Interplay Between Yu-Shiba-Rusinov States and Multiple Andreev Reflections

Motivated by recent scanning tunneling microscopy experiments on single magnetic impurities on superconducting surfaces, we present here a comprehensive theoretical study of the interplay between Yu-Shiba-Rusinov bound states and (multiple) Andreev reflections. Our theory is based on a combination of an Anderson model with broken spin degeneracy and nonequilibrium Green's function techniques that allows us to describe the electronic transport through a magnetic impurity coupled to superconducting leads for arbitrary junction transparency. Using this combination we are able to elucidate the different tunneling processes that give a significant contribution to the subgap transport. In particular, we predict the occurrence of a large variety of Andreev reflections mediated by Yu-Shiba-Rusinov bound states that clearly differ from the standard Andreev processes in non-magnetic systems. Moreover, we provide concrete guidelines on how to experimentally identify the subgap features originating from these tunneling events. Overall, our work provides new insight into the role of the spin degree of freedom in Andreev transport physics.Comment: 15 pages, 10 figure

Quantum algorithms for classical lattice models

We give efficient quantum algorithms to estimate the partition function of (i) the six vertex model on a two-dimensional (2D) square lattice, (ii) the Ising model with magnetic fields on a planar graph, (iii) the Potts model on a quasi 2D square lattice, and (iv) the Z_2 lattice gauge theory on a three-dimensional square lattice. Moreover, we prove that these problems are BQP-complete, that is, that estimating these partition functions is as hard as simulating arbitrary quantum computation. The results are proven for a complex parameter regime of the models. The proofs are based on a mapping relating partition functions to quantum circuits introduced in [Van den Nest et al., Phys. Rev. A 80, 052334 (2009)] and extended here.Comment: 21 pages, 12 figure

Dynamical Coulomb blockade of multiple Andreev reflections

We analyze the dynamical Coulomb blockade of multiple Andreev reflections (MAR) in a superconducting quantum point contact coupled to a macroscopic impedance. We find that at very low transmission the blockade scales as $n^2$ with $n = {Int}(2\Delta/eV)$, where $V$ is the bias voltage and $\Delta$ is the superconducting gap, as it would correspond to the occurrence of "shots" of charge $ne$. For higher transmission the blockade is reduced both due to Pauli principle and to elastic renormalization of the MAR probability, and for certain voltage regions it may even become an "antiblockade", i.e. the current is enhanced due to the coupling with the electromagnetic environment.Comment: 5 pages, 4 figures, submitted to Phys. Rev. Let

Magnetic Interference Patterns and Vortices in Diffusive SNS junctions

We study theoretically the electronic and transport properties of a diffusive superconductor-normal metal-superconductor (SNS) junction in the presence of a perpendicular magnetic field. We show that the field dependence of the critical current crosses over from the well-known Fraunhofer pattern in wide junctions to a monotonous decay when the width of the normal wire is smaller than the magnetic length \xi_H = \sqrt{\Phi_0/H}, where H is the magnetic field and \Phi_0 the flux quantum. We demonstrate that this behavior is a direct consequence of the magnetic vortex structure appearing in the normal region and predict how such structure is manifested in the local density of states.Comment: 6 pages, 3 figure

Long-distance distribution of genuine energy-time entanglement

Any practical realization of entanglement-based quantum communication must be intrinsically secure and able to span long distances avoiding the need of a straight line between the communicating parties. The violation of Bell's inequality offers a method for the certification of quantum links without knowing the inner workings of the devices. Energy-time entanglement quantum communication satisfies all these requirements. However, currently there is a fundamental obstacle with the standard configuration adopted: an intrinsic geometrical loophole that can be exploited to break the security of the communication, in addition to other loopholes. Here we show the first experimental Bell violation with energy-time entanglement distributed over 1 km of optical fibers that is free of this geometrical loophole. This is achieved by adopting a new experimental design, and by using an actively stabilized fiber-based long interferometer. Our results represent an important step towards long-distance secure quantum communication in optical fibers.Comment: 6 pages, 3 figures. Matches published versio

Nonlinear switching and solitons in PT-symmetric photonic systems

One of the challenges of the modern photonics is to develop all-optical devices enabling increased speed and energy efficiency for transmitting and processing information on an optical chip. It is believed that the recently suggested Parity-Time (PT) symmetric photonic systems with alternating regions of gain and loss can bring novel functionalities. In such systems, losses are as important as gain and, depending on the structural parameters, gain compensates losses. Generally, PT systems demonstrate nontrivial non-conservative wave interactions and phase transitions, which can be employed for signal filtering and switching, opening new prospects for active control of light. In this review, we discuss a broad range of problems involving nonlinear PT-symmetric photonic systems with an intensity-dependent refractive index. Nonlinearity in such PT symmetric systems provides a basis for many effects such as the formation of localized modes, nonlinearly-induced PT-symmetry breaking, and all-optical switching. Nonlinear PT-symmetric systems can serve as powerful building blocks for the development of novel photonic devices targeting an active light control.Comment: 33 pages, 33 figure

Mapping all classical spin models to a lattice gauge theory

In our recent work [Phys. Rev. Lett. 102, 230502 (2009)] we showed that the partition function of all classical spin models, including all discrete standard statistical models and all Abelian discrete lattice gauge theories (LGTs), can be expressed as a special instance of the partition function of a 4-dimensional pure LGT with gauge group Z_2 (4D Z_2 LGT). This provides a unification of models with apparently very different features into a single complete model. The result uses an equality between the Hamilton function of any classical spin model and the Hamilton function of a model with all possible k-body Ising-type interactions, for all k, which we also prove. Here, we elaborate on the proof of the result, and we illustrate it by computing quantities of a specific model as a function of the partition function of the 4D Z_2 LGT. The result also allows one to establish a new method to compute the mean-field theory of Z_2 LGTs with d > 3, and to show that computing the partition function of the 4D Z_2 LGT is computationally hard (#P hard). The proof uses techniques from quantum information.Comment: 21 pages, 21 figures; published versio

Density of states and supercurrent in diffusive SNS junctions: role of nonideal interfaces and spin-flip scattering

We present a theoretical study of the density of states and supercurrent in diffusive superconductor-normal metal-superconductor (SNS) junctions. In particular, we study the influence on these two equilibrium properties of both an arbitrary transparency of the SN interfaces and the presence of spin-flip scattering in the normal wire. We show that the minigap that is present in the spectrum of the diffusive wire is very sensitive to the interface transmission. More mportantly, we show that at arbitrary transparency the minigap replaces the Thouless energy as the relevant energy scale for the proximity effect, determining for instance the temperature dependence of the critical current. We also study in detail how the critical current is suppressed by the effect of spin-flip scattering, which can be due to either magnetic impurities or, under certain circumstances, to an external magnetic field. Our analysis based on the quasiclassical theory of diffusive superconductors can be very valuable to establish quantitative comparisons between experiment and theory.Comment: 12 pages, 13 figure