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We study a mechanical oscillator coupled to a two-level system driven by a blue-detuned coherent source in the resolved sideband regime. For weak mechanical damping, we find dynamical instabilities leading to limit cycles. They are signaled by strong fluctuations in the number of emitted photons, with a large Fano factor. The phonon-number fluctuations exhibit a strikingly similar behavior. When the coupling strength becomes comparable to the mechanical frequency, non-classical mechanical states appear. We discuss the relation with cavity optomechanical systems. Candidates for observing these effects include superconducting qubits, NV centers, and single molecules coupled to oscillators.

Generating nonclassical states of mechanical systems is a challenge relevant for testing the foundations of quantum mechanics and developing quantum technologies. Significant effort has been made to search for such states in the stationary behaviour of cavity optomechanical systems. We focus instead on the transient dynamics. We find that in the strong coupling regime the presence of an optical drive causes an initial mechanical coherent state to evolve to a nonclassical state, with strongly negative Wigner function. An analytical treatment for weak drive reveals that these states are quantum superpositions of coherent states. Numerical simulation shows that the presence of Wigner negativity is robust against weak dissipation.

In this article, we develop a description of topological pumps as slow classical dynamical variables coupled by a quantum system. We discuss the cases of quantum Hall pumps, Thouless pumps, and the more recent Floquet pumps based frequency converters. This last case corresponds to a quantum topological coupling between classical modes described by action-angle variables on which we focus. We propose a realization of such a topological coupler based on a superconducting qutrit suitably driven by three modulated drives. A detailed experimental protocol allowing to measure the quantized topological power transfer between the different modes of a superconducting circuit is discussed.

The bulk-boundary correspondence establishes a connection between the bulk topological index of an insulator or superconductor, and the number of topologically protected edge bands or states. For topological superconductors in two dimensions the first Chern number is related to the number of protected bands within the bulk energy gap, and is therefore assumed to give the number of Majorana band states in the system. Here we show that this is not necessarily the case. As an example we consider a hexagonal-lattice topological superconductor based on a model of graphene with Rashba spin orbit coupling, proximity induced s-wave superconductivity, and a Zeeman magnetic field. We explore the full Chern number phase diagram of this model, extending what is already known about its parity. We then demonstrate that despite the high Chern numbers that can be seen in some phases these do not strictly always contain Majorana bound states., Comment: 8 pages, 7 figures

We study the Friedel oscillations induced by a localized impurity in anisotropic graphene. We focus on the limit when the two inequivalent Dirac points merge. We find that in this limit the Friedel oscillations manifest very peculiar features, such as a strong asymmetry and an atypical inverse square-root decay. Our calculations are performed using both a T-matrix approximation and a tight-binding exact diagonalization technique. They allow us to obtain numerically the local density of states as a function of energy and position, as well as an analytical form of the Friedel oscillations in the continuum limit. The two techniques yield results that are in excellent agreement, confirming the accuracy of such methods to approach this problem.