Tricritical Ising Phase Transition in a Ladder of Josephson Junction Array.

Tricritical Ising phase transition (TCI) is known to occur in several quantum many body systems like interacting spin models and Rydberg atom chains. In 1D its operator content is described by the conformal field theory which predicts the presence of 4 relevant operators and among them the Fibonacci field. However, not so many experimental realizations of TCI have been performed in the past. We will present a 2-legs ladder of hybrid superconductor-semiconductor Josephson Junction (JJ) array that displays such tricritical phase diagram. The two legs are coupled at each rung by mean of three parallel JJs leading to an interesting on site interaction. The semiclassical phase diagram hosts a tricritical line and a TCI is expected in the quantum regime once charging energy is taken into account. In particular, a three-frequency Sine-Gordon model arises in the bosonized description. By using the Landau-Ginzburg formulation of the conformal minimal model, possible signatures of operator contents of the conformal field theory are discussed. Furthermore, the thermal response sheds light on the ladder tricritical Ising behaviour once the phase transition is crossed and leads to a quantitative measurement of the central charge.