# The role of spectator modes in the quantum-logic spectroscopy of single trapped molecular ions

## TL;DR

This paper explores how motion of trapped ions affects the detection of molecular ion states using quantum-logic spectroscopy.

## Contribution

The study identifies a Debye-Waller-type effect and shows how cooling spectator modes improves detection fidelity and experimental efficiency.

## Key findings

- Cooling spectator modes enables detection of the rovibrational ground state of N2+ with over 99.99% fidelity.
- The method reduces experimental time by half and improves sensitivity for identifying multiple rotational states.
- Spectator modes not directly involved in the protocol significantly influence the measurement response.

## Abstract

Quantum-logic spectroscopy has become an increasingly important tool for the state detection and readout of trapped atomic and molecular ions which do not possess easily accessible closed-cycling optical transitions. In this approach, the internal state of the target ion is mapped onto a co-trapped auxiliary ion. This mapping is typically mediated by normal modes of motion of the two-ion Coulomb crystal in the trap. The present study investigates the role of spectator modes not directly involved in a measurement protocol relying on a state-dependent optical-dipole force. We identify a Debye-Waller-type effect that modifies the response of the two-ion string to the force. We show that cooling the spectator modes of the string allows for the detection of the rovibrational ground state of an \documentclass[12pt]{minimal}
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\begin{document}$${{{{\rm{N}}}}}_{2}^{+}$$\end{document}N2+ molecular ion with a computed statistical fidelity exceeding 99.99%, improving on previous experiments by more than an order of magnitude while also halving the experimental time. This enhanced sensitivity enables the simultaneous identification of multiple rotational states with markedly weaker signals.

In quantum-logic spectroscopy schemes, the internal state of an atom or molecule without easily accessible closed-cycling transitions is projected onto a co-trapped atom that serves as a probe. Here, the authors investigate the effect of the motion of trapped ions on the state detection of a single nitrogen molecular ion with such a scheme.