Exceptional phase transition in a single Kerr-cat qubit

TL;DR

This paper demonstrates a quantum phase transition in a driven-dissipative Kerr-cat qubit driven by Liouvillian exceptional points, revealing unique quantum coherence signatures and establishing a new platform for non-Hermitian quantum physics.

Contribution

It introduces a novel continuous-variable system based on Kerr-cat qubits to explore Liouvillian exceptional points and quantum phase transitions, expanding the understanding of dissipative quantum criticality.

Findings

Quantum phase transition at Liouvillian exceptional point characterized by dynamical change.

Negativity of Wigner function as a signature of quantum coherence.

Introduction of phase difference as a parameter to quantify the transition.

Abstract

Exceptional points in non-Hermitian quantum systems give rise to novel genuine quantum phenomena. Recent explorations of exceptional-point-induced quantum phase transitions have extended from discrete-variable to continuous-variable-encoded quantum systems. However, quantum phase transitions driven by Liouvillian exceptional points (LEPs) in continuous-variable platforms remain largely unexplored. Here, we construct and investigate a Liouvillian exceptional structure based on a driven-dissipative Kerr-cat qubit. Through numerical simulations, we reveal a quantum phase transition occurring at the LEP characterized by a sudden change in dynamical behavior from underdamped oscillations to overdamped relaxations as visualized via Wigner functions and Bloch sphere trajectories. Notably the negativity of the Wigner function serves as a direct signature of genuine quantum coherence unattainable in conventional single-qubit non-Hermitian systems. Furthermore, we introduce the phase difference between the off-diagonal elements of the Liouvillian eigenmatrices as a novel parameter to quantify the transition. Our results establish the Kerr-cat qubit as a novel continuous-variable setting for exploring dissipative quantum criticality and intrinsic non-Hermitian physics.