Efficient microwave spin control of negatively charged group-IV color centers in diamond

In this paper, we provide a comprehensive overview of the microwave-induced manipulation of electronic spin states in negatively charged group-IV color centers in diamond with a particular emphasis on the influence of strain. Central to our investigation is the consideration of the full vectorial attributes of the magnetic fields involved, which are a <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mi>d</a:mi><a:mi>c</a:mi></a:mrow></a:math> field for lifting the degeneracy of the spin levels and an <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mrow><b:mi>a</b:mi><b:mi>c</b:mi></b:mrow></b:math> field for microwave control between two spin levels. We observe an intricate interdependence between their spatial orientations, the externally applied strain, and the resultant efficacy in spin-state control. In most studies to date the <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mrow><c:mi>a</c:mi><c:mi>c</c:mi></c:mrow></c:math> and <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mrow><d:mi>d</d:mi><d:mi>c</d:mi></d:mrow></d:math> magnetic field orientations have been insufficiently addressed, which has led to the conclusion that strain is indispensable for the effective microwave control of heavier group-IV vacancies, such as tin- and lead-vacancy color centers. In contrast, we find that the alignment of the <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mrow><e:mi>d</e:mi><e:mi>c</e:mi></e:mrow></e:math> magnetic field orthogonal to the symmetry axis and the <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"><f:mrow><f:mi>a</f:mi><f:mi>c</f:mi></f:mrow></f:math> field parallel to it can make the application of strain obsolete for effective spin manipulation. Furthermore, we explore the implications of this field configuration on the spin's optical initialization, readout, and gate fidelities.