Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2004.02959 · Physical Review A

Unresolved sideband photon recoil spectroscopy of molecular ions

Emilie Hindbo Clausen, Vincent Jarlaud, Karin Fisher, Steffen Meyer, Cyrille Solaro, Michael Drewsen

Published Jun 9, 2022• 4 citations
arXivHTMLPDF

Abstract

We reflect on the prospect of exploiting the recoil associated with absorption and emission of photons to perform spectroscopy of a single molecular ion. For this recoil to be detectable, the molecular ion is sympathetically cooled by a laser-cooled atomic ion to near their common quantum-mechanical ground state within a trapping potential. More specifically, we present a general framework for simulating the expected photon recoil spectra in regimes where either the natural transition linewidth ${\mathrm{\ensuremath{\Gamma}}}_{t}$ of the molecular ion or the spectral width ${\mathrm{\ensuremath{\Gamma}}}_{L}$ of the exciting light source exceeds the motional frequencies of the two-ion system. To exemplify the framework, we present two complementary cases: spectroscopy of the broad $3\mathrm{s} ^{2}\mathrm{S}_{1/2}\ensuremath{-}3\mathrm{p} ^{2}\mathrm{P}_{3/2}$ electronic transition (${\mathrm{\ensuremath{\Gamma}}}_{t}/2\ensuremath{\pi}=41.8\phantom{\rule{0.16em}{0ex}}\mathrm{M}\mathrm{Hz}$) of a single $^{24}\mathrm{Mg}^{+}$ ion at $\ensuremath{\lambda}=279.6$ nm by a narrow laser source $({\mathrm{\ensuremath{\Gamma}}}_{L}/2\ensuremath{\pi}\ensuremath{\lesssim}1\phantom{\rule{0.16em}{0ex}}\mathrm{MHz})$ and mid-infrared vibrational spectroscopy of the very narrow $|v=0,J=1\ensuremath{\rangle}\ensuremath{-}|{v}^{\ensuremath{'}}=1,{J}^{\ensuremath{'}}=0\ensuremath{\rangle}$ transition $({\mathrm{\ensuremath{\Gamma}}}_{t}/2\ensuremath{\pi}=2.50\phantom{\rule{0.16em}{0ex}}\mathrm{Hz})$ at $\ensuremath{\lambda}=6.17\phantom{\rule{0.16em}{0ex}}\ensuremath{\mu}\mathrm{m}$ in the $^{1}\mathrm{\ensuremath{\Sigma}}^{+}$ electronic ground state of $^{24}\mathrm{MgH}^{+}$ by a broadband laser source $({\mathrm{\ensuremath{\Gamma}}}_{L}/2\ensuremath{\pi}\ensuremath{\gtrsim}50\phantom{\rule{0.16em}{0ex}}\mathrm{MHz})$. The atomic ion $^{24}\mathrm{Mg}^{+}$ has been picked to introduce a simple system to make comparisons with experimental results while still capturing most of the physics involved in electronic excitations of molecular ions.

DOI
10.1103/physreva.105.063709

Related papers

Quantum logic spectroscopy of atomic and molecular ions

Wan, Yong

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.

•Jan 1, 2014•0 citations

Infrared absorption spectroscopy of a single polyatomic molecular ion

Zhenlin Wu, Tim Duka, Mariano Isaza-Monsalve +8 more

Absorption spectroscopy is a fundamental tool for probing molecular structure. However, performing absorption spectroscopy on individual molecules is challenging due to the low signal-to-noise ratio. Here, we report on a nondestructive absorption spectroscopy on a mid-infrared vibrational transition in a single molecular ion that is co-trapped with an atomic ion. The absorption of a single photon is detected via the momentum transfer from the absorbed photon onto the molecule. This recoil signal is amplified using a non-classical state of motion of the two-ion crystal and subsequently read out via the atomic ion. We characterize the recoil detection method and use it to investigate the interaction between femtosecond laser pulses and the O-H stretching vibration in individual CaOH+ molecular ions. Furthermore, we present the single-photon absorption spectrum obtained for the vibrational transition. This method represents a milestone towards quantum non-demolition measurements of complex polyatomic molecules, providing high-fidelity methods for preparation and measurement of the quantum state of a wide range of molecular species.

quant-pharXiv:2511.19687•Nature•Nov 26, 2025•0 citations

Resolved Sideband Spectroscopy for the Detection of Weak Optical Transitions

James E. Goeders

This thesis reports on the setup of a new ion trap apparatus designed for experiments with single ⁴⁰Ca⁺ ions to perform molecular spectroscopy. The calcium ion is laser cooled, allowing for sympathetic cooling of the nonfluorescing molecular ion. The aim of these experiments is to explore loading and identifying molecular ions in RF-Paul traps, as well as developing new spectroscopic tools to measure transitions of molecular ions via the fluorescence of co-trapped ⁴⁰Ca⁺ ions. Ground state cooling of a mixed ion pair is implemented as a first step towards increasing the sensitivity of our technique to the level necessary to measure transitions with low scattering rates (like those present in molecular ions). Doppler cooling on the S(1/2)->P(1/2) transition of the calcium ion results in the formation of a Coulomb crystal, the behavior of which may be used to infer properties of the molecular ion. Following cooling, sideband spectroscopy on the narrow S(1/2)->D(5/2) quadrupole transition of calcium may be used to identify the mass of single molecular ions. This method is verified via a non-destructive measurement on ⁴⁰CaH⁺ and ⁴⁰Ca¹⁶O⁺. The normal modes of the Coulomb crystal can also be used to extract information from the target ion to the control ion. By driving the blue side of a transition, laser induced heating can be put into the two ion system, which leads to changes in fluorescence of the ⁴⁰Ca⁺ ion, first demonstrated with two Ca⁺ isotopes. Increasing the sensitivity of this technique requires ground state cooling of both the ⁴⁰Ca⁺ ion and the ion of interest, enabling the transfer of the ion's motional state into the ground state with high probability. This thesis demonstrates ground state cooling of the atomic ion and sympathetic cooling of a second ion (⁴⁴Ca⁺). Once in the ground state, heating of the Coulomb crystal by scattering photons off of the spectroscopy ion can be measured by monitoring the resolved motional sidebands of the S(1/2)->D(5/2) transition of ⁴⁰Ca⁺, allowing for spectral lines to be inferred. Future experiments will investigate this technique with molecular ions.

•Jul 2, 2013•2 citations

Infrared absorption spectroscopy of a single polyatomic molecular ion

wzl17, Tim Duka, Mariano Isaza-Monsalve +8 more

Absorption spectroscopy is a fundamental tool for probing molecular structure. However, performing absorption spectroscopy on individual molecules is challenging because of the low signal-to-noise ratio. Here we report on non-destructive absorption spectroscopy on a mid-infrared vibrational transition in a single molecular ion that is co-trapped with an atomic ion. The absorption of a single photon is detected by the momentum transfer from the absorbed photon onto the molecule. This recoil signal is amplifed using a non-classical state of motion of the two-ion crystal and subsequently read out by the atomic ion. We characterize the recoil detection method and use it to investigate the interaction between femtosecond laser pulses and the O–H stretching vibration in individual CaOH⁺ molecular ions. Furthermore, we present the spectrum obtained for the vibrational transition with single-photon sensitivity. This method can provide a way of performing non-destructive state detection of complex polyatomic molecules, for preparation and measurement of the quantum state of a wide range of molecular species. This research was funded by Austrian science fund FWF (10.55776/COE1, 10.55776/PIN3213524), the Austrian Research Promotion Agency (FFG) under the project ‘HDCode’ (FO999921407), and the ERC Horizon 2020 project ERC-2020-STG 948893. This research is funded in part by the Gordon and Betty Moore Foundation through grant GBMF12992. V.Š. was supported by funding from the MEYS of Czech Republic under the project CZ.02.01.01/00/22 008/0004649. M.G. and M.T. acknowledge the National Science Centre, Poland (grant no. 2021/43/B/ST4/03326) for financial support and the high-performance computing infrastructure PLGrid of Poland (HPC centres: ACK Cyfronet AGH) for providing computer facilities and support (computational grant no. PLG/2024/017527). Open access funding provided by University of Innsbruck and Medical University of Innsbruck.

•Oct 14, 2026•0 citations

Laser-cooled atomic ions as probes of molecular ions

Kenneth R. Brown, C. Ricardo Viteri, Craig Robert Clark +3 more

Trapped laser-cooled atomic ions are a new tool for understanding cold molecular ions. The atomic ions not only sympathetically cool the molecular ions to millikelvin temperatures, but the bright atomic ion fluorescence can also serve as a detector of both molecular reactions and molecular spectra. We are working towards the detection of single molecular ion spectra by sympathetic heating spectroscopy. Sympathetic heating spectroscopy uses the coupled motion of two trapped ions to measure the spectra of one ion by observing changes in the fluorescence of the other ion. Sympathetic heating spectroscopy is a generalization of quantum logic spectroscopy, but does not require ions in the motional ground state or coherent control of the ion internal states. We have recently demonstrated this technique using two isotopes of Ca+ [Phys. Rev. A, 81, 043428 (2010)]. Limits of the method and potential applications for molecular spectroscopy are discussed.

AIP conference proceedings•Jan 1, 2015•0 citations

Spectroscopy of Single Trapped Ions and Application to Frequency Standards

HERBERT WALTHER

Single ions trapped and laser cooled provide ideal objects for high resolution spectroscopy and frequency standards. For the latter purpose we are investigating the 5s2 1S0 → 5s5p 3P0 transition of In+. With a natural linewidth of only 1.1 Hz this resonance offers very high resolution and is highly immune to frequency shifts due to external electromagnetic fields, because it connects two levels with vanishing electronic magnetic momenta [1]. The wavelength of this clock transition is 236.5 nm and is technically very convenient, since it coincides with the fourth harmonic of the 946 nm Nd:YAG laser line. So this intrinsically frequency stable solid-state laser can be used to excite the transition [2]. For laser cooling and fluorescence detection of the indium ion the 5s2 1So -> 5s5p 3P1 transition at 230.6 nm can be employed. The use of the relatively narrow intercombination line for laser cooling allows us to study optical sideband cooling in the strong binding regime, where the oscillation frequencies of the ion in the trap (around 1 MHz) are larger than the optical linewidth of 360 kHz. In this parameter range laser cooling is possible to the quantum ground state of the vibrational motion in the trap corresponding to a temperature of roughly 100 μK. The same low temperature was obtained with sideband cooling of a small Coulomb crystal consisting of two ions, creating an interesting new quantum few-particle system.

Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)•Jan 1, 1998•0 citations
We reflect on the prospect of exploiting the recoil associated with absorption and emission of photons to perform spectroscopy of a single molecular ion. For this recoil to be detectable, the molecular ion is sympathetically cooled by a laser-cooled atomic ion to near their common quantum-mechanical ground state within a trapping potential. More specifically, we present a general framework for simulating the expected photon recoil spectra in regimes where either the natural transition linewidth \ensuremathΓt{\mathrm{\ensuremath{\Gamma}}}_{t}\ensuremathΓt​ of the molecular ion or the spectral width \ensuremathΓL{\mathrm{\ensuremath{\Gamma}}}_{L}\ensuremathΓL​ of the exciting light source exceeds the motional frequencies of the two-ion system. To exemplify the framework, we present two complementary cases: spectroscopy of the broad 3s2S1/2\ensuremath−3p2P3/23\mathrm{s} ^{2}\mathrm{S}_{1/2}\ensuremath{-}3\mathrm{p} ^{2}\mathrm{P}_{3/2}3s2S1/2​\ensuremath−3p2P3/2​ electronic transition (\ensuremathΓt/2\ensuremathπ=41.8MHz{\mathrm{\ensuremath{\Gamma}}}_{t}/2\ensuremath{\pi}=41.8\phantom{\rule{0.16em}{0ex}}\mathrm{M}\mathrm{Hz}\ensuremathΓt​/2\ensuremathπ=41.8MHz) of a single 24Mg+^{24}\mathrm{Mg}^{+}24Mg+ ion at \ensuremathλ=279.6\ensuremath{\lambda}=279.6\ensuremathλ=279.6 nm by a narrow laser source (\ensuremathΓL/2\ensuremathπ\ensuremath≲1MHz)({\mathrm{\ensuremath{\Gamma}}}_{L}/2\ensuremath{\pi}\ensuremath{\lesssim}1\phantom{\rule{0.16em}{0ex}}\mathrm{MHz})(\ensuremathΓL​/2\ensuremathπ\ensuremath≲1MHz) and mid-infrared vibrational spectroscopy of the very narrow ∣v=0,J=1\ensuremath⟩\ensuremath−∣v\ensuremath′=1,J\ensuremath′=0\ensuremath⟩|v=0,J=1\ensuremath{\rangle}\ensuremath{-}|{v}^{\ensuremath{'}}=1,{J}^{\ensuremath{'}}=0\ensuremath{\rangle}∣v=0,J=1\ensuremath⟩\ensuremath−∣v\ensuremath′=1,J\ensuremath′=0\ensuremath⟩ transition (\ensuremathΓt/2\ensuremathπ=2.50Hz)({\mathrm{\ensuremath{\Gamma}}}_{t}/2\ensuremath{\pi}=2.50\phantom{\rule{0.16em}{0ex}}\mathrm{Hz})(\ensuremathΓt​/2\ensuremathπ=2.50Hz) at \ensuremathλ=6.17\ensuremathμm\ensuremath{\lambda}=6.17\phantom{\rule{0.16em}{0ex}}\ensuremath{\mu}\mathrm{m}\ensuremathλ=6.17\ensuremathμm in the 1\ensuremathΣ+^{1}\mathrm{\ensuremath{\Sigma}}^{+}1\ensuremathΣ+ electronic ground state of 24MgH+^{24}\mathrm{MgH}^{+}24MgH+ by a broadband laser source (\ensuremathΓL/2\ensuremathπ\ensuremath≳50MHz)({\mathrm{\ensuremath{\Gamma}}}_{L}/2\ensuremath{\pi}\ensuremath{\gtrsim}50\phantom{\rule{0.16em}{0ex}}\mathrm{MHz})(\ensuremathΓL​/2\ensuremathπ\ensuremath≳50MHz). The atomic ion 24Mg+^{24}\mathrm{Mg}^{+}24Mg+ has been picked to introduce a simple system to make comparisons with experimental results while still capturing most of the physics involved in electronic excitations of molecular ions.
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.
Absorption spectroscopy is a fundamental tool for probing molecular structure. However, performing absorption spectroscopy on individual molecules is challenging due to the low signal-to-noise ratio. Here, we report on a nondestructive absorption spectroscopy on a mid-infrared vibrational transition in a single molecular ion that is co-trapped with an atomic ion. The absorption of a single photon is detected via the momentum transfer from the absorbed photon onto the molecule. This recoil signal is amplified using a non-classical state of motion of the two-ion crystal and subsequently read out via the atomic ion. We characterize the recoil detection method and use it to investigate the interaction between femtosecond laser pulses and the O-H stretching vibration in individual CaOH+ molecular ions. Furthermore, we present the single-photon absorption spectrum obtained for the vibrational transition. This method represents a milestone towards quantum non-demolition measurements of complex polyatomic molecules, providing high-fidelity methods for preparation and measurement of the quantum state of a wide range of molecular species.
This thesis reports on the setup of a new ion trap apparatus designed for experiments with single ⁴⁰Ca⁺ ions to perform molecular spectroscopy. The calcium ion is laser cooled, allowing for sympathetic cooling of the nonfluorescing molecular ion. The aim of these experiments is to explore loading and identifying molecular ions in RF-Paul traps, as well as developing new spectroscopic tools to measure transitions of molecular ions via the fluorescence of co-trapped ⁴⁰Ca⁺ ions. Ground state cooling of a mixed ion pair is implemented as a first step towards increasing the sensitivity of our technique to the level necessary to measure transitions with low scattering rates (like those present in molecular ions). Doppler cooling on the S(1/2)->P(1/2) transition of the calcium ion results in the formation of a Coulomb crystal, the behavior of which may be used to infer properties of the molecular ion. Following cooling, sideband spectroscopy on the narrow S(1/2)->D(5/2) quadrupole transition of calcium may be used to identify the mass of single molecular ions. This method is verified via a non-destructive measurement on ⁴⁰CaH⁺ and ⁴⁰Ca¹⁶O⁺. The normal modes of the Coulomb crystal can also be used to extract information from the target ion to the control ion. By driving the blue side of a transition, laser induced heating can be put into the two ion system, which leads to changes in fluorescence of the ⁴⁰Ca⁺ ion, first demonstrated with two Ca⁺ isotopes. Increasing the sensitivity of this technique requires ground state cooling of both the ⁴⁰Ca⁺ ion and the ion of interest, enabling the transfer of the ion's motional state into the ground state with high probability. This thesis demonstrates ground state cooling of the atomic ion and sympathetic cooling of a second ion (⁴⁴Ca⁺). Once in the ground state, heating of the Coulomb crystal by scattering photons off of the spectroscopy ion can be measured by monitoring the resolved motional sidebands of the S(1/2)->D(5/2) transition of ⁴⁰Ca⁺, allowing for spectral lines to be inferred. Future experiments will investigate this technique with molecular ions.
Absorption spectroscopy is a fundamental tool for probing molecular structure. However, performing absorption spectroscopy on individual molecules is challenging because of the low signal-to-noise ratio. Here we report on non-destructive absorption spectroscopy on a mid-infrared vibrational transition in a single molecular ion that is co-trapped with an atomic ion. The absorption of a single photon is detected by the momentum transfer from the absorbed photon onto the molecule. This recoil signal is amplifed using a non-classical state of motion of the two-ion crystal and subsequently read out by the atomic ion. We characterize the recoil detection method and use it to investigate the interaction between femtosecond laser pulses and the O–H stretching vibration in individual CaOH⁺ molecular ions. Furthermore, we present the spectrum obtained for the vibrational transition with single-photon sensitivity. This method can provide a way of performing non-destructive state detection of complex polyatomic molecules, for preparation and measurement of the quantum state of a wide range of molecular species. This research was funded by Austrian science fund FWF (10.55776/COE1, 10.55776/PIN3213524), the Austrian Research Promotion Agency (FFG) under the project ‘HDCode’ (FO999921407), and the ERC Horizon 2020 project ERC-2020-STG 948893. This research is funded in part by the Gordon and Betty Moore Foundation through grant GBMF12992. V.Š. was supported by funding from the MEYS of Czech Republic under the project CZ.02.01.01/00/22 008/0004649. M.G. and M.T. acknowledge the National Science Centre, Poland (grant no. 2021/43/B/ST4/03326) for financial support and the high-performance computing infrastructure PLGrid of Poland (HPC centres: ACK Cyfronet AGH) for providing computer facilities and support (computational grant no. PLG/2024/017527). Open access funding provided by University of Innsbruck and Medical University of Innsbruck.
Trapped laser-cooled atomic ions are a new tool for understanding cold molecular ions. The atomic ions not only sympathetically cool the molecular ions to millikelvin temperatures, but the bright atomic ion fluorescence can also serve as a detector of both molecular reactions and molecular spectra. We are working towards the detection of single molecular ion spectra by sympathetic heating spectroscopy. Sympathetic heating spectroscopy uses the coupled motion of two trapped ions to measure the spectra of one ion by observing changes in the fluorescence of the other ion. Sympathetic heating spectroscopy is a generalization of quantum logic spectroscopy, but does not require ions in the motional ground state or coherent control of the ion internal states. We have recently demonstrated this technique using two isotopes of Ca+ [Phys. Rev. A, 81, 043428 (2010)]. Limits of the method and potential applications for molecular spectroscopy are discussed.
Single ions trapped and laser cooled provide ideal objects for high resolution spectroscopy and frequency standards. For the latter purpose we are investigating the 5s2 1S0 → 5s5p 3P0 transition of In+. With a natural linewidth of only 1.1 Hz this resonance offers very high resolution and is highly immune to frequency shifts due to external electromagnetic fields, because it connects two levels with vanishing electronic magnetic momenta [1]. The wavelength of this clock transition is 236.5 nm and is technically very convenient, since it coincides with the fourth harmonic of the 946 nm Nd:YAG laser line. So this intrinsically frequency stable solid-state laser can be used to excite the transition [2]. For laser cooling and fluorescence detection of the indium ion the 5s2 1So -> 5s5p 3P1 transition at 230.6 nm can be employed. The use of the relatively narrow intercombination line for laser cooling allows us to study optical sideband cooling in the strong binding regime, where the oscillation frequencies of the ion in the trap (around 1 MHz) are larger than the optical linewidth of 360 kHz. In this parameter range laser cooling is possible to the quantum ground state of the vibrational motion in the trap corresponding to a temperature of roughly 100 μK. The same low temperature was obtained with sideband cooling of a small Coulomb crystal consisting of two ions, creating an interesting new quantum few-particle system.