Probing XY phase transitions in a Josephson junction array with tunable frustration

Abstract

The seminal theoretical works of Berezinskii, Kosterlitz, and Thouless presented a new paradigm for phase transitions in condensed matter that are driven by topological excitations. These transitions have been extensively studied in the context of two-dimensional XY models -- coupled compasses -- and have generated interest in the context of quantum simulation. Here, we use a circuit quantum-electrodynamics architecture to study the critical behavior of engineered XY models through their dynamical response. In particular, we examine not only the unfrustrated case but also the fully-frustrated case which leads to enhanced degeneracy associated with the spin rotational [U$(1)$] and discrete chiral ($Z_2$) symmetries. The nature of the transition in the frustrated case has posed a challenge for theoretical studies while direct experimental probes remain elusive. Here we identify the transition temperatures for both the unfrustrated and fully-frustrated XY models by probing a Josephson junction array close to equilibrium using weak microwave excitations and measuring the temperature dependence of the effective damping obtained from the complex reflection coefficient. We argue that our probing technique is primarily sensitive to the dynamics of the U$(1)$ part.

10 pages, 7 figures

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• Observation of Chiral-Mode Domains in a Frustrated XY Model on Optical Triangular Lattices
• Insulating Phase in Two-dimensional Josephson-Junction Arrays Investigated by Nonlinear Transport
• 10-GHz-clock time-multiplexed non-degenerate optical parametric oscillator network with a variable planar lightwave circuit interferometer
• Spontaneous supercurrents and vortex depinning in two-dimensional arrays of ${\phi }_0$-junctions
• Emergent Intermediate Phase in the $J_1$-$J_2$ XY model from Tensor Network Approaches
• Quantum Coherence in Loopless Superconductive Networks