High-Precision Calculation of the Hyperfine Structure of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>HD</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:math>Ion

Bakalov, D.; Korobov, V. I.; Schiller, S.

doi:10.1103/physrevlett.97.243001

Cited by 81 publications

(141 citation statements)

References 31 publications

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“…Finally, we investigated the effect due to the uncertainty of the spin coefficient E 4 (see Eq. 1), which is estimated to be 50 kHz [17]. Comparing fits with E 4 values differing by 50 kHz, we find that this has a negligibly small effect of ∼1 Hz on the result for ν 0 .…”

Section: Zeeman Stark and Other Shiftsmentioning

confidence: 80%

“…Note that after diagonalization, the quantum numbers F ,S are only approximately good, and a hyperfine eigenstate can be expressed in the 'pure' basis states |FSJM J � in the form with real-valued coefficients β FSJ . In [17] the hyperfine levels in vibrationally excited states in HD + are calculated with an error margin of ~50 kHz. This uncertainty might propagate through a spectral analysis employing a lineshape model which includes the theoretical hyperfine (1)…”

Section: Hyperfine Structure and Rotational Statesmentioning

confidence: 99%

“…In [17] the hyperfine energy levels and eigenstates in HD + are calculated by diagonalization of the effective spin Hamiltonian where the spin coefficients, E i , are obtained by averaging the Breit-Pauli Hamiltonian over the nonrelativistic wavefunctions, L is the rotational angular momentum operator, and s e , l p and l d are the electron, proton and deuteron spin operators. K d and K Q are spherical tensors composed of angular momenta, whose explicit form is given in [17]. The strongest coupling is the proton-electron spin-spin interaction [the term in E 4 in Eq.…”

Section: Hyperfine Structure and Rotational Statesmentioning

confidence: 99%

“…The frequencies of these transitions are typically in the (near-) infrared with linewidths below 10 Hz, which makes them amenable to high-resolution laser spectroscopy. Optical clocks based on trapped atomic ions have shown that laser spectroscopy at very high accuracy (below one part in 10 17 ) is possible [6]. Recent theoretical studies point out that also for molecular hydrogen ions experimental uncertainties in the 10 −16 range should be possible [7,8].…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2016

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Section: Zeeman Stark and Other Shiftsmentioning

confidence: 80%

Section: Hyperfine Structure and Rotational Statesmentioning

confidence: 99%

Section: Hyperfine Structure and Rotational Statesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

et al. 2016

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“…This will enable preparation of the ions also in a specific hyperfine sublevel of the rovibrational ground state and precise measurements of the HD + hyperfine structure as well as improved absolute frequency measurements of rovibrational transition frequencies 17,27,28 .…”

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confidence: 99%

All-optical preparation of molecular ions in the rovibrational ground state

et al. 2010

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In the field of cold quantum matter, control of the motional degrees of freedom of both neutral and charged gas-phase molecules has been achieved for a wide range of species 1-11 . However, cooling of the internal degrees of freedom remains challenging. Recently, transfer to the internal ground state by sophisticated optical techniques has been demonstrated for neutral alkali dimers created in single quantum states from ultracold atoms 12-15 . Here we demonstrate cooling of the rotational degree of freedom of heteronuclear diatomic molecules with a thermal distribution of internal states, using a simple, robust and general optical-pumping scheme with two low-power continuous-wave lasers. With trapped and translationally cooled hydrogen deuteride (HD + ) molecular ions as a model system, we achieve 78(4)% rovibrational ground-state population. The rotationally, vibrationally and translationally cold molecular ion ensemble is suitable for a number of applications, such as generation of long-lived coherences or frequency metrology of fundamental constants 16,17 .The study of cold molecular systems promises new insights and advances in many fields of physics and physical chemistry. As in atomic physics, the key to tapping the full potential of molecules is the ability to accurately control the external and internal degrees of freedom of the particles. The complex internal structure of molecules has however so far precluded direct application of many techniques developed for trapping and cooling of atoms, demanding modified or completely new approaches. Now, a large toolbox for trapping and cooling the motional degrees of freedom of both neutral and charged molecules is available 18 . Although general schemes for cooling the internal degrees of freedom of molecules have been proposed 19,20 , the most general method available at present is cryogenic buffer-gas cooling, which is efficient only for molecules in the vibrational ground state and limits the translational temperature to a few hundred millikelvin 7 . Coherent transfer to the rovibrational ground state 11-14 is most suitable when most of the molecules are initially in the same quantum state, as is the case for molecules produced by associating cold atoms.For heteronuclear molecular ensembles for which the population is distributed among many rotational levels in the v = 0 vibrational manifold, optical pumping has been proposed as an approach to rotational cooling 21,22 . We demonstrate here that a scheme using two laser fields driving a fundamental and an overtone vibrational electric dipole transition 21 yields a large ground-state population and briefly discuss the applicability of the scheme to various diatomic molecular species. Figure 1 shows the energy levels (without hyperfine structure) and electric dipole transitions of the HD + molecule relevant for the experiment. The initial internal-state distribution is given by a Boltzmann distribution reflecting thermal equilibrium with the T ∼ = 300 K blackbody radiation field emitted by the experimental Inst...

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Precision Calculations for Three-Body Molecular Bound States

Karr¹,

Haidar²,

Hilico³

et al. 2020

Recent Progress in Few-Body Physics

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Although they do not lend themselves to analytical resolution, three-body atomic or molecular systems are still simple enough to allow for very precise theoretical predictions of their energy levels, which makes them attractive candidates for fundamental tests and determination of fundamental physical constants. Focusing on the hydrogen molecular ions (H + 2 , HD + , D + 2 ), we outline the methods which have been used to improve the theoretical accuracy by several orders of magnitude over the last two decades. The three-body Schrödinger equation can be solved with extreme precision by variational methods with trial functions involving exponentials of interparticle distances. Quantum electrodynamics (QED) corrections are evaluated in the framework of nonrelativistic QED (NRQED). The current status of theory and possibilities of further improvement are briefly sketched.

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High-Precision Calculation of the Hyperfine Structure of theHD+Ion

Cited by 81 publications

References 31 publications

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

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

All-optical preparation of molecular ions in the rovibrational ground state

Precision Calculations for Three-Body Molecular Bound States

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