Metastable doubly charged Rydberg trimers

We examine an effectively one-electron system with three positive nuclei composed of a <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mmultiscripts><a:mi>Rb</a:mi><a:none/><a:mo>*</a:mo><a:mprescripts/><a:none/><a:mn>87</a:mn></a:mmultiscripts></a:math> Rydberg atom interacting with a pair of <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mmultiscripts><b:mi>Rb</b:mi><b:none/><b:mo>+</b:mo><b:mprescripts/><b:none/><b:mn>87</b:mn></b:mmultiscripts></b:math> ions and predict the existence of metastable vibrationally bound states of <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mmultiscripts><c:mi>Rb</c:mi><c:mn>3</c:mn><c:mrow><c:mn>2</c:mn><c:mo>+</c:mo></c:mrow><c:mprescripts/><c:none/><c:mn>87</c:mn></c:mmultiscripts></c:math>. These molecules are long-range trimers whose stability rests on the presence of core-shell electrons and favorable scaling of the Rydberg atom's quadrupole moment with the principal quantum number <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mi>n</d:mi></d:math>. Unlike recently observed ion-Rydberg dimers, whose binding is due to internal flipping of the Rydberg atom's dipole moment, the binding of <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mmultiscripts><e:mi>Rb</e:mi><e:mn>3</e:mn><e:mrow><e:mn>2</e:mn><e:mo>+</e:mo></e:mrow><e:mprescripts/><e:none/><e:mn>87</e:mn></e:mmultiscripts></e:math> arises from the interaction of the ions with the Rydberg atom's quadrupole moment. The stability of these trimers is highly sensitive to <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"><f:mi>n</f:mi></f:math>. For <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"><g:mrow><g:mi>n</g:mi><g:mo>≤</g:mo><g:mn>35</g:mn></g:mrow></g:math>, we estimate that the lifetime of the bound states should be limited by intercore tunneling of the Rydberg electron, which creates an instability in the system. However, we predict that the rate of this process decreases significantly with <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"><h:mi>n</h:mi></h:math>, such that already for <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"><i:mrow><i:mi>n</i:mi><i:mo>=</i:mo><i:mn>38</i:mn></i:mrow></i:math> it is comparable in magnitude to the rate of spontaneous emission of the Rydberg state. The decreasing depth of the binding potential at larger <j:math xmlns:j="http://www.w3.org/1998/Math/MathML"><j:mi>n</j:mi></j:math> will further lead to an increase in the tunneling rate of the vibrational states from the molecular binding potential to dissociative regions of the adiabatic potential energy surface. Nonetheless, at <k:math xmlns:k="http://www.w3.org/1998/Math/MathML"><k:mrow><k:mi>n</k:mi><k:mo>=</k:mo><k:mn>38</k:mn></k:mrow></k:math>, this mechanism is only relevant for the highest-excited vibrational states in the binding potential. Published by the American Physical Society 2024