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arXiv:1811.11383 · Comptes Rendus Physique

Josephson ladders as a model system for 1D quantum phase transitions

M. T. Bell, Benoît Douçot, M. E. Gershenson, L. B. Ioffe, Aleksandra Petković

Published Sep 1, 2018• 14 citations
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Abstract

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.

DOI
10.1016/j.crhy.2018.09.002

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We investigate the effect of next-nearest-neighbor hopping on topological quantum phase transitions (QPTs) that are characterized by the number of Majorana zero modes in one-dimensional (1D) p-wave superconducting systems. We also numerically analyze the scaling behavior and the universality of the Berry phase (BP) of the ground state close to the critical point. For critical line (I), the derivative of the ground-state BP is nonanalytic at the phase boundaries. For the phase boundary (II), a noncontractible BP of the ground state itself is also a witness of quantum phase transition.
A Josephson junction subject to an ohmic dissipative environment undergoes a zero-temperature quantum phase transition called Schmid-Bulgadaev transition form an insulating state to a superconducting state upon increasing the impedance of the environment above the resistance quantum. Superconducting qubits based on Josephson junction chains represent a system where it is possible to dynamically explore both sides of this transition by probing the scattering of individual plasma modes of the junction chain on a SQUID at the boundary which was achieved in recent experiments. Here, we provide a theoretical analysis of the scattering in the system paying special attention to the non-perturbative superconducting regime. We find that in this regime, a specific diagrammatic resummation must be performed in order to correctly account for fluctuation renormalization of the SQUID's potential. We find analytic expressions for the modes' frequency shifts and quality factors which together provide a full description of scattering. We argue that the non-perturbative nature of the superconducting phase manifests itself through a power-law dependence of the frequency shifts on the SQUID flux and through non-monotonous dependence of the quality factors on the mode frequency. Our predictions may be readily verified in modern low-temperature experiments.
Quantum physics in one spatial dimension is remarkably rich, yet even with strong interactions and disorder, surprisingly tractable. This is due to the fact that the low-energy physics of nearly all one-dimensional systems can be cast in terms of the Luttinger liquid, a key concept that parallels that of the Fermi liquid in higher dimensions. Although there have been many theoretical proposals to use linear chains and ladders of Josephson junctions to create novel quantum phases and devices, only modest progress has been made experimentally. One major roadblock has been understanding the role of disorder in such systems. We present experimental results that establish the insulating state of linear chains of submicron Josephson junctions as Luttinger liquids pinned by random offset charges, providing a one-dimensional implementation of the Bose glass, strongly validating the quantum many-body theory of one-dimensional disordered systems. The ubiquity of such an electronic glass in Josephson-junction chains has important implications for their proposed use as a fundamental current standard, which is based on synchronization of coherent tunneling of flux quanta (quantum phase slips).
We study the zero-temperature phase diagram of a dissipationless and disorder-free Josephson junction chain. Namely, we determine the critical Josephson energy below which the chain becomes insulating as a function of the ratio of two capacitances: the capacitance of each Josephson junction and the capacitance between each superconducting island and the ground. We develop an imaginary-time path integral quantum Monte Carlo algorithm in the charge representation, which enables us to efficiently handle the electrostatic part of the chain Hamiltonian. We find that a large part of the phase diagram is determined by anharmonic corrections which are not captured by the standard Kosterlitz-Thouless renormalization group description of the transition.
The interplay of interactions and disorder in low-dimensional superconductors supports the formation of multiple quantum phases as possible instabilities of the superconductor-insulator transition (SIT) at a singular quantum critical point. We explore a one-dimensional model which exhibits such a variety of phases in the strongly quantum fluctuations regime. Specifically, we study the effect of weak disorder on a two-leg Josephson ladder with comparable Josephson and charging energies $({E}_{J}\ensuremath{\sim}{E}_{C})$. An additional key feature of our model is the requirement of perfect Z2{\mathbb{Z}}_{2}Z2​ symmetry, respected by all parameters including the disorder. Using a perturbative renormalization-group (RG) analysis, we derive the phase diagram and identify at least one intermediate phase between a full-fledged superconductor and a disorder-dominated insulator. Most prominently, for repulsive interactions on the rungs we identify two distinct mixed phases: In both of them the longitudinal charge mode is a gapless superconductor, however one phase exhibits a dipolar charge density order on the rungs, while the other is disordered. This latter phase is characterized by coexisting superconducting (phase-locked) and charge-ordered rungs, and encompasses the potential of evolving into a Griffith's phase characteristic of the random-field Ising model in the strong disorder limit.