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Sterdyniak A.,University of Innsbruck | Bernevig B.A.,Princeton University | Cooper N.R.,TCM Group | Regnault N.,Princeton University | Regnault N.,CNRS Pierre Aigrain Laboratory
Physical Review B - Condensed Matter and Materials Physics

An interesting route to the realization of topological Chern bands in ultracold atomic gases is through the use of optical flux lattices. These models differ from the tight-binding real-space lattice models of Chern insulators that are conventionally studied in solid-state contexts. Instead, they involve the coherent coupling of internal atomic (spin) states, and can be viewed as tight-binding models in reciprocal space. By changing the form of the coupling and the number N of internal spin states, they give rise to Chern bands with controllable Chern number and with nearly flat energy dispersion. We investigate in detail how interactions between bosons occupying these bands can lead to the emergence of fractional quantum Hall states, such as the Laughlin and Moore-Read states. In order to test the experimental realization of these phases, we study their stability with respect to band dispersion and band mixing. We also probe interesting topological phases that emerge in these systems when the Chern number is greater than 1. © 2015 American Physical Society. Source

Pillet J.-D.,CEA Saclay Nuclear Research Center | Quay C.H.L.,CEA Saclay Nuclear Research Center | Quay C.H.L.,University Paris - Sud | Morfin P.,CNRS Pierre Aigrain Laboratory | And 4 more authors.
Nature Physics

Carbon nanotubes (CNTs) are not intrinsically superconducting but they can carry a supercurrent when connected to superconducting electrodes1-4. This supercurrent is mainly transmitted by discrete entangled electron-hole states confined to the nanotube, called Andreev bound states (ABS). These states are a key concept in mesoscopic superconductivity as they provide a universal description of Josephson-like effects in quantum-coherent nanostructures (for example molecules, nanowires, magnetic or normal metallic layers) connected to superconducting leads5. We report here the first tunnelling spectroscopy of individually resolved ABS, in a nanotube-superconductor device. Analysing the evolution of the ABS spectrum with a gate voltage, we show that the ABS arise from the discrete electronic levels of the molecule and that they reveal detailed information about the energies of these levels, their relative spin orientation and the coupling to the leads. Such measurements hence constitute a powerful new spectroscopic technique capable of elucidating the electronic structure of CNT-based devices, including those with well-coupled leads. This is relevant for conventional applications (for example, superconducting or normal transistors, superconducting quantum interference devices3 (SQUIDs)) and quantum information processing (for example, entangled electron pair generation6,7, ABS-based qubits8). Finally, our device is a new type of d.c.-measurable SQUID. © 2010 Macmillan Publishers Limited. All rights reserved. Source

Filippone M.,CNRS Pierre Aigrain Laboratory | Dusuel S.,Lycee Saint Louis | Vidal J.,University Pierre and Marie Curie
Physical Review A - Atomic, Molecular, and Optical Physics

We consider a set of fully connected spin models that display first- or second-order transitions and for which we compute the ground-state entanglement in the thermodynamical limit. We analyze several entanglement measures (concurrence, Rényi entropy, and negativity) and show that, in general, discontinuous transitions lead to a jump of these quantities at the transition point. Interestingly, we also find examples where this is not the case. © 2011 American Physical Society. Source

Wu Y.-L.,Princeton University | Estienne B.,Paris-Sorbonne University | Estienne B.,CNRS Theoretical and High Energy Physics | Regnault N.,Princeton University | And 2 more authors.
Physical Review Letters

Quasiholes in certain fractional quantum Hall states are promising candidates for the experimental realization of non-Abelian anyons. They are assumed to be localized excitations, and to display non-Abelian statistics when sufficiently separated, but these properties have not been explicitly demonstrated except for the Moore-Read state. In this work, we apply the newly developed matrix product state technique to examine these exotic excitations. For the Moore-Read and the Z3 Read-Rezayi states, we estimate the quasihole radii, and determine the correlation lengths associated with the exponential convergence of the braiding statistics. We provide the first microscopic verification for the Fibonacci nature of the Z3 Read-Rezayi quasiholes. We also present evidence for the failure of plasma screening in the nonunitary Gaffnian wave function. © 2014 American Physical Society. Source

Herrmann L.G.,Ecole Normale Superieure de Paris | Herrmann L.G.,CNRS Pierre Aigrain Laboratory | Herrmann L.G.,University of Regensburg | Portier F.,CEA Saclay Nuclear Research Center | And 5 more authors.
Physical Review Letters

We report on conductance measurements in carbon nanotube based double quantum dots connected to two normal electrodes and a central superconducting finger. By operating our devices as beam splitters, we provide evidence for crossed Andreev reflections tunable in situ. This opens an avenue to more sophisticated quantum opticslike experiments with spin entangled electrons. © 2010 The American Physical Society. Source

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