quantum systems far from equilibrium is challenging, in particular when the environment is mesoscopic, when it develops nonequilibrium features during the evolution, or when the memory effects cannot be disregarded. Here, we derive a master equation that explicitly accounts for system-bath correlations and includes, at a coarse-grained level, a dynamically evolving bath. Such a master equation applies to a wide variety of physical systems including those described by Random Matrix Theory or the Eigenstate Thermalization Hypothesis. We obtain a local detailed balance condition which, interestingly, does not forbid the emergence of stable negative temperature states in unison with the definition of temperature through the Boltzmann entropy. We benchmark the master equation against the exact evolution and observe a very good agreement in a situation where the conventional Born-Markov-secular master equation breaks down. Interestingly, the present description of the dynamics is robust and it remains accurate even if some of the assumptions are relaxed. Even though our master equation describes a dynamically evolving bath not described by a Gibbs state, we provide a consistent nonequilibrium thermodynamic framework and derive the first and second law as well as the Clausius inequality. Our work paves the way for studying a variety of nanoscale quantum technologies including engines, refrigerators, or heat pumps beyond the conventionally employed assumption of a static thermal bath.
Topological pumping and duality transformations are paradigmatic concepts in condensed matter and statistical mechanics. In this paper, we extend the concept of topological pumping of particles to topological pumping of quantum correlations. We propose a scheme to find pumping protocols for highly-correlated states by mapping them to uncorrelated ones. We show that one way to achieve this is to use dualities, because they are non-local transformations that preserve the topological properties of the system. By using them, we demonstrate that topological pumping of kinks and cluster-like excitations can be realized. We find that the entanglement of these highly-correlated excitations is strongly modified during the pumping process and the interactions enhance the robustness against disorder. Our work paves the way to explore topological pumping beyond the notion of particles and opens a new avenue to investigate the relation between correlations and topology.
We simulate various topological phenomena in condense matter, such as formation of different topological phases, boundary and edge states, through two types of quantum walk with step-dependent coins. Particularly, we show that one-dimensional quantum walk with step-dependent coin simulates all types of topological phases in BDI family, as well as all types of boundary and edge states. In addition, we show that step-dependent coins provide the number of steps as a controlling factor over the simulations. In fact, with tuning number of steps, we can determine the occurrences of boundary, edge states and topological phases, their types and where they should be located. These two features make quantum walks versatile and highly controllable simulators of topological phases, boundary, edge states, and topological phase transitions. We also report on emergences of cell-like structures for simulated topological phenomena. Each cell contains all types of boundary (edge) states and topological phases of BDI family.