Synthesizing a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mover accent="true"><mml:mi>σ</mml:mi><mml:mo></mml:mo></mml:mover><mml:mi>z</mml:mi></mml:msub></mml:math> spin-dependent force for optical, metastable, and ground-state trapped-ion qubits
O. Băzăvan, S. Saner, Mariella Minder, A. C. Hughes, R. T. Sutherland, David Lucas, R. Srinivas, C. J. Ballance
Abstract
A single bichromatic field near resonant to a qubit transition is typically used for ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\sigma}}}_{x}$ or ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\sigma}}}_{y}$ M\o{}lmer-S\o{}rensen-type interactions in trapped-ion systems. Using this field configuration, it is also possible to synthesize a ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\sigma}}}_{z}$ spin-dependent force by merely adjusting the beat-note frequency. Here, we expand on previous work and present a comprehensive theoretical and experimental investigation of this scheme with a laser near resonant to a quadrupole transition in $^{88}\mathrm{Sr}^{+}$. Further, we characterize its robustness to optical phase and qubit frequency offsets, and demonstrate its versatility by entangling optical, metastable, and ground-state qubits.