## Epitaxial III-V Quantum Dots for Quantum Optical Information S&T: Pros and Cons

Benito Alén (MBE: Quantum Nanostructures Group (IMM-CSIC))

Quantum optical experiments performed on single atoms and ions had inspired the rapid development of solid-state Quantum Optical Information S&T. In the study and exploitation of quantum properties of semiconductor nanostructures, much of the state of the art is defined by experiments done with epitaxial III-V quantum dots (QDs). There are many properties of III-V QDs which make them especially appealing compared with other systems. Either stand alone or embedded in optical microcavities, III-V QDs naturally emit single photons and entangled photon pairs in the relevant telecomm spectral ranges [1-4]. Moreover, just as any other semiconductor, they can be electrically driven from a low power battery, both to emit quantum light [5,6] or to manipulate quantum states [7,8]. These and other proofs of concept make of III-V QDs amenable for highly integrated quantum optical information technologies, yet, to bring expectations to reality, rather important technical and fundamental problems must be solved first. In this talk, I will introduce some of the current challenges in the field and describe how our activities at the MBE: Quantum Nanostructures Group (IMM-CSIC) try to address them [9-10]. References: [1] P. Michler et al, «A Quantum Dot Single-Photon Turnstile Device», Science, 290 2282 (2000) [2] C. Santori et al, «Indistinguishable photons from a single-photon device», Nature 419, 594 (2002) [3] M. Birowosuto et al, «Fast Purcell-Enhanced Single Photon Source in 1,550-mm Telecom Band from a Resonant Quantum Dot-Cavity Coupling». Scientific Reports 2, 321 (2012) [4] J. Kim et al «Two-Photon Interference from a Bright Single-Photon Source at Telecom Wavelengths». Optica 3, 577 (2016) [5] Z. Yuan et al, «Electrically Driven Single-Photon Source», Science 295, 102, (2002) [6] C. L. Salter et al, «An entangled-light-emitting diode», Nature 465, 594, (2010) [7] E. D. Kim et al., «Fast Spin Rotations by Optically Controlled Geometric Phases in a Charge-Tunable InAs Quantum Dot», Phys. Rev. Lett. 104, 167401 (2010) [8] W. Liu et al., «In situ tunable g factor for a single electron confined inside an InAs quantum dot», Phys. Rev. B 84 121304 (2011) [9] J. Herranz et al «Role of re-growth interface preparation process for spectral linewidth reduction of single InAs site-controlled quantum dots». Nanotechnology 26 195301 (2015) [10] J. M. Llorens et al., «Type II InAs/GaAsSb quantum dots: Highly tunable exciton geometry and topology», Applied Physics Letters 107, 183101 (2015)

Seminar Room, Serrano 121 (CFMAC)

## Edge states at phase boundaries and their stability

Juan Manuel Pérez Pardo (Dpto. de Matemáticas, Universidad Carlos III de Madrid)

Quantum field theories can be used to construct effective modells to describe condensed matter systems. One of the main differences between condensed matter systems and fundamental particle physics is that, in the former, the materials where the effective field theory lives are of finite size and have boundaries. This difference is crucial and brings extra features like the appearance of edge states. I will show that the appearance of edge states is related with the type of boundary conditions describing the effective model and the difficulties that might arise when one considers different boundary conditions. For doing that I will consider two different situations, scalar theories and fermionic theories. Surprisingly, in the latter case, there is a threshold size for the sample below which the edge states disappear.

Seminar Room, Serrano 121 (CFMAC)

## Modifications of molecular structure and reactions under strong light-matter coupling

Johannes Feist (Dpto. Física Teórica de la Materia Condensada (UAM))

Strong coupling is achieved when the coherent energy exchange between a confined electromagnetic field mode and material excitations becomes faster than the decay and decoherence of either constituent. This creates a paradigmatic hybrid quantum system with eigenstates that have mixedlight-matter character (polaritons). Organic molecules are a particularly useful system to achieve strong coupling at room temperature, since they possess excitons (bound electron-hole pairs) with large transition dipole moments and binding energies. While most models of strong coupling are based on two-level systems, this is far from a realistic description for molecules with many nuclear (rovibrational) degrees of freedom. The influence of strong coupling on these internal degrees of freedom has only come into focus recently. Pioneering experiments have shown modifications of material properties and chemical reaction rates under strong coupling, which cannot be explained by simple two-level models. In order to address this mismatch, we developed a first-principles model combining the tools of cavity QED with well-known molecular models in order to fully take into account electronic, nuclear and photonic degrees of freedom. I will first discuss the applicability of the Born-Oppenheimer approximation, which is challenged by the introduction of the new intermediate timescale of energy exchange between the molecule(s) and the field. We then show how photochemical reactions such as photoisomerization can be almost completely suppressed under strong coupling. Surprisingly, this suppression works more efficiently when many molecules are coupled to a single light mode due to a “collective protection” effect within the delocalized polaritonic state.

Seminar Room, Serrano 121 (CFMAC)

## El computador cuántico

Carlos Sabín Lestayo (Instituto de Física Fundamental)

En esta charla explicamos qué es un computador cuántico, de qué objetos se compone, y cuáles son las operaciones que realiza. Explicamos también en qué consiste el computador cuántico de IBM y realizaremos pequeñas demostraciones sobre cómo se utiliza para, por ejemplo, realizar teletransporte cuántico.

Seminar Room, Serrano 121 (CFMAC)

## Dissipative long-range entanglement generation between electronic spins

Mónica Benito (Instituto de Ciencia de Materiales de Madrid (ICMM), CSIC))

We propose a scheme for deterministic preparation of steady-state entanglement between remote qubits, defined by electron spins confined in spatially separated quantum dots. Our approach relies on an electronic quantum bus, consisting either of quantum Hall edge channels or surface acoustic waves, that can mediate long-range coupling between localized spins over distances of tens of micrometers. Since the entanglement is actively stabilized by dissipative dynamics, our scheme is inherently robust against noise and imperfections.

Seminar Room, Serrano 121 (CFMAC)

## Symmetry-Protected Heat Transport in Quantum Hall Physics

Ángel Rivas (Dpto. de Física teórica I, UCM)

The study of non-equilibrium properties in topological quantum systems is of practical and fundamental importance. Here, we will discuss stationary properties of a two-dimensional boson topological insulator coupled to two thermal baths in the quantum open-system formalism [1]. Novel phenomena appear like chiral edge heat currents that are the out-of-equilibrium counterparts of the zero-temperature edge currents. A new set of discrete symmetries protect these topological heat currents, differing from the zero-temperature limit, and with a purely dissipative origin. Remarkably, one of these currents flows opposite to the decreasing external temperature gradient. As the starting point, we will review some basics about quantum Hall physics and consider the case of a single external reservoir showing prominent results like thermal erasure effects and topological thermal currents. Finally we will comment about the possibility to experimentally observe these new phenomenology with platforms like photonics chips and optical lattices. [1] A. Rivas and M. A. Martin-Delgado, Topological Heat Transport and Symmetry-Protected Boson Currents, arXiv:1606.07651

Seminar Room, Serrano 121 (CFMAC)

## Zero-Mode Rotating Surface States in 3D Dirac and Weyl Semimetals under Radiation

Rafael Molina (Instituto de Estructura de la Materia, CSIC)

Topological semimetals are exciting new materials whose discovery became possible thanks to the refined understanding of exotic phenomena in topological band theory. We investigate the development of novel surface states when 3D Dirac or Weyl semimetals are placed under circularly polarized electromagnetic radiation. We find that the hybridization between inverted Floquet bands opens, in general, a gap, which closes at so-called exceptional points found for complex values of the momentum. This corresponds to the appearance of midgap surface states in the form of evanescent waves decaying from the surface exposed to the radiation. We observe a phenomenon reminiscent of Landau quantization by which the midgap surface states get a large degeneracy proportional to the radiation flux traversing the surface of the semimetal. We show that all of these surface states carry angular current, leading to an angular modulation of their charge that rotates with the same frequency of the radiation, which should manifest in the observation of a macroscopic chiral current in the irradiated surface. Reference: J. González, R.A. Molina, PRL 116, 156803 (2016).

Seminar Room, Serrano 121 (CFMAC)

## Polaritons: classical and/or quantum aspects

Fabrice P. Laussy (Dpto. de Física Teórica de la Materia Condensada, Universidad Autónoma de Madrid)

Polaritons arise as the eigenstates of light-matter coupling hamiltonians (1). They have enjoyed considerable attention since their discovery in 1992, since they bring together solid state, condensed-matter, atomic and cavity QED physics. Interest has been growing exponentially with subsequent reports of their Boseâ€“Einstein condensation in (Nature 2006), of their superfluid propagation (Nature 2009), of their quantum-hydrodynamics and solitonic attributes (2010-2012), and, more recently, exotic phases, band-engineering, exceptional points (Nature 2015) and other topological features. They are a fantastic playground for theorists and experimentalists alike allowing a wide breadth of exploration in a variety of topics. In this talk, I will survey some of the most striking polaritonic feasts and review the efforts to bring them down to the single-particle quantum regime, culminating with our recent announcement of polariton entanglement (2). I will also take advantage of this system to present our proposal of quantum spectroscopy, based on sweeping continuously varying quantum statistics from a quantum source driving a target (3). (1) Microcavities, Kavokin et al., Oxford University Press 2011 (2) Entangling a polariton with one photon: effect of interactions at the single-particle level, Cuevas et al., arXiv:1609.01244 (3) Exciting Polaritons with Quantum Light, López Carreño et al., Phys. Rev. Lett. 115:196402 2015

Seminar Room, Serrano 121 (CFMAC)

## Simulating spin-boson models with trapped ions

Andreas Lemmer (Institute of Theoretical Physics, University of Ulm, Germany)

The spin-boson model considers a single spin coupled to a bath of harmonic oscillators. It is a paradigmatic model for the emergence of dissipation and decoherence in quantum systems. Although the model is seemingly simple, no closed analytic solution is known to date. On the other hand, a number of numerical methods have been developed to study the dynamics of spin-boson models. However, also numerics are challenged for environments that lead to highly non-Markovian dynamics, e.g. highly structured environments with long lived vibrational modes. Therefore a physical simulator with a high degree of control is desirable. Trapped atomic ions provide a clean and highly controllable system where dynamical quantities are directly accessible. In this talk I will present a method to simulate the dynamics of spin-boson models with macroscopic and non-Markovian environments with trapped ions.

Seminar Room, Serrano 121 (CFMAC)

## Machine Learning: Between the hype and the new possibilities

Emilio Alba (CTO of Quantum Bussiness Analytics)

Machine Learning is at the forefront of a renewed interest in (big) data analytics and statistical analysis. In this talk we try to briefly describe what it is, make the case for its increasing role in technological applications, and open a discussion on its bright and dark effects on physics as a whole – and the realm of Quantum Information/Simulations in particular.

Seminar Room, Serrano 121 (CFMAC)

## Quantum simulation with a boson sampling circuit

Diego González Olivares (Instituto de Física Fundamental, CSIC)

Boson sampling is a model of quantum computation that was proposed by S. Aaroson and A. Arkhipov as a restricted model for post-classical computation whose architecture should be experimentally achievable with current, state of the art technologies. We have studied a system that consists of 2M matter qubits that interact through a boson sampling circuit, i.e., an M-port interferometer, embedded in two di erent architectures. We have proven that, under the conditions required to derive a master equation, the qubits evolve according to e ective bipartite XY spin Hamiltonians, with or without local and collective dissipation terms. This opens the door to the simulation of any bipartite spin or hard-core boson models and exploring dissipative phase transitions as the competition between coherent and incoherent exchange of excitations. We have also shown that, in the purely dissipative regime, this model has a large number of exact and approximate dark states, whose structure and decay rates can be estimated analytically. We argue that this system may be used for the adiabatic preparation of boson sampling states encoded in the matter qubits.

Seminar Room, Serrano 121 (CFMAC)

## V-shape artificial atom based on superconducting quantum circuit

Olivier Buisson (Institut Néel, CNRS (Grenoble))

We present an experimental study on two superconducting transmon qubits coupled via a large inductance [1]. The resulting circuit exhibits a symmetric and an antisymmetric oscillation [2] which we use as a transmon and ancilla qubit, respectively.We observe a cross-anharmonicity between the two oscillations which is explained by the Josephson nonlinearity [1].This coupling leads the artificial atom to a have V-shape energy diagram. We have predicted that such V-shape artificial atom, inside a circuit cavity quantum electrodynamics architecture, allows to read out the transmon qubit state by using the ancilla qubit frequency [3]. In comparison with the most widely employed readout scheme for superconducting qubits, the dispersive readout, our approach promises a quantum non-demolition measurement with a significantly stronger measurement signal and without suffering from Purcell effect. In a measurement chain based on a state-of-the-art Josephson parametric amplifier, we predict a QND fidelity of up to 99.9% for a measurement time down to 60 ns [3]. [1] É. Dumur, et al, “A V-shape superconducting artificial atom based on two inductively coupled transmons”, Phys. Rev. B 92, 020515 (2015). [2] F. Lecocq, et al, ‘Coherent Frequency Conversion in a Superconducting Artificial Atom with Two Internal Degrees of Freedom’, Physical Review Letters 108, 107001 (2012). [3] I. Diniz, et al, ‘Ultrafast quantum nondemolition measurements based on a diamond shaped artificial atom’, Physical Review A 87, 033837 (2013).

Seminar Room, Serrano 121 (CFMAC)

## Chiral Quantum Optics with Spins, Photons, and Phonons

Tomás Ramos (Institute for Theoretical Physics, University of Innsbruck and Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences)

Quantum optics studies the interaction between light and matter on the most fundamental level, namely, as energy exchanges between single photons and single quantum emitters. In the case of an excited atom interacting with the electromagnetic vacuum, this coupling is fundamentally isotropic, leading to a spontaneously emitted photon with no preferred direction. Nevertheless, recent advances in trapping atoms close to nanophotonic waveguides have shown that the strong confinement of light can naturally lead to situations in which excited atoms decay asymmetrically into left- and right-moving photons along the waveguide. This directional light-matter interaction has been recently called ‘chiral’, and opens fascinating perspectives for realizing directional quantum networks with photons as quantum information carriers, as well as novel many-body quantum phases of light and matter. In this context, we study the implications of chiral interactions on the driven-dissipative dynamics of many quantum emitters coupled via a one-dimensional waveguide. In particular, we determine how the interplay between coherent drive, chiral interactions and collective decay can lead a chain of two-level atoms to a steady state that is pure and multi-partite entangled, which can be interpreted as a novel non-equilibrium magnetic phase of matter. In addition, we propose various purely atomic realizations of this model, where not only the emitters but also the waveguides are realized with atomic degrees of freedom such as Rydberg atoms, trapped ions, or Bose condensed atoms. Therefore, instead of photons, phonons or spin excitations mediate the chiral interactions, giving a high degree of control over the resulting open many-body dynamics for the emitters. These engineered atomic setups also provide a route to controllably access physics beyond the Markovian quantum optics paradigm. For instance, using modern many-body numerical methods, we include the full dynamics of the atomic waveguide on the same footing as the emitters and thereby describe non-Markovian effects such as retardation in the exchange of excitations between emitters and non-linear dispersive effects. On the other hand, the same framework allows for the realization of `on-chip’ chiral quantum networks, which we illustrate with basic building blocks for quantum information applications, such as state transfer protocols or time-reversal of wave-packets.

Small Meeting Room, Serrano 121 (CFMAC)

## Majorana bound states from exceptional points in non-topological superconductors

Ramón Aguado (Instituto de Ciencia de Materiales de Madrid (ICMM), CSIC))

Recent experimental efforts towards the detection of Majorana bound states have focused on creating the conditions for topological superconductivity. In this talk, I will discuss an alternative route, which achieves zero-energy Majorana bound states when a topologically trivial superconductor is strongly coupled to a helical normal region. Such a junction can be experimentally realised by e.g. proximitizing a finite section of a nanowire with spin-orbit coupling, and combining electrostatic depletion and a Zeeman field to drive the non-proximitized portion into a helical phase. Majorana zero modes emerge in these junctions without fine-tuning as a result of charge-conjugation symmetry, and can be ultimately linked to the existence of `exceptional points’ (EPs) in parameter space (non-hermitian degeneracies extensively studied in photonics [1-3], but seldom discussed in electronic systems), where two quasibound Andreev levels bifurcate into two quasibound Majorana zero modes. After the EP, one of the latter becomes non-decaying and fully localised as the junction approaches perfect Andreev reflection. As I will show, these Majoranas generated through EPs exhibit the full range of properties associated to conventional closed-system Majorana bound states, while not requiring topological superconductivity [4]. [1]The physics of exceptional points, W. D. Heiss, J. Phys. A 45, 444016 (2012). [2]Spawning rings of exceptional points out of Dirac cones, Bo Zhen et al, Nature 525, 354 (2015) [3]Topologically protected defect states in open photonic systems with non-hermitian charge-conjugation and parity-time symmetry, Simon Malzard, Charles Poli, Henning Schomerus, Phys. Rev. Lett. 115, 200402 (2015) [4]Majorana bound states from exceptional points in non-topological superconductors, P. San-Jose, J. Cayao, E. Prada and R. Aguado, Scientific Reports, 6, 21427 (2016)

Seminar Room, Serrano 121 (CFMAC)

## Quantum fluctuation relations for generalized Gibbs ensembles

Jordi Mur-Petit (Clarendon Laboratory, University of Oxford, Oxford, UK)

Experimental advances in the control and measurement of quantum systems are driving the development of quantum technologies across multiple experimental platforms, from trapped ions and cold atoms, to superconducting circuits, to nanomechanical setups [1]. The need for an accurate understanding of the non-equilibrium dynamics of such microscopic devices and their interactions with the environment has lead to a revival of the field of quantum thermodynamics, including the derivation of fluctuation relations for processes far from equilibrum [2]. Recent work has shown how single quantum systems can be used as probes to extract statistics of the work done in such processes [3], and how this can be used to measure their temperature with precision even in the strongly-interacting regime [4]. In this talk, I will present our extension of these proposals to measuring correlation functions, and on the derivation of more general quantum fluctuation relations for systems with conserved quantities whose equilibrium state is described by a generalized Gibbs ensemble. [1] G. Kurizki, P. Bertet, Y. Kubo, K. Mølmer, D. Petrosyan, P. Rabl, and J. Schmiedmayer, ‘Quantum technologies with hybrid systems’, PNAS 110, 3866-3873 (2014). [2] P. Hänggi and P. Talkner, ‘The other QFT’, Nature Phys. 11, 108 (2015). [3] R. Dorner et al., Phys. Rev. Lett. 110, 230601 (2013); L. Mazzola et al., ibid. 110, 230602 (2013); T. Batalhão et al., ibid. 113, 140601 (2013). [4] T. H. Johnson et al., arXiv:1508.02992 (2015).

Seminar Room, Serrano 121 (CFMAC)

## Quantum Acoustics: Using surface acoustic waves as quantum bus between solid-state qubits

Geza Giedke (Donostia International Physics Centre)

Surface acoustic waves (SAW) in piezoactive materials offer a versatile means to address, manipulate and couple different solid-state qubits. We show that state-of-the-art SAW resonators allow to reach the strong coupling regime for several well-studied qubits, including quantum dots, trapped ions, nitrogen vacancy centers. In combination with acoustic waveguides, this system can be utilized efficiently as a quantum bus, serving as an on-chip, mechanical cavityQED equivalent and enabling long-range coupling of a wide range of qubits.

Seminar Room, Serrano 121 (CFMAC)

## Multi-Photon scattering and bound states

Tao Shi (Max-Planck-Instiut für Quantenoptik)

We developed a photon scattering theory [1–3] to study multi-photon transports and bound state behaviors in low dimensional confined systems (e.g., the photonic waveguides and the photonic crystals) coupled to some quantum emitters. Using the path integral formalism, we show the exact results for the transmission spectra and second order correlation functions of scattered photons, which agree with the Markovian results from the quantum regression theorem. This formalism provides a systematical and convenient way to investigate the exotic photon statistics in the system with strong single-photon nonlinearities (e.g., Rydberg-EIT systems) and the generations of single photon (bundles) [4]. By considering the Markovian effects, we show that a single two-level impurity can bind multi-photons around it to form N -photon bound states [5] in the nonlinear photon bath. [1] T. Shi and C. P. Sun, Phys. Rev. B 79, 205111 (2009). [2] T. Caneva, M. T. Manzoni, T. Shi, J. S. Douglas, J. I. Cirac, and D. E. Chang, New J. of Phys. 17, 113001 (2015). [3] T.Shi, D. E. Chang, J. I. Cirac, Phys. Rev. A 92, 053834 (2015). [4] Y. Chang, A. González-Tudela, C. Sánchez-Muñoz, C. Navarrete-Benlloch, and T. Shi, arXiv:1510.07307 (2015). [5] T. Shi, Y. H. Wu, A. Gonzalez-Tudela, J. I. Cirac, arXiv:1512.07238.

Seminar Room, Serrano 121 (CFMAC)

## Undecidability of the spectral gap

David Pérez García (Departamento de Análisis Matemático (UCM))

The spectral gap—the energy difference between the ground state and first excited state—is central to quantum many-body physics. Many challenging open problems, such as the Haldane conjecture, existence of gapped topological spin liquid phases, or the Yang-Mills conjecture, concern spectral gaps. These and other problems are particular cases of the general spectral gap problem: given a quantum many-body Hamiltonian, is it gapped or gapless? In this work, we prove that the spectral gap problem is undecidable. We construct families of quantum spin systems on a 2D lattice with translationally-invariant, nearest-neighbour interactions for which this is an undecidable problem. This result extends to undecidability of other low energy properties, such as existence of algebraically decaying ground-state correlations. The proof combines Hamiltonian complexity techniques with aperiodic tilings, to construct a Hamiltonian whose ground state encodes the evolution of a quantum phase-estimation algorithm followed by a universal Turing Machine. The spectral gap depends on the outcome of the corresponding Halting Problem. Our result implies that there exists no algorithm to determine whether an arbitrary model is gapped or gapless. It also implies that there exist models for which the presence or absence of a spectral gap is not defined by the axioms of mathematics.

Seminar Room, Serrano 121 (CFMAC)

## Uniqueness of the Fock quantization of Dirac fields with unitary dynamics

Beatriz Elizaga (Instituto de Estructura de la Materia (CSIC))

It is well known that linear canonical transformations are not generally implemented as unitary operators in QFT. Such transformations include the dynamics that arises from the field equations on the background spacetime. This evolution is specially relevant in nonstationary backgrounds, where there is no time-translational symmetry that can be exploited to select a quantum theory. We investigate whether it is possible to find a Fock representation for the canonical anticommutation relations of a Dirac field, propagating on a homogeneous and isotropic cosmological background, such that the field evolution is unitarily implementable. First, we restrict our attention to Fock representations that are invariant under the group of spatial isometries of the background. Then, we prove that there indeed exist Fock representations such that the dynamics is implementable as a unitary operator. Finally, once a convention for the notion of particles and antiparticles is set, we show that these representations are all unitarily equivalent.

Seminar Room, Serrano 121 (CFMAC)

## The complex Dirac Delta, Plemelj formula and integral representations

Jaime Julve (IFF, CSIC)

The extension of the Dirac Delta distribution (DD) to the complex field is needed for dealing with the complex energy solutions of the Schrödinger equation, typically when calculating their inner products. In quantum scattering theory the DD usually arises as an integral representation involving plane waves of real momenta.We shall deal with the complex extension of these representationsby using a Gaussian regularization. Their interpretation as distributions requires prescribing the integration path besides the space of test functions. An extension of the Sokhotski-Plemelj formula is obtained.

Seminar Room, Serrano 121 (CFMAC)

## Quantum versus Thermal annealing, the role of Temperature Chaos

Victor Martín Mayor (Física Teórica I, UCM)

Recent advances in quantum technology have led to the development and manufacturing of experimental programmable quantum annealing optimizers that contain hundreds of quantum bits. These optimizers, commonly referred to as `D-Wave’ chips,promise to solve practical optimization problems potentially faster than conventional `classical’ computers. Attempts to quantify the quantum nature of these chips have been met with both excitement and skepticism but have also brought up numerous fundamental questions pertaining to the distinguishability of experimental quantum annealers from their classical thermal counterparts. Inspired by recent results in spin-glass theory that recognize `temperature chaos’ as the underlying mechanism responsible for the computational intractability of hard optimization problems, we devise a general method to quantify the performance of quantum annealers on optimization problems suffering from varying degrees of temperature chaos: A superior performance of quantum annealers over classical algorithms on these would serve as a strong telltale sign of quantum behavior. We utilize our method to experimentally study the D-Wave Two chip on different temperature-chaotic problems and find, surprisingly, that its performance scales unfavorably as compared to several analogous classical algorithms. We detect, quantify and discuss several purely classical effects that possibly mask the quantum behavior of the chip.

Seminar Room, Serrano 121 (CFMAC)

## Unpaired Majorana modes in Josephson junctions arrays with gapless bulk excitations

Manuel del Pino (Department of Physics and Astronomy, Rutgers)

The search for Majorana bound states in solid-state physics has been limited to materials which display a gap in their bulk spectrum. We will show that such unpaired states appear in certain quasi-one-dimensional Josephson junctions arrays with gapless bulk excitations [1]. The bulk modes mediate a coupling between Majorana bound states via the Ruderman-Kittel-Yosida-Kasuya mechanism. As a consequence, the lowest energy doublet acquires a finite energy difference. For realistic set of parameters this energy splitting remains much smaller than the energy of the bulk eigenstates even for short chains of length L~10. In this talk, we first explain the JJA system and how to model it with an Ising-like Hamiltonian. Then, a qualitative argument is employed to obtain the low-energy effective theory using unpaired Majorana modes. We will show numerical results which confirm the validity of this effective theory and discuss problems that may arise in the experimental realization of our proposal. [1] M. Pino, A. M. Tsvelik, and L. B. Ioffe, Phys. Rev. Lett. 115, 197001 (2015)

Seminar Room, Serrano 121 (CFMAC)