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arXiv:1807.08309 · Physical Review A

Photon-recoil spectroscopy: Systematic shifts and nonclassical enhancements

Marius T. Schulte, Niels Lörch, Piet O. Schmidt, Klemens Hammerer

Published Dec 5, 2018• 3 citations
arXivHTMLPDF

Abstract

In photon-recoil spectroscopy, signals are extracted from recoils imparted by the spectroscopy light on the motion of trapped ions as demonstrated by Hempel et al. [C. Hempel et al., Nat. Photon. 7, 630 (2013)] and Wan et al. [Y. Wan et al., Nat. Commun. 5, 3096 (2014)]. The method exploits the exquisite efficiency in the detection of phonons achievable in ion crystals and is thus particularly suitable for species with broad noncycling transitions where detection of fluorescence photons is impractical. Here we develop a theoretical model for the description of photon-recoil spectroscopy based on a Fokker-Planck equation for the Wigner function of the phonon mode. Our model correctly explains systematic shifts due to Doppler heating and cooling as observed in the experiment. Furthermore, we investigate quantum metrological schemes for enhancing the spectroscopic sensitivity based on the preparation and detection of nonclassical states of the phonon mode.

DOI
10.1103/physreva.98.063808

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In photon-recoil spectroscopy, signals are extracted from recoils imparted by the spectroscopy light on the motion of trapped ions as demonstrated by Hempel et al. [C. Hempel et al., Nat. Photon. 7, 630 (2013)] and Wan et al. [Y. Wan et al., Nat. Commun. 5, 3096 (2014)]. The method exploits the exquisite efficiency in the detection of phonons achievable in ion crystals and is thus particularly suitable for species with broad noncycling transitions where detection of fluorescence photons is impractical. Here we develop a theoretical model for the description of photon-recoil spectroscopy based on a Fokker-Planck equation for the Wigner function of the phonon mode. Our model correctly explains systematic shifts due to Doppler heating and cooling as observed in the experiment. Furthermore, we investigate quantum metrological schemes for enhancing the spectroscopic sensitivity based on the preparation and detection of nonclassical states of the phonon mode.
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 24Mg+^{24}\mathrm{Mg}^{+}24Mg+ 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 24MgH+^{24}\mathrm{MgH}^{+}24MgH+ 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 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 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.
We demonstrate an efficient high-precision optical spectroscopy technique for single trapped ions with nonclosed transitions. In a double-shelving technique, the absorption of a single photon is first amplified to several phonons of a normal motional mode shared with a cotrapped cooling ion of a different species, before being further amplified to thousands of fluorescence photons emitted by the cooling ion using the standard electron shelving technique. We employ this extension of the photon recoil spectroscopy technique to perform the first high precision absolute frequency measurement of the 2D(3/2)→2P(1/2) transition in calcium, resulting in a transition frequency of f=346 000 234 867(96) kHz. Furthermore, we determine the isotope shift of this transition and the 2S(1/2)→2P(1/2) transition for 42Ca+, 44Ca+, and 48Ca+ ions relative to 40Ca+ with an accuracy below 100 kHz. Improved field and mass shift constants of these transitions as well as changes in mean square nuclear charge radii are extracted from this high resolution data.