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Communications Physics

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

Mikolaj Roguski, Aleksandr Shlykov, Ziv Meir, Stefan Willitsch

Published Nov 25, 2025• 0 citations
Publisher

Abstract

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 $${{{{\rm{N}}}}}_{2}^{+}$$ N 2 + 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.

DOI
10.1038/s42005-025-02373-x

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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 N2+_2^+2+​ 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.
Scaling trapped-ion quantum sensors from single ions to large ensembles is a key challenge for next-generation precision measurements. At the same time, many ion species of interest for optical clocks and tests of fundamental physics lack closed cycling transitions required for direct laser cooling and state detection. Collective quantum logic spectroscopy addresses both limitations by coupling an ensemble of sensor, or spectroscopy, ions to one or more logic ions that provide sympathetic cooling and state readout. Here, we establish the fundamental performance limits and operating regimes of this protocol, identifying how the interaction strength, interrogation time, and logic-ensemble size govern sensitivity, dynamic range, and robustness to experimental imperfections. We show that quantum-limited sensitivity can be retained even with a single logic ion, while increasing the number of logic ions substantially improves readout efficiency and robustness. Beyond precision metrology, the same collective interface enables many-body measurements relevant to quantum information processing, including parity measurements and stabilizer-like syndrome extraction. Our results establish collective quantum logic spectroscopy as a scalable framework for optical clocks, quantum-enhanced sensing, and trapped-ion quantum information processing.
Laser spectroscopy is a versatile tool to investigate the internal structure of atoms, molecules and nuclei.High precision spectroscopy requires laser cooling to reduce Doppler broadening and Doppler shifts.Sympathetic cooling extends these advantages to species which do not have an appropriate transition for laser cooling and allows precision spectroscopy of previously inaccessible species using the quantum logic technique.The original implementation of quantum logic spectroscopy relies on the long lifetime of the excited spectroscopy state to realize a transfer sequence.Precision spectroscopy of transitions with a short-lived excited state is typically performed using laser induced uorescence or laser absorption spectroscopy.Neither of these methods has reached the fundamental quantum projection noise limit and are rather limited by photon shot noise.For these situations, we develop the technique of photon recoil spectroscopy as an extension of quantum logic spectroscopy to broad transitions.The common motion of a sideband-cooled two-ion crystal is excited by photon recoil during photon absorption on the spectroscopically investigated ion.This motional excitation is transferred to an internal state excitation on the co-trapped ion of a dierent species and detected with high eciency.We demonstrate the technique on the 2 S 1/2 ↔ 2 P 1/2 transition of the 40 Ca + ion and resolve the line center to 1/300 of its observed linewidth.The simplicity and versatility of the technique promises applications to other previously inaccessible species.A variation of the technique is proposed for rotational state preparation of molecular ions.A moving optical lattice is employed to exert a state-dependent force on the molecule.This would allow the detection of the rotational state of the molecular ion and therefore enable precision spectroscopy of specic rovibrational transitions in the molecule.
We present theoretical and experimental progress towards a new approach for the precision spectroscopy, coherent manipulation and state-to-state chemistry of single isolated molecular ions in the gas phase. Our method uses a molecular beam for creating packets of rotationally cold neutrals from which a single molecule is state-selectively ionized and trapped inside a radiofrequency ion trap. In addition to the molecular ion, a single co-trapped atomic ion is used to cool the molecular external degrees of freedom to the ground state of the trap and to detect the molecular state using state-selective coherent motional excitation from a modulated optical-dipole force acting on the molecule. We present a detailed discussion and theoretical characterization of the present approach. We simulate the molecular signal experimentally using a single atomic ion, indicating that different rovibronic molecular states can be resolved and individually detected with our method. The present approach for the coherent control and non-destructive detection of the quantum state of a single molecular ion opens up new perspectives for precision spectroscopies relevant for, e.g., tests of fundamental physical theories and the development of new types of clocks based on molecular vibrational transitions. It will also enable the observation and control of chemical reactions of single particles on the quantum level. While focusing on N2+ as a prototypical example in the present work, our method is applicable to a wide range of diatomic and polyatomic molecules.
Spectroscopy Achieving efficient quantum control of ultracold molecular systems may open opportunities in molecular precision spectroscopy, quantum information, and related fields. Sinhal et al. report a quantumnondemolition protocol for the detection of the spin-rovibronic state of a single trapped cold molecular ion co-trapped with an atomic ion. They show that monitoring the motion of Ca+ after coherent motional excitation of the Ca+-N2+ string makes it possible to detect the N2+ state without destroying either the molecule or the state itself. The procedure can be repeated multiple times while preserving the high readout fidelity. Science , this issue p. [1213][1] [1]: /lookup/doi/10.1126/science.aaz9837
Abstract Precision spectroscopy has been the driving force for progress of our physical understanding and still is a promising tool for the investigation of new physics. Molecules offer transitions which allow tests that are not possible in atomic systems. However, usually precision spectroscopy of molecules is challenging due to the lack of cycling transitions for state preparation and state detection. For molecular ions, this obstacle can be overcome by quantum logic spectroscopy, where dissipation for state preparation and detection is provided by a co-trapped atomic ion exploiting the shared eigenstates of motion. Here, we propose a full quantum logic spectroscopy scheme for molecular oxygen ions and theoretically investigate the feasibility of quantum logic-assisted state detection and preparation. Furthermore, we provide coupling rates for a direct single-photon quadrupole excitation of a vibrational overtone transition that can serve as a sensitive reference for tests of a possible variation of the proton-to-electron mass ratio.