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arXiv:2408.14549 · Physical review. B./Physical review. B

Engineering a Josephson junction chain for the simulation of the quantum clock model

Matteo M. Wauters, Lorenzo Maffi, Michele Burrello

Published Jan 15, 2025• 3 citations
arXivHTMLPDF

Abstract

The continuous improvement of fabrication techniques and high-quality semiconductor-superconductor interfaces allows for an unprecedented tunability of Josephson junction arrays (JJA), making them a promising candidate for analog quantum simulations of many-body phenomena. While most experimental proposals so far focused on quantum simulations of ensembles of two-level systems, the possibility of tuning the current-phase relation beyond the sinusoidal regime paves the way for studying statistical physics models with larger local Hilbert spaces. Here, we investigate a particular JJA architecture that can be mapped into a ${\mathbb{Z}}_{3}$ clock model. Through matrix-product-states simulations and bosonization analysis, we show that few experimentally accessible control parameters allow for the exploration of the rich phase diagrams of the associated low-energy field theories. Our results expand the horizon for analog quantum simulations with JJAs towards models that can not be efficiently captured with qubit architectures.

DOI
10.1103/physrevb.111.045418

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The continuous improvement of fabrication techniques and high-quality semiconductor-superconductor interfaces allows for an unprecedented tunability of Josephson junction arrays (JJA), making them a promising candidate for analog quantum simulations of many-body phenomena. While most experimental proposals so far focused on quantum simulations of ensembles of two-level systems, the possibility of tuning the current-phase relation beyond the sinusoidal regime paves the way for studying statistical physics models with larger local Hilbert spaces. Here, we investigate a particular JJA architecture that can be mapped into a Z3{\mathbb{Z}}_{3}Z3​ clock model. Through matrix-product-states simulations and bosonization analysis, we show that few experimentally accessible control parameters allow for the exploration of the rich phase diagrams of the associated low-energy field theories. Our results expand the horizon for analog quantum simulations with JJAs towards models that can not be efficiently captured with qubit architectures.
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Josephson junction arrays (JJAs) are engineered many-body quantum systems consisting of several superconducting islands connected by thin tunnel barriers - Josephson junctions (JJs). They are of interest both from a fundamental point of view (e.g. addressing questions of macroscopic quantum physics, providing model systems in which to study complex many-body phenomena) and from the prospect of technological applications (e.g. quantum computing, metrology, metamaterials). In this thesis we present various tools and techniques for the theoretical study of JJAs, and then put these tools to use in the modelling of two particular experiments on JJAs. In our presentation of the physics of JJAs, we emphasise phenomena unique to arrays (i.e. not seen in single junction devices such as qubits). We investigate charge transport through the the bilinear array, consisting of two linear chains of JJs, and show that it exhibits both Coulomb drag and depinning. We predict new phenomena arising from the interplay between Coulomb drag and depinning at voltages higher than have so far been experimentally reported. We then turn our attention to recent experiments in which planar JJAs were placed in 3-D microwave cavities, with vortices being injected via an externally applied magnetic eld. We calculate the impedance spectrum using linear response theory, which enables us to see when new vortices enter the system in the form of sharp changes in the resonance frequency.
Superconductor-semiconductor Josephson junction arrays are a uniquely tunable platform for studying collective quantum phenomena, particularly in the regime where localized Andreev bound states can hybridize across the lattice when the physical separation between adjacent junctions is smaller than their coherence length (ξABS>dJJξ_{\text{ABS}}>d_{\text{JJ}}ξABS​>dJJ​). Here, we investigate three distinct Al-InAs Josephson junction arrays: a square array and super-honeycomb array fabricated within this ξABS>dJJ{ξ_{\text{ABS}}>d_{\text{JJ}}}ξABS​>dJJ​ regime, as well as a larger-spacing super-honeycomb control device designed such that ξABS≲ ⁣ dJJξ_{\text{ABS}}\lesssim\!~d_{\text{JJ}}ξABS​≲ dJJ​. Under an out-of-plane field, critical current peaks emerge at rational filling factors, reflecting stable vortex configurations in the lattices. In the super-honeycomb lattice, vortices localize to distinct non-identical plaquettes at different filling factors, as predicted by frustrated XY model simulations. A rotating in-plane field yields periodic critical current oscillations that reflect the Rashba spin-orbit coupling inherent to the InAs quantum well. Surprisingly, at f=1f = 1f=1, the closely spaced super-honeycomb array exhibits a distinct critical current minimum as the magnitude of the in-plane field increases, a signature absent in the square array and large-spacing super-honeycomb array. These results indicate that this signature is jointly influenced by the unique geometry of the super-honeycomb vortex lattice and by long-range inter-junction hybridization.
Control and manipulation of quantum states by measurements and bath engineering in open quantum systems, like in a quantum computer, have emerged as new paradigms in many-body physics. Taking a prototypical example of Josephson junction arrays (JJAs), we show how monitoring through continuous weak measurements and feedback can transform an insulating steady state in JJAs to a superconductor (SC) and vice versa. We show that the quantum feedback, when not too large, is crucial to realize such a superconducting steady state by maintaining an effective temperature in a semiclassical limit. However, we show that large feedback can destroy superconductivity by enhancing quantum phase fluctuations. Thus, dissipation and phase fluctuations in the presence of monitoring have fundamental differences from those in the well-studied case of JJAs in contact with an equilibrium Ohmic bath. In general, a description in terms of only an effective temperature is not adequate for the monitored JJAs. Using a variational approximation, and by considering various limiting cases, we demonstrate that these differences can give rise to reentrant SC-insulator phase transitions leading to an unusual inverse transition from a seemingly low-effective-temperature insulating normal state to a superconducting state at intermediate temperature.
Superconducting Josephson junction arrays (JJAs) are prototypical systems consisting of an array of superconducting islands connected by small Josephson junctions which provide an explicit realization of the canonical XY model of condensed matter physics.In this study we show how circuit quantumelectrodynamics (QED) techniques, perfected for implementing high-quality quantum bits, enable the exploration of new high-frequency regimes of JJAs.By making use of extremely low excitation power and heating of the array, we can probe physics of these systems using one single photon on average.
Recent experiments on Josephson junction arrays (JJAs) in microwave cavities have opened up a new avenue for investigating the properties of these devices while minimizing the amount of external noise coming from the measurement apparatus itself. These experiments have already shown promise for probing many-body quantum effects in JJAs. In this work, we develop a general theoretical description of such experiments by deriving a quantum phase model for planar JJAs containing quantized vortices. The dynamical susceptibility of this model is calculated for some simple circuits, and signatures of the injection of additional vortices are identified. The effects of decoherence are considered via a Lindblad master equation.