Manipulation of Individual Hyperfine States in Cold Trapped Molecular Ions and Application toHD+Frequency Metrology

Abstract

Advanced techniques for manipulation of internal states, standard in atomic physics, are demonstrated for a charged molecular species for the first time. We address individual hyperfine states of ro-vibrational levels of a diatomic ion by optical excitation of individual hyperfine transitions, and achieve controlled transfer of population into a selected hyperfine state. We use molecular hydrogen ions (HD + ) as a model system and employ a novel frequency-comb-based, continuous-wave 5 µm laser spectrometer. The achieved spectral resolution is the highest obtained so far in the optical domain on a molecular ion species. As a consequence, we are also able to perform the most precise test yet of the ab-initio theory of a molecule.Cold trapped molecules [1, 2] currently represent an intense field of activity relying on sophisticated methods of molecule production, translational and internal cooling, spectroscopy and sensitive detection. Many applications, such as chemical reaction studies [3, 4], tests of molecular quantum theory [5], fundamental physics [6, 7] and quantum computing [8] would benefit strongly from the availability of advanced manipulation techniques, already standard in atomic physics. These are not straightforward for molecules, and for charged molecules have not been demonstrated yet. Production methods for molecular ions (usually by electron impact ionization) and, if heteronuclear, their interaction with the black-body radiation of the surrounding vacuum chamber, usually lead to significant population of a substantial number of internal states. A first, important step in the manipulation of internal states of molecular ions is population transfer between rotational states (heteronuclear molecules usually being cold vibrationally, i.e. are all in the v = 0 ground vibrational state). It has been demonstrated that a significant fraction (ca. 75%) of an ensemble of diatomic molecular ions can be pumped into the vibrational and rotational ground level (v = 0, N = 0) [9, 10], see Fig. 1.For a general diatomic molecule, however, this pumping is usually not capable of preparing molecules in a single quantum state, because spin interactions generate a hyperfine structure with several states in each ro-vibrational level. For example, a diatomic molecule with one unpaired electron (s e = 1/2), and nuclei with nuclear spins I 1 = 1/2, I 2 = 1 (such as HD + ) has 4 hyperfine states in zero magnetic field if the rotational angular momentum N = 0, but 10 if N = 1, and 12 if N ≥ 2, see Fig. 2 a. The ability to address selectively molecules in one particular hyperfine state (or even in a single quantum state with a particular magnetic quantum number J z ) and to transfer molecules from one hyperfine state to another are clearly important tools of a molecular quantum toolbox that can be part of a full quantum state preparation procedure.Complicating the addressing, the number of strong transitions between two given ro-vibrational levels (v, N ), (v , N ) is equal to the larger of the two numbers of hyperfine s...

Vibronic Spectroscopy of Sympathetically Cooled CaH+

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“…The spectroscopy of cold trapped ions is an important tool for the determination of molecular species in the interstellar medium [1,2] and the precise measurement of fundamental physical constants [3,4,5]. Application of methods from the laser-cooling of atomic ions has led to new advances in taming both external and internal quantum states of trapped molecular ions.…”

High-precision spectroscopy of the HD+ molecule at the 1-p.p.b. level

“…However, the most precise measurement of a ro-vibrational transition in HD + so far resulted in a 2.7 p.p.b. (2.4σ) discrepancy with more accurate theoretical data [11]. The question whether this offset is a statistical outlier, or caused by an experimental systematic effect or possible 'new physics' has remained unanswered.…”

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Reversing hydride-ion formation in quantum-information experiments withBe+

“…[18]. Given the difficulty of detecting scattered photons from dilute molecular-ion samples, rotational-state-selective PD has emerged as a critical tool for molecular ion spectroscopy [15,19] and precision measurements [16,20], while rotationally-insensitive dissociation schemes provide valuable tests of molecular * Electronic address: brian.sawyer@boulder.nist.gov ) after 9000 pulses of 157 nm photodissociation light at 1.6 mJ/pulse. We measure an increase in the Be + fraction from 81% to 97% of the constant total ion number in the crystal.…”