Engineering continuous-variable entanglement in mechanical oscillators with optimal control

TL;DR

This paper presents an optimal control method to generate and verify entangled states in mechanical oscillators of trapped ions, including Gaussian and non-Gaussian states, using phase modulation of laser interactions.

Contribution

It introduces a dynamical phase modulation protocol for deterministic entanglement of mechanical oscillators in trapped ions, enabling preparation of both Gaussian and non-Gaussian entangled states.

Findings

Successfully prepared Two-Mode Squeezed Vacuum states with measurable EPR entanglement.

Violated Bell inequality demonstrating nonlocal correlations.

Demonstrated flexibility by creating non-Gaussian entangled superposition states.

Abstract

We demonstrate an optimal quantum control strategy for the deterministic preparation of entangled harmonic oscillator states in trapped ions. The protocol employs dynamical phase modulation of laser-driven Jaynes-Cummings and anti-Jaynes-Cummings interactions. We prepare Two-Mode Squeezed Vacuum (TMSV) states in the mechanical motions of a trapped ion and characterize the states with phase-space tomography. First, we verify continuous-variable entanglement by measuring an Einstein-Podolsky-Rosen entanglement parameter of 0.0132(7), which is below the threshold of 0.25 for Reid's EPR criterion. Second, we perform a continuous-variable Bell test and find a violation of the Clauser-Horne-Shimony-Holt inequality, measuring 2.26(3), which is above the entanglement threshold of 2. We also demonstrate the flexibility of our method by preparing a non-Gaussian entangled oscillator state--a superposition of TMSV states.