Multi-ion Frequency Reference Using Dynamical Decoupling

We present the experimental realization of a continuous dynamical decoupling scheme which suppresses leading frequency shifts in a multi-ion frequency reference based on <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mmultiscripts><a:mrow><a:msup><a:mrow><a:mi>Ca</a:mi></a:mrow><a:mrow><a:mo>+</a:mo></a:mrow></a:msup></a:mrow><a:mprescripts/><a:none/><a:mrow><a:mn>40</a:mn></a:mrow></a:mmultiscripts></a:mrow></a:math>. By near-resonant magnetic coupling of the <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msub><c:mrow><c:mmultiscripts><c:mrow><c:mi mathvariant="normal">S</c:mi></c:mrow><c:mprescripts/><c:none/><c:mrow><c:mn>2</c:mn></c:mrow></c:mmultiscripts></c:mrow><c:mrow><c:mn>1</c:mn><c:mo>/</c:mo><c:mn>2</c:mn></c:mrow></c:msub></c:math> and <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:msub><f:mrow><f:mmultiscripts><f:mrow><f:mi mathvariant="normal">D</f:mi></f:mrow><f:mprescripts/><f:none/><f:mrow><f:mn>2</f:mn></f:mrow></f:mmultiscripts></f:mrow><f:mrow><f:mn>5</f:mn><f:mo>/</f:mo><f:mn>2</f:mn></f:mrow></f:msub></f:math> Zeeman sublevels using radio-frequency dressing fields, engineered transitions with reduced sensitivity to magnetic-field fluctuations are obtained. A second stage detuned dressing field reduces the influence of amplitude noise in the first stage driving fields and decreases 2nd-rank tensor shifts, such as the electric quadrupole shift. Suppression of the quadratic dependence of the quadrupole shift to <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mrow><i:mn>3</i:mn><i:mo stretchy="false">(</i:mo><i:mn>2</i:mn><i:mo stretchy="false">)</i:mo><i:mtext> </i:mtext><i:mtext> </i:mtext><i:mi>mHz</i:mi><i:mo>/</i:mo><i:mi mathvariant="normal">μ</i:mi><i:msup><i:mrow><i:mi mathvariant="normal">m</i:mi></i:mrow><i:mrow><i:mn>2</i:mn></i:mrow></i:msup></i:mrow></i:math> and coherence times of 290(20) ms on the optical transition are demonstrated even within a laboratory environment with significant magnetic field noise. Besides removing inhomogeneous line shifts in multi-ion clocks, the demonstrated dynamical decoupling technique may find applications in quantum computing and simulation with trapped ions by a tailored design of decoherence-free subspaces. Published by the American Physical Society 2024