Generating Two-Mode Squeezed Vacuum States in Trapped Ions: Entanglement and Sensing

We explore creating two-mode squeezed vacuum (TMSV) states in the mechanical motion of trapped ions using optimal quantum control. Utilizing phase-modulated lasers and tailored qubit-boson interactions, we generate TMSV states with coherent squeezing in the position and momentum quadratures. The resulting states exhibit non-classical correlations that violate the inferred Heisenberg uncertainty principle for two continuous variable properties, indicating entanglement between the two mechanical oscillators. The optimal state preparation protocol can be readily extended to create other highly-nonclassical states in multiple bosonic modes, opening new opportunities for quantum-enhanced sensing.