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Liu QH, Tan Y, Cheng CF, Hu SM. Precision spectroscopy of molecular hydrogen. Phys Chem Chem Phys 2023; 25:27914-27925. [PMID: 37843424 DOI: 10.1039/d3cp03042c] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2023]
Abstract
Precision measurements on the hydrogen molecule are of fundamental importance in understanding molecular theory. Comparison of accurate experimental data and theoretical results are used to test the quantum electrodynamics theory and determine physical constants used in the calculation. We review recent advances and perspectives in the precision spectroscopy of molecular hydrogen, representing state-of-the-art molecular spectroscopy methods and cutting-edge high-precision calculations.
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Affiliation(s)
- Qian-Hao Liu
- Department of Chemical Physics, University of Science and Technology of China, Hefei, 230026, China.
| | - Yan Tan
- Department of Chemical Physics, University of Science and Technology of China, Hefei, 230026, China.
| | - Cun-Feng Cheng
- Department of Chemical Physics, University of Science and Technology of China, Hefei, 230026, China.
| | - Shui-Ming Hu
- Department of Chemical Physics, University of Science and Technology of China, Hefei, 230026, China.
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2
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Schwegler N, Holzapfel D, Stadler M, Mitjans A, Sergachev I, Home JP, Kienzler D. Trapping and Ground-State Cooling of a Single H_{2}^{+}. PHYSICAL REVIEW LETTERS 2023; 131:133003. [PMID: 37831997 DOI: 10.1103/physrevlett.131.133003] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/14/2022] [Revised: 04/24/2023] [Accepted: 07/24/2023] [Indexed: 10/15/2023]
Abstract
We demonstrate co-trapping and sideband cooling of a H_{2}^{+}-^{9}Be^{+} ion pair in a cryogenic Paul trap. We study the chemical lifetime of H_{2}^{+} and its dependence on the apparatus temperature, achieving lifetimes of up to 11_{-3}^{+6} h at 10 K. We demonstrate cooling of two of the modes of translational motion to an average phonon number of 0.07(1) and 0.05(1), corresponding to a temperature of 22(1) and 55(3) μK, respectively. Our results provide a basis for quantum logic spectroscopy experiments of H_{2}^{+}, as well as other light ions such as HD^{+}, H_{3}^{+}, and He^{+}.
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Affiliation(s)
- N Schwegler
- Institute for Quantum Electronics, Department of Physics, Eidgenössische Technische Hochschule Zürich, Otto-Stern-Weg 1, 8093 Zurich, Switzerland
| | - D Holzapfel
- Institute for Quantum Electronics, Department of Physics, Eidgenössische Technische Hochschule Zürich, Otto-Stern-Weg 1, 8093 Zurich, Switzerland
| | - M Stadler
- Institute for Quantum Electronics, Department of Physics, Eidgenössische Technische Hochschule Zürich, Otto-Stern-Weg 1, 8093 Zurich, Switzerland
| | - A Mitjans
- Institute for Quantum Electronics, Department of Physics, Eidgenössische Technische Hochschule Zürich, Otto-Stern-Weg 1, 8093 Zurich, Switzerland
| | - I Sergachev
- Institute for Quantum Electronics, Department of Physics, Eidgenössische Technische Hochschule Zürich, Otto-Stern-Weg 1, 8093 Zurich, Switzerland
| | - J P Home
- Institute for Quantum Electronics, Department of Physics, Eidgenössische Technische Hochschule Zürich, Otto-Stern-Weg 1, 8093 Zurich, Switzerland
| | - D Kienzler
- Institute for Quantum Electronics, Department of Physics, Eidgenössische Technische Hochschule Zürich, Otto-Stern-Weg 1, 8093 Zurich, Switzerland
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3
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Beyer M, Roth JC, Edwards E, DeMille D. Frequency-doubled Nd:YAG MOPA laser system with programmable rectangular pulses up to 200 microseconds. OPTICS EXPRESS 2021; 29:20370-20378. [PMID: 34266127 DOI: 10.1364/oe.427832] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/14/2021] [Accepted: 05/28/2021] [Indexed: 06/13/2023]
Abstract
A compact frequency-doubled diode-pumped Nd:YAG master-oscillator power-amplifier laser system with programmable microsecond pulse length has been developed. Analog pulse shaping of the output from a single-frequency continuous-wave Nd:YAG oscillator, and subsequent amplification, allowed the generation of rectangular pulses with pulse lengths on the order of the Nd:YAG fluorescence lifetime. Temporally flat-top pulses of 1064 nm light with 520 mJ pulse energy, 2.6 kW peak power, and 200 μs duration, with linewidth below 10 kHz, were obtained at a repetition rate of 2 Hz. Second harmonic generation in a LBO crystal yielded pulses of 262 mJ and 1.3 kW peak power at 532 nm. The peak power can be maintained within 2.9% over the duration of the laser pulse, and long-term intensity stability of 1.1% was observed. The spatially flat-top beam at 1064 nm used in the amplifier is converted to a Gaussian beam at 532 nm with beam quality factor M2 = 1.41(14) during the second harmonic generation. This system has potential as a pump source for Ti:sapphire, dye, or optical parametric amplifiers to generate tunable high-power single-frequency radiation for applications in precision measurements and laser slowing.
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Abstract
This article proposes a new method for sensing THz waves that can allow electric field measurements traceable to the International System of Units and to the fundamental physical constants by using the comparison between precision measurements with cold trapped HD+ ions and accurate predictions of molecular ion theory. The approach exploits the lightshifts induced on the two-photon rovibrational transition at 55.9 THz by a THz wave around 1.3 THz, which is off-resonantly coupled to the HD+ fundamental rotational transition. First, the direction and the magnitude of the static magnetic field applied to the ion trap is calibrated using Zeeman spectroscopy of HD+. Then, a set of lightshifts are converted into the amplitudes and the phases of the THz electric field components in an orthogonal laboratory frame by exploiting the sensitivity of the lightshifts to the intensity, the polarization and the detuning of the THz wave to the HD+ energy levels. The THz electric field measurement uncertainties are estimated for quantum projection noise-limited molecular ion frequency measurements with the current accuracy of molecular ion theory. The method has the potential to improve the sensitivity and accuracy of electric field metrology and may be extended to THz magnetic fields and to optical fields.
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Alighanbari S, Giri GS, Constantin FL, Korobov VI, Schiller S. Precise test of quantum electrodynamics and determination of fundamental constants with HD+ ions. Nature 2020; 581:152-158. [DOI: 10.1038/s41586-020-2261-5] [Citation(s) in RCA: 62] [Impact Index Per Article: 15.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/18/2018] [Accepted: 02/12/2020] [Indexed: 11/09/2022]
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Beyer M, Hölsch N, Hussels J, Cheng CF, Salumbides EJ, Eikema KSE, Ubachs W, Jungen C, Merkt F. Determination of the Interval between the Ground States of Para- and Ortho-H_{2}. PHYSICAL REVIEW LETTERS 2019; 123:163002. [PMID: 31702363 DOI: 10.1103/physrevlett.123.163002] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/18/2019] [Indexed: 06/10/2023]
Abstract
Nuclear-spin-symmetry conservation makes the observation of transitions between quantum states of ortho- and para-H_{2} extremely challenging. Consequently, the energy-level structure of H_{2} derived from experiment consists of two disjoint sets of level energies, one for para-H_{2} and the other for ortho-H_{2}. We use a new measurement of the ionization energy of para-H_{2} [E_{I}(H_{2})/(hc)=124 417.491 098(31) cm^{-1}] to determine the energy separation [118.486 770(50) cm^{-1}] between the ground states of para- and ortho-H_{2} and thus link the energy-level structure of the two nuclear-spin isomers of this fundamental molecule. Comparison with recent theoretical results [M. Puchalski et al., Phys. Rev. Lett. 122, 103003 (2019)PRLTAO0031-900710.1103/PhysRevLett.122.103003] enables the derivation of an upper bound of 1.5 MHz for a hypothetical global shift of the energy-level structure of ortho-H_{2} with respect to that of para-H_{2}.
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Affiliation(s)
- M Beyer
- Laboratorium für Physikalische Chemie, ETH Zürich, 8093 Zürich, Switzerland
| | - N Hölsch
- Laboratorium für Physikalische Chemie, ETH Zürich, 8093 Zürich, Switzerland
| | - J Hussels
- Department of Physics and Astronomy, LaserLaB, Vrije Universiteit Amsterdam, de Boelelaan 1081, 1081 HV Amsterdam, Netherlands
| | - C-F Cheng
- Department of Physics and Astronomy, LaserLaB, Vrije Universiteit Amsterdam, de Boelelaan 1081, 1081 HV Amsterdam, Netherlands
| | - E J Salumbides
- Department of Physics and Astronomy, LaserLaB, Vrije Universiteit Amsterdam, de Boelelaan 1081, 1081 HV Amsterdam, Netherlands
| | - K S E Eikema
- Department of Physics and Astronomy, LaserLaB, Vrije Universiteit Amsterdam, de Boelelaan 1081, 1081 HV Amsterdam, Netherlands
| | - W Ubachs
- Department of Physics and Astronomy, LaserLaB, Vrije Universiteit Amsterdam, de Boelelaan 1081, 1081 HV Amsterdam, Netherlands
| | - Ch Jungen
- Department of Physics and Astronomy, University College London, London WC1E 6BT, United Kingdom
| | - F Merkt
- Laboratorium für Physikalische Chemie, ETH Zürich, 8093 Zürich, Switzerland
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Cheng CF, Hussels J, Niu M, Bethlem HL, Eikema KSE, Salumbides EJ, Ubachs W, Beyer M, Hölsch N, Agner JA, Merkt F, Tao LG, Hu SM, Jungen C. Dissociation Energy of the Hydrogen Molecule at 10^{-9} Accuracy. PHYSICAL REVIEW LETTERS 2018; 121:013001. [PMID: 30028156 DOI: 10.1103/physrevlett.121.013001] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/19/2018] [Indexed: 06/08/2023]
Abstract
The ionization energy of ortho-H_{2} has been determined to be E_{I}^{o}(H_{2})/(hc)=124 357.238 062(25) cm^{-1} from measurements of the GK(1,1)-X(0,1) interval by Doppler-free, two-photon spectroscopy using a narrow band 179-nm laser source and the ionization energy of the GK(1,1) state by continuous-wave, near-infrared laser spectroscopy. E_{I}^{o}(H_{2}) was used to derive the dissociation energy of H_{2}, D_{0}^{N=1}(H_{2}), at 35 999.582 894(25) cm^{-1} with a precision that is more than one order of magnitude better than all previous results. The new result challenges calculations of this quantity and represents a benchmark value for future relativistic and QED calculations of molecular energies.
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Affiliation(s)
- C-F Cheng
- Department of Physics and Astronomy, LaserLaB, Vrije Universiteit Amsterdam, de Boelelaan 1081, 1081 HV Amsterdam, The Netherlands
| | - J Hussels
- Department of Physics and Astronomy, LaserLaB, Vrije Universiteit Amsterdam, de Boelelaan 1081, 1081 HV Amsterdam, The Netherlands
| | - M Niu
- Department of Physics and Astronomy, LaserLaB, Vrije Universiteit Amsterdam, de Boelelaan 1081, 1081 HV Amsterdam, The Netherlands
| | - H L Bethlem
- Department of Physics and Astronomy, LaserLaB, Vrije Universiteit Amsterdam, de Boelelaan 1081, 1081 HV Amsterdam, The Netherlands
| | - K S E Eikema
- Department of Physics and Astronomy, LaserLaB, Vrije Universiteit Amsterdam, de Boelelaan 1081, 1081 HV Amsterdam, The Netherlands
| | - E J Salumbides
- Department of Physics and Astronomy, LaserLaB, Vrije Universiteit Amsterdam, de Boelelaan 1081, 1081 HV Amsterdam, The Netherlands
| | - W Ubachs
- Department of Physics and Astronomy, LaserLaB, Vrije Universiteit Amsterdam, de Boelelaan 1081, 1081 HV Amsterdam, The Netherlands
| | - M Beyer
- Laboratorium für Physikalische Chemie, ETH Zürich, 8093 Zürich, Switzerland
| | - N Hölsch
- Laboratorium für Physikalische Chemie, ETH Zürich, 8093 Zürich, Switzerland
| | - J A Agner
- Laboratorium für Physikalische Chemie, ETH Zürich, 8093 Zürich, Switzerland
| | - F Merkt
- Laboratorium für Physikalische Chemie, ETH Zürich, 8093 Zürich, Switzerland
| | - L-G Tao
- Hefei National Laboratory for Physical Sciences at Microscale, iChem center, University of Science and Technology China, Hefei, 230026 China
| | - S-M Hu
- Hefei National Laboratory for Physical Sciences at Microscale, iChem center, University of Science and Technology China, Hefei, 230026 China
| | - Ch Jungen
- Laboratoire Aimé Cotton du CNRS, Bâtiment 505, Université de Paris-Sud, F-91405 Orsay, France and Department of Physics and Astronomy, University College London, London WC1E 6BT, United Kingdom
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Jansen P, Semeria L, Merkt F. Determination of the Spin-Rotation Fine Structure of He_{2}^{+}. PHYSICAL REVIEW LETTERS 2018; 120:043001. [PMID: 29437449 DOI: 10.1103/physrevlett.120.043001] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/13/2017] [Indexed: 06/08/2023]
Abstract
Measuring spin-rotation intervals in molecular cations is challenging, particularly so when the ions do not have electric-dipole-allowed rovibrational transitions. We present a method, based on an angular-momentum basis transformation, to determine the spin-rotational fine structure of molecular ions from the fine structure of high Rydberg states. The method is illustrated by the determination of the so far unknown spin-rotation fine structure of the fundamentally important He_{2}^{+} ion in the X ^{2}Σ_{u}^{+} state. The fine-structure splittings of the v^{+}=0, N^{+}=1, 3, and 5 levels of He_{2}^{+} are 7.96(14), 17.91(32), and 28.0(6) MHz, respectively. The experiment relies on the use of single-mode cw radiation to record spectra of high Rydberg states of He_{2} from the a ^{3}Σ_{u}^{+} metastable state.
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Affiliation(s)
- Paul Jansen
- Laboratory of Physical Chemistry, ETH Zurich, CH-8093 Zurich, Switzerland
| | - Luca Semeria
- Laboratory of Physical Chemistry, ETH Zurich, CH-8093 Zurich, Switzerland
| | - Frédéric Merkt
- Laboratory of Physical Chemistry, ETH Zurich, CH-8093 Zurich, Switzerland
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Semeria L, Jansen P, Merkt F. Precision measurement of the rotational energy-level structure of the three-electron molecule He 2. J Chem Phys 2016; 145:204301. [PMID: 27908106 DOI: 10.1063/1.4967256] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The term values of all rotational levels of the 4He2+ X+ 2Σu+ (ν+=0) ground vibronic state with rotational quantum number N+ ≤ 19 have been determined with an accuracy of 8 × 10-4 cm-1 (∼25 MHz) by multichannel-quantum-defect-theory-assisted Rydberg spectroscopy of metastable He2∗. Comparison of these term values with term values recently calculated ab initio by Tung et al. [J. Chem. Phys. 136, 104309 (2012)] reveals discrepancies that rapidly increase with increasing rotational quantum number and reach values of 0.07 cm-1 (∼2.1 GHz) at N+ = 19.
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Affiliation(s)
- Luca Semeria
- Laboratory of Physical Chemistry, ETH Zurich, CH-8093 Zurich, Switzerland
| | - Paul Jansen
- Laboratory of Physical Chemistry, ETH Zurich, CH-8093 Zurich, Switzerland
| | - Frédéric Merkt
- Laboratory of Physical Chemistry, ETH Zurich, CH-8093 Zurich, Switzerland
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Beyer M, Merkt F. Observation and Calculation of the Quasibound Rovibrational Levels of the Electronic Ground State of H2+. PHYSICAL REVIEW LETTERS 2016; 116:093001. [PMID: 26991172 DOI: 10.1103/physrevlett.116.093001] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/17/2015] [Indexed: 06/05/2023]
Abstract
Although the existence of quasibound rotational levels of the X^{+} ^{2}Σ_{g}^{+} ground state of H_{2}^{+} was predicted a long time ago, these states have never been observed. Calculated positions and widths of quasibound rotational levels located close to the top of the centrifugal barriers have not been reported either. Given the role that such states play in the recombination of H(1s) and H^{+} to form H_{2}^{+}, this lack of data may be regarded as one of the largest unknown aspects of this otherwise accurately known fundamental molecular cation. We present measurements of the positions and widths of the lowest-lying quasibound rotational levels of H_{2}^{+} and compare the experimental results with the positions and widths we calculate using a potential model for the X^{+} state of H_{2}^{+} which includes adiabatic, nonadiabatic, relativistic, and radiative corrections to the Born-Oppenheimer approximation.
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Affiliation(s)
- Maximilian Beyer
- Laboratorium für Physikalische Chemie, ETH Zürich, 8093 Zürich, Switzerland
| | - Frédéric Merkt
- Laboratorium für Physikalische Chemie, ETH Zürich, 8093 Zürich, Switzerland
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Jansen P, Semeria L, Hofer LE, Scheidegger S, Agner JA, Schmutz H, Merkt F. Precision Spectroscopy in Cold Molecules: The Lowest Rotational Interval of He_{2}^{+} and Metastable He_{2}. PHYSICAL REVIEW LETTERS 2015; 115:133202. [PMID: 26451553 DOI: 10.1103/physrevlett.115.133202] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/19/2015] [Indexed: 06/05/2023]
Abstract
Multistage Zeeman deceleration was used to generate a slow, dense beam of translationally cold He_{2} molecules in the metastable a ^{3}Σ_{u}^{+} state. Precision measurements of the Rydberg spectrum of these molecules at high values of the principal quantum number n have been carried out. The spin-rotational state selectivity of the Zeeman-deceleration process was exploited to reduce the spectral congestion, minimize residual Doppler shifts, resolve the Rydberg series around n=200 and assign their fine structure. The ionization energy of metastable He_{2} and the lowest rotational interval of the X^{+} ^{2}Σ_{u}^{+} (ν^{+}=0) ground state of ^{4}He_{2}^{+} have been determined with unprecedented precision and accuracy by Rydberg-series extrapolation. Comparison with ab initio predictions of the rotational energy level structure of ^{4}He_{2}^{+} [W.-C. Tung, M. Pavanello, and L. Adamowicz, J. Chem. Phys. 136, 104309 (2012)] enabled us to quantify the magnitude of relativistic and quantum-electrodynamics contributions to the fundamental rotational interval of He_{2}^{+}.
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Affiliation(s)
- Paul Jansen
- Laboratory of Physical Chemistry, ETH Zurich, CH-8093 Zurich, Switzerland
| | - Luca Semeria
- Laboratory of Physical Chemistry, ETH Zurich, CH-8093 Zurich, Switzerland
| | | | - Simon Scheidegger
- Laboratory of Physical Chemistry, ETH Zurich, CH-8093 Zurich, Switzerland
| | - Josef A Agner
- Laboratory of Physical Chemistry, ETH Zurich, CH-8093 Zurich, Switzerland
| | - Hansjürg Schmutz
- Laboratory of Physical Chemistry, ETH Zurich, CH-8093 Zurich, Switzerland
| | - Frédéric Merkt
- Laboratory of Physical Chemistry, ETH Zurich, CH-8093 Zurich, Switzerland
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