Quantum behavior of a superconducting Duffing oscillator at the dissipative phase transition

TL;DR

This paper investigates the quantum behavior of a superconducting Duffing oscillator at a dissipative phase transition, revealing metastability, quantum state phases, and a unified classical-quantum picture of hysteresis.

Contribution

It demonstrates the existence of long-lived metastable states and observes a first-order dissipative phase transition in a quantum nonlinear oscillator.

Findings

Metastable states have long lifetimes in the hysteresis regime.

Observation of a first-order dissipative phase transition.

Identification of coherent and squeezed quantum phases separated by a critical point.

Abstract

Understanding the non-deterministic behavior of deterministic nonlinear systems has been an implicit dream since Lorenz named it the "butterfly effect". A prominent example is the hysteresis and bistability of the Duffing oscillator, which in the classical description is attributed to the coexistence of two steady states in a double-well potential. However, this interpretation fails in the quantum-mechanical perspective, where a single unique steady state is allowed in the whole parameter space. Here, we measure the non-equilibrium dynamics of a superconducting Duffing oscillator and reconcile the classical and quantum descriptions in a unified picture of quantum metastability. We demonstrate that the two classically regarded steady states are in fact metastable states. They have a remarkably long lifetime in the classical hysteresis regime but must eventually relax into a single unique steady state allowed by quantum mechanics. By engineering the lifetime of the metastable states sufficiently large, we observe a first-order dissipative phase transition, which mimics a sudden change of the mean field in a 11-site Bose-Hubbard lattice. We also reveal the two distinct phases of the transition by quantum state tomography, namely a coherent-state phase and a squeezed-state phase separated by a critical point. Our results reveal a smooth quantum state evolution behind a sudden dissipative phase transition, and they form an essential step towards understanding hysteresis and instability in non-equilibrium systems.