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Contamin LC, Jarjat L, Legrand W, Cottet A, Kontos T, Delbecq MR. Zero energy states clustering in an elemental nanowire coupled to a superconductor. Nat Commun 2022; 13:6188. [PMID: 36261661 PMCID: PMC9581951 DOI: 10.1038/s41467-022-33960-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/07/2022] [Accepted: 10/05/2022] [Indexed: 11/13/2022] Open
Abstract
Nanoelectronic hybrid devices combining superconductors and a one-dimensional nanowire are promising platforms to realize topological superconductivity and its resulting exotic excitations. The bulk of experimental studies in this context are transport measurements where conductance peaks allow to perform a spectroscopy of the low lying electronic states and potentially to identify signatures of the aforementioned excitations. The complexity of the experimental landscape calls for a benchmark in an elemental situation. The present work tackles such a task using an ultra-clean carbon nanotube circuit. Specifically, we show that the combination of magnetic field, weak disorder and superconductivity can lead to states clustering at low energy, as predicted by the random matrix theory predictions. Such a phenomenology is very general and should apply to most platforms trying to realize topological superconductivity in 1D systems, thus calling for alternative probes to reveal it.
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Affiliation(s)
- Lauriane C Contamin
- Laboratoire de Physique de l'École normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris Cité, F-75005, Paris, France
| | - Lucas Jarjat
- Laboratoire de Physique de l'École normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris Cité, F-75005, Paris, France
| | - William Legrand
- Laboratoire de Physique de l'École normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris Cité, F-75005, Paris, France
| | - Audrey Cottet
- Laboratoire de Physique de l'École normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris Cité, F-75005, Paris, France
| | - Takis Kontos
- Laboratoire de Physique de l'École normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris Cité, F-75005, Paris, France
| | - Matthieu R Delbecq
- Laboratoire de Physique de l'École normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris Cité, F-75005, Paris, France.
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2
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Pérez-González B, Gómez-León Á, Platero G. Topology detection in cavity QED. Phys Chem Chem Phys 2022; 24:15860-15870. [PMID: 35758058 DOI: 10.1039/d2cp01806c] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We explore the physics of topological lattice models immersed in c-QED architectures for arbitrary coupling strength with the photon field. We propose the use of the cavity transmission as a topological marker and study its behaviour. For this, we develop an approach combining the input-output formalism with a Mean-Field plus fluctuations description of the setup. We illustrate our results with the specific case of a fermionic Su-Schrieffer-Heeger (SSH) chain coupled to a single-mode cavity. Our findings confirm that the cavity can indeed act as a quantum sensor for topological phases, where the initial state preparation plays a crucial role. Additionally, we discuss the persistence of topological features when the coupling strength increases, in terms of an effective Hamiltonian, and calculate the entanglement entropy. Our approach can be applied to other fermionic systems, opening a route to the characterization of their topological properties in terms of experimental observables.
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Affiliation(s)
- Beatriz Pérez-González
- Instituto de Ciencia de Materiales de Madrid, ICMM-CSIC, Calle Sor Juana Inés de la Cruz, n°3, 28049 Madrid, Spain.
| | - Álvaro Gómez-León
- Instituto de Física Fundamental, IFF-CSIC, Calle Serrano 113b, 28006 Madrid, Spain
| | - Gloria Platero
- Instituto de Ciencia de Materiales de Madrid, ICMM-CSIC, Calle Sor Juana Inés de la Cruz, n°3, 28049 Madrid, Spain.
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3
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Ricco LS, Kozin VK, Seridonio AC, Shelykh IA. Accessing the degree of Majorana nonlocality in a quantum dot-optical microcavity system. Sci Rep 2022; 12:1983. [PMID: 35132133 PMCID: PMC8821597 DOI: 10.1038/s41598-022-05855-y] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/13/2021] [Accepted: 01/04/2022] [Indexed: 11/16/2022] Open
Abstract
We explore the tunneling transport properties of a quantum dot embedded in an optical microcavity and coupled to a semiconductor-superconductor one-dimensional nanowire (Majorana nanowire) hosting Majorana zero modes (MZMs) at their edges. Conductance profiles reveal that strong light-matter coupling can be employed to distinguish between the cases of highly nonlocal MZMs, overlapped MZMs and MZMs with less degree of nonlocal feature. Moreover, we show that it is possible to access the degree of Majorana nonlocality (topological quality factor) by changing the dot spectrum through photon-induced transitions tuned by an external pump applied to the microcavity.
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Affiliation(s)
- L S Ricco
- Science Institute, University of Iceland, Dunhagi-3, 107, Reykjavík, Iceland.
| | - V K Kozin
- Science Institute, University of Iceland, Dunhagi-3, 107, Reykjavík, Iceland
- Department of Physics, ITMO University, St. Petersburg, 197101, Russia
| | - A C Seridonio
- Department of Physics and Chemistry, School of Engineering, São Paulo State University (Unesp), Ilha Solteira, SP, 15385-000, Brazil
- Department of Physics, IGCE, São Paulo State University (Unesp), Rio Claro, SP, 13506-970, Brazil
| | - I A Shelykh
- Science Institute, University of Iceland, Dunhagi-3, 107, Reykjavík, Iceland
- Department of Physics, ITMO University, St. Petersburg, 197101, Russia
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Nie W, Peng ZH, Nori F, Liu YX. Topologically Protected Quantum Coherence in a Superatom. PHYSICAL REVIEW LETTERS 2020; 124:023603. [PMID: 32004058 DOI: 10.1103/physrevlett.124.023603] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/24/2019] [Revised: 10/01/2019] [Indexed: 06/10/2023]
Abstract
Exploring the properties and applications of topological quantum states is essential to better understand topological matter. Here, we theoretically study a quasi-one-dimensional topological atom array. In the low-energy regime, the atom array is equivalent to a topological superatom. Driving the superatom in a cavity, we study the interaction between light and topological quantum states. We find that the edge states exhibit topology-protected quantum coherence, which can be characterized from the photon transmission. This quantum coherence helps us to find a superradiance-subradiance transition, and we also study its finite-size scaling behavior. The superradiance-subradiance transition also exists in symmetry-breaking systems. More importantly, it is shown that the quantum coherence of the subradiant edge state is robust to random noises, allowing the superatom to work as a topologically protected quantum memory. We suggest a relevant experiment with three-dimensional circuit QED. Our study may have applications in quantum computation and quantum optics based on topological edge states.
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Affiliation(s)
- Wei Nie
- Institute of Microelectronics, Tsinghua University, Beijing 100084, China
- Frontier Science Center for Quantum Information, Beijing, China
| | - Z H Peng
- Key Laboratory of Low-Dimensional Quantum Structures and Quantum Control of Ministry of Education, Key Laboratory for Matter Microstructure and Function of Hunan Province, Department of Physics and Synergetic Innovation Center for Quantum Effects and Applications, Hunan Normal University, Changsha 410081, China
| | - Franco Nori
- Theoretical Quantum Physics Laboratory, RIKEN Cluster for Pioneering Research, Wako-shi, Saitama 351-0198, Japan
- Physics Department, The University of Michigan, Ann Arbor, Michigan 48109-1040, USA
| | - Yu-Xi Liu
- Institute of Microelectronics, Tsinghua University, Beijing 100084, China
- Frontier Science Center for Quantum Information, Beijing, China
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5
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Desjardins MM, Contamin LC, Delbecq MR, Dartiailh MC, Bruhat LE, Cubaynes T, Viennot JJ, Mallet F, Rohart S, Thiaville A, Cottet A, Kontos T. Synthetic spin-orbit interaction for Majorana devices. NATURE MATERIALS 2019; 18:1060-1064. [PMID: 31427741 DOI: 10.1038/s41563-019-0457-6] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/04/2019] [Accepted: 07/15/2019] [Indexed: 06/10/2023]
Abstract
The interplay of superconductivity with non-trivial spin textures is promising for the engineering of non-Abelian Majorana quasiparticles. Spin-orbit coupling is crucial for the topological protection of Majorana modes as it forbids other trivial excitations at low energy but is typically intrinsic to the material1-7. Here, we show that coupling to a magnetic texture can induce both a strong spin-orbit coupling of 1.1 meV and a Zeeman effect in a carbon nanotube. Both of these features are revealed through oscillations of superconductivity-induced subgap states under a change in the magnetic texture. Furthermore, we find a robust zero-energy state-the hallmark of devices hosting localized Majorana modes-at zero magnetic field. Our findings are generalizable to any low-dimensional conductor, and future work could include microwave spectroscopy and braiding operations, which are at the heart of modern schemes for topological quantum computation.
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Affiliation(s)
- M M Desjardins
- Laboratoire de Physique de l'Ecole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris Diderot, Sorbonne Paris Cité, Paris, France
| | - L C Contamin
- Laboratoire de Physique de l'Ecole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris Diderot, Sorbonne Paris Cité, Paris, France
| | - M R Delbecq
- Laboratoire de Physique de l'Ecole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris Diderot, Sorbonne Paris Cité, Paris, France
| | - M C Dartiailh
- Laboratoire de Physique de l'Ecole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris Diderot, Sorbonne Paris Cité, Paris, France
| | - L E Bruhat
- Laboratoire de Physique de l'Ecole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris Diderot, Sorbonne Paris Cité, Paris, France
| | - T Cubaynes
- Laboratoire de Physique de l'Ecole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris Diderot, Sorbonne Paris Cité, Paris, France
| | - J J Viennot
- Univ. Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, CNRS, Grenoble, France
| | - F Mallet
- Laboratoire de Physique de l'Ecole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris Diderot, Sorbonne Paris Cité, Paris, France
| | - S Rohart
- Laboratoire de Physique des Solides, Université Paris-Saclay, CNRS UMR 8502, Orsay, France
| | - A Thiaville
- Laboratoire de Physique des Solides, Université Paris-Saclay, CNRS UMR 8502, Orsay, France
| | - A Cottet
- Laboratoire de Physique de l'Ecole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris Diderot, Sorbonne Paris Cité, Paris, France
| | - T Kontos
- Laboratoire de Physique de l'Ecole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris Diderot, Sorbonne Paris Cité, Paris, France.
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6
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Wang XQ, Zhang SF, Wang Q, Jiang C, Gong WJ. Signatures of Majorana doublet in the Fano-Rashba interferometer. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2019; 31:305303. [PMID: 31018184 DOI: 10.1088/1361-648x/ab1bee] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
We theoretically study the quantum transport through a Fano-Rashba interferometer with an embedded Majorana doublet which generates at one end of the DIII-class topological superconductor. It shows that the Rasbha spin-orbit interaction in the reference arm drives the apparent and terminal-dependence spin polarization of the electron tunneling and crossed Andreev reflection, accompanied by their opposite directions. However, spin degeneracy holds in the local Andreev reflection. Next once the Majorana doublet is replaced by the Andreev bound state, the spin-polarization properties of the Andreev reflections are interchanged. Therefore, the Fano-Rashba interferometer can be a promising candidate for differentiating the Majorana doublet from other bound states.
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Affiliation(s)
- Xiao-Qi Wang
- College of Sciences, Northeastern University, Shenyang 110819, People's Republic of China
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7
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Trif M, Simon P. Braiding of Majorana Fermions in a Cavity. PHYSICAL REVIEW LETTERS 2019; 122:236803. [PMID: 31298884 DOI: 10.1103/physrevlett.122.236803] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/11/2018] [Revised: 02/06/2019] [Indexed: 06/10/2023]
Abstract
We study the dynamical process of braiding Majorana bound states (MBS) in the presence of the coupling to photons in a microwave cavity. We show theoretically that the π/4 phase associated with the braiding of MBS, as well as the parity of the ground state are imprinted into the photonic field of the cavity, which can be detected by dispersive readout techniques. These manifestations are purely dynamical, they occur in the absence of any splitting of the MBS that are exchanged, and they disappear in the static setups studied previously. Conversely, the cavity can affect the braiding phase, which in turn should allow for cavity controlled braiding.
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Affiliation(s)
- Mircea Trif
- Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - Pascal Simon
- Laboratoire de Physique des Solides, CNRS, Univ. Paris-Sud, University Paris-Saclay, 91405 Orsay Cedex, France
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Osca J, Serra L. Circular dichroism of chiral Majorana states. BEILSTEIN JOURNAL OF NANOTECHNOLOGY 2018; 9:1194-1199. [PMID: 29765796 PMCID: PMC5942379 DOI: 10.3762/bjnano.9.110] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 12/11/2017] [Accepted: 03/13/2018] [Indexed: 06/08/2023]
Abstract
Background: Majorana states in condensed matter devices may be of a localized nature, such as in hybrid semiconductor/superconductor nanowires, or chirally propagating along the edges such as in hybrid 2D quantum-anomalous Hall/superconductor structures. Results: We calculate the circular dichroism due to chiral Majorana states in a hybrid structure made of a quantum-anomalous Hall insulator and a superconductor. The optical absorption of chiral Majorana states is characterized by equally spaced absorption peaks of both positive and negative dichroism. In the limit of a very long structure (a 2D ribbon) peaks of a single sign are favored. Conclusion: Circular-dichroism spectroscopy of chiral Majorana states is suggested as a relevant probe for these peculiar states of topological matter.
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Affiliation(s)
- Javier Osca
- Institut de Física Interdisciplinària i de Sistemes Complexos IFISC (CSIC-UIB), E-07122 Palma de Mallorca, Spain
| | - Llorenç Serra
- Institut de Física Interdisciplinària i de Sistemes Complexos IFISC (CSIC-UIB), E-07122 Palma de Mallorca, Spain
- Departament de Física, Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain
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Cottet A, Dartiailh MC, Desjardins MM, Cubaynes T, Contamin LC, Delbecq M, Viennot JJ, Bruhat LE, Douçot B, Kontos T. Cavity QED with hybrid nanocircuits: from atomic-like physics to condensed matter phenomena. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2017; 29:433002. [PMID: 28925381 DOI: 10.1088/1361-648x/aa7b4d] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Circuit QED techniques have been instrumental in manipulating and probing with exquisite sensitivity the quantum state of superconducting quantum bits coupled to microwave cavities. Recently, it has become possible to fabricate new devices in which the superconducting quantum bits are replaced by hybrid mesoscopic circuits combining nanoconductors and metallic reservoirs. This mesoscopic QED provides a new experimental playground to study the light-matter interaction in electronic circuits. Here, we present the experimental state of the art of mesoscopic QED and its theoretical description. A first class of experiments focuses on the artificial atom limit, where some quasiparticles are trapped in nanocircuit bound states. In this limit, the circuit QED techniques can be used to manipulate and probe electronic degrees of freedom such as confined charges, spins, or Andreev pairs. A second class of experiments uses cavity photons to reveal the dynamics of electron tunneling between a nanoconductor and fermionic reservoirs. For instance, the Kondo effect, the charge relaxation caused by grounded metallic contacts, and the photo-emission caused by voltage-biased reservoirs have been studied. The tunnel coupling between nanoconductors and fermionic reservoirs also enable one to obtain split Cooper pairs, or Majorana bound states. Cavity photons represent a qualitatively new tool to study these exotic condensed matter states.
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Affiliation(s)
- Audrey Cottet
- Laboratoire Pierre Aigrain, Ecole Normale Supérieure, CNRS UMR 8551, Laboratoire associé aux universités Pierre et Marie Curie et Denis Diderot, 24, rue Lhomond, 75231 Paris Cedex 05, France
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