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Comptes Rendus Physique
Volume 19, n° 6
pages 484-497 (septembre 2018)
Doi : 10.1016/j.crhy.2018.09.002

Josephson ladders as a model system for 1D quantum phase transitions
Une chaîne supraconductrice comme simulateur de transitions de phases quantiques en une dimension

Matthew T. Bell a, Benoît Douçot b, Michael E. Gershenson c, Lev B. Ioffe b, , Aleksandra Petković d
a Department of Electrical Engineering, University of Massachusetts Boston, Boston, MA 02125, USA 
b LPTHE, Université Pierre-et-Marie-Curie, 75005 Paris, France 
c Department of Physics and Astronomy, Rutgers University, Piscataway, NJ 08854, USA 
d LPT, IRSAMC, Université Paul-Sabatier, 31062 Toulouse cedex 4, France 

Corresponding author.

We propose a novel platform for the study of quantum phase transitions in one dimension (1D QPT). The system consists of a specially designed chain of asymmetric SQUIDs; each SQUID contains several Josephson junctions with one junction shared between the nearest-neighbor SQUIDs. We develop the theoretical description of the low-energy part of the spectrum. In particular, we show that the system exhibits a quantum phase transition of Ising type. In the vicinity of the transition, the low-energy excitations of the system can be described by Majorana fermions. This allows us to compute the matrix elements of the physical perturbations in the low-energy sector. In the microwave experiments with this system, we explored the phase boundaries between the ordered and disordered phases and the critical behavior of the system's low-energy modes close to the transition. Due to the flexible chain design and control of the parameters of individual Josephson junctions, future experiments will be able to address the effects of non-integrability and disorder on the 1D QPT.

The full text of this article is available in PDF format.

Nous proposons une nouvelle plateforme pour l'étude des transitions de phase quantiques en une dimension. Le système consiste en une chaîne de boucles de SQUID asymétriques spécialement configurées : chaque SQUID contient plusieurs jonctions Josephson, dont une partagée avec le SQUID voisin. Des expériences sous micro-ondes électromagnétiques nous ont permis d'explorer les lignes de transition entre phase ordonnée et phase désordonnée, ainsi que le comportement critique des états excités de plus basse énergie au voisinage de cette transition. Grâce à la flexibilité de la configuration des SQUIDS et à la possibilité de contrôler individuellement les paramètres de chaque jonction Josephson, ce système permettra d'explorer, lors de prochaines expériences, les effets de la non-intégrabilité ou du désordre sur cette transition de phase quantique en une dimension.

The full text of this article is available in PDF format.

Keywords : Quantum simulations, Quantum phase transitions, Arrays of Josephson junctions, Transverse field Ising model

Mots-clés : Simulations quantiques, Transitions de phase quantiques, Chaînes des jonctions Josephson, Chaîne d'Ising quantique en champ transverse

1  Short-scale quantum fluctuations may renormalize the value of   by shifting it down:  . This effect is numerically small ( ) for the chains studied experimentally and qualitatively irrelevant, so we neglect it in the following discussion.
2  The junction energies given below were computed by using the data for the junction area, measured resistance of the test junctions and Ambegaokar–Baratoff relation. This computation gives reliable values for   and  , but significantly overestimates the value of the Josephson energy for smaller junctions.

© 2018  Published by Elsevier Masson SAS de la part de Académie des sciences.
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