Emergent quantum phase transition of Josephson junction coupled to a high-impedance multimode resonator Luca Giacomelli (Laboratoire MPQ, Université Paris)
ABSTRACT:
The physics of a single Josephson junction coupled to a resistive environment is a long-standing fundamental problem at the center of an intense debate about the existence and properties of the superconducting to insulating Schmid-Bulgadaev transition. To circumvent the potential subtleties in the original derivation, we investigate the emergent criticality of a junction coupled to a multimode resonator when the number of modes is increased [1]. By solving the system via exact diagonalization, we show that at the transition point the spectrum displays universality (scale invariance) not only at low frequencies. This reflects in finite-frequency spectral signatures of the phase transition, in agreement with recent experiments. The spectrum at the critical point is successfully compared with analytical and numerical results obtained in the past [2]. Finally, we prove a low-energy exact self-duality of the model, that emerges from two different finite-size circuits with different conserved quantities [3]. This confirms and generalizes the approximate self duality that is usually invoked, and proves the independence of the transition point on the ratio of Josephson to charging energy.
[1] Giacomelli L., Ciuti C. (2024) « Emergent quantum phase transition of a Josephson junction coupled to a high impedance multimode resonator ».Nature Communications, 15(1), 5455.
[2] Paris, Giacomelli, Daviet, Ciuti, Dupuis, Mora (2025) « Resilience of the quantum critical line in the Schmid transition ». Physical Review B, 111(6), 064509.
[3] Giacomelli L., Devoret M. H., Ciuti C. (2025) « Exact Duality at Low Energy in a Josephson Tunnel Junction Coupled to a Transmission Line ». arXiv:2504.14651.