Quantum Turing bifurcation: Transition from quantum amplitude death to quantum oscillation death

TL;DR

This paper demonstrates the quantum analogue of the Turing bifurcation in coupled quantum oscillators, showing a transition from homogeneous to inhomogeneous steady states, bridging classical and quantum pattern formation.

Contribution

It introduces the quantum Turing bifurcation in coupled quantum van der Pol oscillators, a phenomenon not previously observed in the quantum domain.

Findings

Quantum Turing bifurcation causes state transition in quantum oscillators.

Simulation confirms the bifurcation in the quantum master equation.

Analytical support from noisy classical model analysis.

Abstract

An important transition from a homogeneous steady state to an inhomogeneous steady state via the Turing bifurcation in coupled oscillators was reported in [Phys. Rev. Lett. {\bf 111}, 024103 (2013)]. However, the same in the quantum domain is yet to be observed. In this paper, we discover the quantum analogue of the Turing bifurcation in coupled quantum oscillators. We show that a homogeneous steady state is transformed into an inhomogeneous steady state through this bifurcation in coupled quantum van der Pol oscillators. We demonstrate our results by a direct simulation of the quantum master equation in the Lindblad form. We further support our observations through an analytical treatment of the noisy classical model. Our study explores the paradigmatic Turing bifurcation at the quantum-classical interface and opens up the door towards its broader understanding.