Realization of a Fast Triple-Magic All-Optical Qutrit in Sr88

The optical clock states of alkaline earth and alkaline earthlike atoms are the fundament of state-of-the-art optical atomic clocks. An important prerequisite for the operation of optical clocks is the magic trapping conditions where electronic and motional dynamics decouple. Here, we identify and experimentally demonstrate simultaneous magic trapping for two clock transitions in <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mmultiscripts><a:mrow><a:mi>Sr</a:mi></a:mrow><a:mprescripts/><a:none/><a:mrow><a:mn>88</a:mn></a:mrow></a:mmultiscripts></a:mrow></a:math>, realizing so-called triple-magic conditions at a specially chosen magic angle. Under these conditions, we operate an all-optical qutrit comprising the ground state <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mrow><c:mmultiscripts><c:mrow><c:msub><c:mrow><c:mi>S</c:mi></c:mrow><c:mrow><c:mn>0</c:mn></c:mrow></c:msub></c:mrow><c:mprescripts/><c:none/><c:mrow><c:mn>1</c:mn></c:mrow></c:mmultiscripts></c:mrow></c:math>, and the two metastable clock states <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mrow><e:mmultiscripts><e:mrow><e:msub><e:mrow><e:mi>P</e:mi></e:mrow><e:mrow><e:mn>0</e:mn></e:mrow></e:msub></e:mrow><e:mprescripts/><e:none/><e:mrow><e:mn>3</e:mn></e:mrow></e:mmultiscripts></e:mrow></e:math> and <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mrow><g:mmultiscripts><g:mrow><g:msub><g:mrow><g:mi>P</g:mi></g:mrow><g:mrow><g:mn>2</g:mn></g:mrow></g:msub></g:mrow><g:mprescripts/><g:none/><g:mrow><g:mn>3</g:mn></g:mrow></g:mmultiscripts></g:mrow></g:math>. We demonstrate fast optical control in an atom array using two- and three-photon couplings to realize high-fidelity manipulation between all qutrit states. At the magic angle, we probe the coherence achievable in magic-angle-tuned traps and find atom-atom coherence times between the metastable states as long as 715(30) ms. Our work opens several new directions, including qutrit-based quantum metrology on optical transitions and high-fidelity and high-coherence manipulation on the <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mrow><i:mmultiscripts><i:mrow><i:mi>Sr</i:mi></i:mrow><i:mprescripts/><i:none/><i:mrow><i:mn>88</i:mn></i:mrow></i:mmultiscripts></i:mrow></i:math> fine-structure qubit.