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Hollósy P, Jeszenszki P, Mátyus E. One-Particle Operator Representation over Two-Particle Basis Sets for Relativistic QED Computations. J Chem Theory Comput 2024; 20:5122-5132. [PMID: 38857902 DOI: 10.1021/acs.jctc.4c00270] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/12/2024]
Abstract
This work is concerned with two-spin-1/2-fermion relativistic quantum mechanics, and it is about the construction of one-particle projectors using an inherently two-particle, "explicitly correlated" basis representation necessary for good numerical convergence of the interaction energy. It is demonstrated that a faithful representation of the one-particle operators, which appear in intermediate but essential computational steps, can be constructed over a many-particle basis set by accounting for the full Hilbert space beyond the physically relevant antisymmetric subspace. Applications of this development can be foreseen for the computation of quantum-electrodynamics corrections for a correlated relativistic reference state and high-precision relativistic computations of medium-to-high-Z helium-like systems, for which other two-particle projection techniques are unreliable.
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Affiliation(s)
- Péter Hollósy
- Institute of Chemistry, ELTE, Eötvös Loránd University, Pázmány Péter Sétány 1/A, Budapest H-1117, Hungary
| | - Péter Jeszenszki
- Institute of Chemistry, ELTE, Eötvös Loránd University, Pázmány Péter Sétány 1/A, Budapest H-1117, Hungary
| | - Edit Mátyus
- Institute of Chemistry, ELTE, Eötvös Loránd University, Pázmány Péter Sétány 1/A, Budapest H-1117, Hungary
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2
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Mátyus E, Ferenc D, Jeszenszki P, Margócsy Á. The Bethe-Salpeter QED Wave Equation for Bound-State Computations of Atoms and Molecules. ACS PHYSICAL CHEMISTRY AU 2023; 3:222-240. [PMID: 37249939 PMCID: PMC10214514 DOI: 10.1021/acsphyschemau.2c00062] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/04/2022] [Revised: 01/07/2023] [Accepted: 01/09/2023] [Indexed: 05/31/2023]
Abstract
Interactions in atomic and molecular systems are dominated by electromagnetic forces and the theoretical framework must be in the quantum regime. The physical theory for the combination of quantum mechanics and electromagnetism, quantum electrodynamics has been "established" by the mid-twentieth century, primarily as a scattering theory. To describe atoms and molecules, it is important to consider bound states. In the nonrelativistic quantum mechanics framework, bound states can be efficiently computed using robust and general methodologies with systematic approximations developed for solving wave equations. With the sight of the development of a computational quantum electrodynamics framework for atomic and molecular matter, the field theoretic Bethe-Salpeter wave equation expressed in space-time coordinates, its exact equal-time variant, and emergence of a relativistic wave equation, is reviewed. A computational framework, with initial applications and future challenges in relation with precision spectroscopy, is also highlighted.
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3
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Sinhal M, Johnson A, Willitsch S. Frequency stabilisation and SI tracing of mid-infrared quantum-cascade lasers for precision molecular spectroscopy. Mol Phys 2022. [DOI: 10.1080/00268976.2022.2144519] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Affiliation(s)
- Mudit Sinhal
- Department of Chemistry, University of Basel, Basel, Switzerland
| | - Anatoly Johnson
- Department of Chemistry, University of Basel, Basel, Switzerland
| | - Stefan Willitsch
- Department of Chemistry, University of Basel, Basel, Switzerland
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4
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Sala L, Luxford TFM, Ranković M, Kočišek J. Viewpoints on the 11th International Meeting on Atomic and Molecular Physics and Chemistry. J Phys Chem A 2022; 126:8557-8561. [DOI: 10.1021/acs.jpca.2c07768] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/13/2022]
Affiliation(s)
- Leo Sala
- J. Heyrovský Institute of Physical Chemistry v.v.i., The Czech Academy of Sciences, Dolejškova 3, 18223Prague, Czech Republic
| | - Thomas F. M. Luxford
- J. Heyrovský Institute of Physical Chemistry v.v.i., The Czech Academy of Sciences, Dolejškova 3, 18223Prague, Czech Republic
| | - Miloš Ranković
- J. Heyrovský Institute of Physical Chemistry v.v.i., The Czech Academy of Sciences, Dolejškova 3, 18223Prague, Czech Republic
| | - Jaroslav Kočišek
- J. Heyrovský Institute of Physical Chemistry v.v.i., The Czech Academy of Sciences, Dolejškova 3, 18223Prague, Czech Republic
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Schullian O, Antila HS, Heazlewood BR. A variable time step self-consistent mean field DSMC model for three-dimensional environments. J Chem Phys 2022; 156:124309. [PMID: 35364882 DOI: 10.1063/5.0083033] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A self-consistent mean field direct simulation Monte Carlo (SCMFD) algorithm was recently proposed for simulating collision environments for a range of one-dimensional model systems. This work extends the one-dimensional SCMFD approach to three dimensions and introduces a variable time step (3D-vt-SCMFD), enabling the modeling of a considerably wider range of different collision environments. We demonstrate the performance of the augmented method by modeling a varied set of test systems: ideal gas mixtures, Poiseuille flow of argon, and expansion of gas into high vacuum. For the gas mixtures, the 3D-vt-SCMFD method reproduces the properties (mean free path, mean free time, collision frequency, and temperature) in excellent agreement with theoretical predictions. From the Poiseuille flow simulations, we extract flow profiles that agree with the solution to the Navier-Stokes equations in the high-density limit and resemble free molecular flow at low densities, as expected. The measured viscosity from 3D-vt-SCMF is ∼15% lower than the theoretical prediction from Chapman-Enskog theory. The expansion of gas into vacuum is examined in the effusive regime and at the hydrodynamic limit. In both cases, 3D-vt-SCMDF simulations produce gas beam density, velocity, and temperature profiles in excellent agreement with analytical models. In summary, our tests show that 3D-vt-SCMFD is robust and computationally efficient, while also illustrating the diversity of systems the SCMFD model can be successfully applied to.
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Affiliation(s)
- O Schullian
- Department of Theory and Bio-Systems, Max Planck Institute of Colloids and Interfaces, Potsdam-Golm Science Park, 14476 Potsdam, Germany
| | - H S Antila
- Department of Theory and Bio-Systems, Max Planck Institute of Colloids and Interfaces, Potsdam-Golm Science Park, 14476 Potsdam, Germany
| | - B R Heazlewood
- Department of Physics, University of Liverpool, Liverpool L69 7ZE, United Kingdom
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6
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Jeszenszki P, Ferenc D, Mátyus E. Variational Dirac–Coulomb explicitly correlated computations for atoms and molecules. J Chem Phys 2022; 156:084111. [DOI: 10.1063/5.0075096] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The Dirac–Coulomb equation with positive-energy projection is solved using explicitly correlated Gaussian functions. The algorithm and computational procedure aims for a parts-per-billion convergence of the energy to provide a starting point for further comparison and further developments in relation with high-resolution atomic and molecular spectroscopy. Besides a detailed discussion of the implementation of the fundamental spinor structure, permutation, and point-group symmetries, various options for the positive-energy projection procedure are presented. The no-pair Dirac–Coulomb energy converged to a parts-per-billion precision is compared with perturbative results for atomic and molecular systems with small nuclear charge numbers. Paper II [D. Ferenc, P. Jeszenszki, and E. Mátyus, J. Chem. Phys. 156, 084110 (2022).] describes the implementation of the Breit interaction in this framework.
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Affiliation(s)
- Péter Jeszenszki
- ELTE, Eötvös Loránd University, Institute of Chemistry, Pázmány Péter sétány 1/A, Budapest H-1117, Hungary
| | - Dávid Ferenc
- ELTE, Eötvös Loránd University, Institute of Chemistry, Pázmány Péter sétány 1/A, Budapest H-1117, Hungary
| | - Edit Mátyus
- ELTE, Eötvös Loránd University, Institute of Chemistry, Pázmány Péter sétány 1/A, Budapest H-1117, Hungary
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7
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Ireland R, Jeszenszki P, Mátyus E, Martinazzo R, Ronto M, Pollak E. Lower Bounds for Nonrelativistic Atomic Energies. ACS PHYSICAL CHEMISTRY AU 2021; 2:23-37. [PMID: 35098243 PMCID: PMC8796283 DOI: 10.1021/acsphyschemau.1c00018] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 07/27/2021] [Indexed: 11/29/2022]
Abstract
A recently developed lower bound theory for Coulombic problems (E. Pollak, R. Martinazzo, J. Chem. Theory Comput. 2021, 17, 1535) is further developed and applied to the highly accurate calculation of the ground-state energy of two- (He, Li+, and H-) and three- (Li) electron atoms. The method has been implemented with explicitly correlated many-particle basis sets of Gaussian type, on the basis of the highly accurate (Ritz) upper bounds they can provide with relatively small numbers of functions. The use of explicitly correlated Gaussians is developed further for computing the variances, and the necessary modifications are here discussed. The computed lower bounds are of submilli-Hartree (parts per million relative) precision and for Li represent the best lower bounds ever obtained. Although not yet as accurate as the corresponding (Ritz) upper bounds, the computed bounds are orders of magnitude tighter than those obtained with other lower bound methods, thereby demonstrating that the proposed method is viable for lower bound calculations in quantum chemistry applications. Among several aspects, the optimization of the wave function is shown to play a key role for both the optimal solution of the lower bound problem and the internal check of the theory.
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Affiliation(s)
- Robbie
T. Ireland
- Institute
of Chemistry, ELTE, Eötvös
Loránd University, Pázmány Péter sétány 1/A, Budapest, H-1117, Hungary,School of
Chemistry, University of Glasgow, University Avenue, G12 8QQ, Glasgow, United Kingdom
| | - Peter Jeszenszki
- Institute
of Chemistry, ELTE, Eötvös
Loránd University, Pázmány Péter sétány 1/A, Budapest, H-1117, Hungary
| | - Edit Mátyus
- Institute
of Chemistry, ELTE, Eötvös
Loránd University, Pázmány Péter sétány 1/A, Budapest, H-1117, Hungary,E-mail:
| | - Rocco Martinazzo
- Department
of Chemistry, University of Milan, Milan, 20122, Italy,Institute of Molecular Science and Technologies
(ISTM), Consiglio
Nazionale delle Ricerche (CNR), Milan, 20133, Italy,
| | - Miklos Ronto
- Chemical
and Biological Physics Department, Weizmann
Institute of Science, 76100, Rehovot, Israel
| | - Eli Pollak
- Chemical
and Biological Physics Department, Weizmann
Institute of Science, 76100, Rehovot, Israel,
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Rayment MH, Hogan SD. Quantum-state-dependent decay rates of electrostatically trapped Rydberg NO molecules. Phys Chem Chem Phys 2021; 23:18806-18822. [PMID: 34612419 PMCID: PMC8900602 DOI: 10.1039/d1cp01930a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/30/2021] [Accepted: 07/22/2021] [Indexed: 11/21/2022]
Abstract
Nitric oxide (NO) molecules travelling in pulsed supersonic beams have been prepared in long-lived Rydberg-Stark states by resonance-enhanced two-colour two-photon excitation from the X 2Π1/2 (v'' = 0, J'' = 3/2) ground state, through the A 2Σ+ (v' = 0, N' = 0, J' = 1/2) intermediate state. These excited molecules were decelerated from 795 ms-1 to rest in the laboratory-fixed frame of reference, in the travelling electric traps of a transmission-line Rydberg-Stark decelerator. The decelerator was operated at 30 K to minimise effects of blackbody radiation on the molecules during deceleration and trapping. The molecules were electrostatically trapped for times of up to 1 ms, and detected in situ by pulsed electric field ionisation. Measurements of the rate of decay from the trap were performed for states with principal quantum numbers between n = 32 and 50, in Rydberg series converging to the N+= 0, 1, and 2 rotational states of NO+. For the range of Rydberg states studied, the measured decay times of between 200 μs and 400 μs were generally observed to reduce as the value of n was increased. For some particular values of n deviations from this trend were seen. These observations are interpreted, with the aid of numerical calculations, to arise as a result of contributions to the decay rates, on the order of 1 kHz, from rotational and vibrational channel interactions. These results shed new light on the role of weak intramolecular interactions on the slow decay of long-lived Rydberg states in NO.
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Affiliation(s)
- M H Rayment
- Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, UK.
| | - S D Hogan
- Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, UK.
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Clausen G, Jansen P, Scheidegger S, Agner JA, Schmutz H, Merkt F. Ionization Energy of the Metastable 2 ^{1}S_{0} State of ^{4}He from Rydberg-Series Extrapolation. PHYSICAL REVIEW LETTERS 2021; 127:093001. [PMID: 34506206 DOI: 10.1103/physrevlett.127.093001] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/28/2021] [Accepted: 07/12/2021] [Indexed: 06/13/2023]
Abstract
In a recent breakthrough in first-principles calculations of two-electron systems, Patkóś, Yerokhin, and Pachucki [Phys. Rev. A 103, 042809 (2021)PLRAAN2469-992610.1103/PhysRevA.103.042809] have performed the first complete calculation of the Lamb shift of the helium 2 ^{3}S_{1} and 2 ^{3}P_{J} triplet states up to the term in α^{7}m. Whereas their theoretical result of the frequency of the 2 ^{3}P←2 ^{3}S transition perfectly agrees with the experimental value, a more than 10σ discrepancy was identified for the 3 ^{3}D←2 ^{3}S and 3 ^{3}D←2 ^{3}P transitions, which hinders the determination of the He^{2+} charge radius from atomic spectroscopy. We present here a new measurement of the ionization energy of the 2 ^{1}S_{0} state of He [960 332 040.491(32) MHz] which we use in combination with the 2 ^{3}S_{1}←2 ^{1}S_{0} interval measured by Rengelink et al. [Nat. Phys. 14, 1132 (2018).NPAHAX1745-247310.1038/s41567-018-0242-5] and the 2 ^{3}P←2 ^{3}S_{1} interval measured by Zheng et al. [Phys. Rev. Lett. 119, 263002 (2017)PRLTAO0031-900710.1103/PhysRevLett.119.263002] and Cancio Pastor et al. [Phys. Rev. Lett. 92, 023001 (2004)PRLTAO0031-900710.1103/PhysRevLett.92.023001] to derive experimental ionization energies of the 2 ^{3}S_{1} state [1152 842 742.640(32) MHz] and the 2 ^{3}P centroid energy [876 106 247.025(39) MHz]. These values reveal disagreements with the α^{7}m Lamb shift prediction by 6.5σ and 10σ, respectively, and support the suggestion by Patkóš et al. of an unknown theoretical contribution to the Lamb shifts of the 2 ^{3}S and 2 ^{3}P states of He.
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Affiliation(s)
- Gloria Clausen
- Laboratory of Physical Chemistry, ETH Zurich, CH-8093 Zurich, Switzerland
| | - Paul Jansen
- 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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Wirthl V, Maisenbacher L, Weitenberg J, Hertlein A, Grinin A, Matveev A, Pohl R, Hänsch TW, Udem T. Improved active fiber-based retroreflector with intensity stabilization and a polarization monitor for the near UV. OPTICS EXPRESS 2021; 29:7024-7048. [PMID: 33726212 DOI: 10.1364/oe.417455] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/23/2020] [Accepted: 01/31/2021] [Indexed: 06/12/2023]
Abstract
We present an improved active fiber-based retroreflector (AFR) providing high-quality wavefront-retracing anti-parallel laser beams in the near UV. We use our improved AFR for first-order Doppler-shift suppression in precision spectroscopy of atomic hydrogen, but our setup can be adapted to other applications where wavefront-retracing beams with defined laser polarization are important. We demonstrate how weak aberrations produced by the fiber collimator may remain unobserved in the intensity of the collimated beam but limit the performance of the AFR. Our general results on characterizing these aberrations with a caustic measurement can be applied to any system where a collimated high-quality laser beam is required. Extending the collimator design process by wave optics propagation tools, we achieved a four-lens collimator for the wavelength range 380-486 nm with the beam quality factor of M2 ≃ 1.02, limited only by the not exactly Gaussian beam profile from the single-mode fiber. Furthermore, we implemented precise fiber-collimator alignment and improved the collimation control by combining a precision motor with a piezo actuator. Moreover, we stabilized the intensity of the wavefront-retracing beams and added in-situ monitoring of polarization from polarimetry of the retroreflected light.
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Ferenc D, Korobov VI, Mátyus E. Nonadiabatic, Relativistic, and Leading-Order QED Corrections for Rovibrational Intervals of ^{4}He_{2}^{+} (X ^{2}Σ_{u}^{+}). PHYSICAL REVIEW LETTERS 2020; 125:213001. [PMID: 33274993 DOI: 10.1103/physrevlett.125.213001] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/18/2020] [Accepted: 09/23/2020] [Indexed: 06/12/2023]
Abstract
The rovibrational intervals of the ^{4}He_{2}^{+} molecular ion in its X ^{2}Σ_{u}^{+} ground electronic state are computed by including the nonadiabatic, relativistic, and leading-order quantum-electrodynamics corrections. Good agreement of theory and experiment is observed for the rotational excitation series of the vibrational ground state and the fundamental vibration. The lowest-energy rotational interval is computed to be 70.937 69(10) cm^{-1} in agreement with the most recently reported experimental value, 70.937 589(23)(60)_{sys} cm^{-1} [L. Semeria et al., Phys. Rev. Lett. 124, 213001 (2020)PRLTAO0031-900710.1103/PhysRevLett.124.213001].
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Affiliation(s)
- Dávid Ferenc
- Institute of Chemistry, ELTE, Eötvös Loránd University, Pázmány Péter sétány 1/A, Budapest H-1117, Hungary
| | - Vladimir I Korobov
- Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna 141980, Russia
| | - Edit Mátyus
- Institute of Chemistry, ELTE, Eötvös Loránd University, Pázmány Péter sétány 1/A, Budapest H-1117, Hungary
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Najafian K, Meir Z, Willitsch S. From megahertz to terahertz qubits encoded in molecular ions: theoretical analysis of dipole-forbidden spectroscopic transitions in N 2. Phys Chem Chem Phys 2020; 22:23083-23098. [PMID: 33048077 DOI: 10.1039/d0cp03906c] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Recent advances in quantum technologies have enabled the precise control of single trapped molecules on the quantum level. Exploring the scope of these new technologies, we studied theoretically the implementation of qubits and clock transitions in the spin, rotational, and vibrational degrees of freedom of molecular nitrogen ions including the effects of magnetic fields. The relevant spectroscopic transitions span six orders of magnitude in frequency, illustrating the versatility of the molecular spectrum for encoding quantum information. We identified two types of magnetically insensitive qubits with very low ("stretched"-state qubits) or even zero ("magic" magnetic-field qubits) linear Zeeman shifts. The corresponding spectroscopic transitions are predicted to shift by as little as a few mHz for an amplitude of magnetic-field fluctuations on the order of a few mG, translating into Zeeman-limited coherence times of tens of minutes encoded in the rotations and vibrations of the molecule. We also found that the Q(0) line of the fundamental vibrational transition is magnetic-dipole allowed by interaction with the first excited electronic state of the molecule. The Q(0) transitions, which benefit from small systematic shifts for clock operation and is thus well suited for testing a possible variation in the proton-to-electron mass ratio, were so far not considered in single-photon spectra. Finally, we explored possibilities to coherently control the nuclear-spin configuration of N2+ through the magnetically enhanced mixing of nuclear-spin states.
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Affiliation(s)
- Kaveh Najafian
- Department of Chemistry, University of Basel, Klingelbergstrasse 80, 4056 Basel, Switzerland.
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