Critical behavior in ultra-strong-coupled oscillators

TL;DR

This paper explores the ultra-strong coupling regime of x-x coupled harmonic oscillators, revealing a phase transition in the system's unitary operation that enables continuous entanglement generation even from thermal states.

Contribution

It introduces a novel description of the coupled oscillators as a Mach-Zehnder interferometer with a quadratic operation, identifying a critical transition from phase rotation to squeezing.

Findings

Sharp transition from phase rotator to squeezer with increasing coupling

Continuous entanglement generation in ultra-strong coupling regime

Entanglement persists from thermal states but is rapidly destroyed by temperature

Abstract

We investigate the strong coupling regime of a linear $x$-$x$ coupled harmonic oscillator system, by performing a direct diagonalization of the hamiltonian. It is shown that the $x$-$x$ coupled hamiltonian can be equivalently described by a Mach-Zehnder-type interferometer with a quadratic unitary operation in each of its arms. We show a sharp transition of the unitary operation from an elliptical phase rotator to an elliptical squeezer as the coupling gets stronger, which leads to the continuous generation of entanglement, even for a significantly thermal state, in the ultra-strong coupled regime. It is also shown that this critical regime cannot be achieved by a classical Hookian coupling. Finally, the effect of a finite-temperature environment is analyzed, showing that entanglement can still be generated from a thermal state in the ultra-strong coupled regime, but is destroyed rapidly.