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Hu JW, Han YC. Investigation of photoassociation with full-dimensional thermal-random-phase wavefunctions. J Chem Phys 2021; 155:064108. [PMID: 34391372 DOI: 10.1063/5.0059543] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
By taking the femtosecond two-photon photoassociation (PA) of magnesium atoms as an example, we propose a method to calculate the thermally averaged population, which is transferred from the ground X1Σg + state to the target (1)1Πg state, based on the solution of full-dimensional time-dependent Schrödinger equation. In this method, named as method A, we use thermal-random-phase wavefunctions with the random phases expanded in both the vibrational and rotational degrees of freedom to model the thermal ensemble of the initial eigenstates. This method is compared with the other two methods (B and C) at different temperatures. Method B is also based on thermal-random-phase wavefunctions, except that the random-phase expansion is merely used for the vibrational degree of freedom. Method C is based on the independent propagation of every initial eigenstate, instead of the thermal-random-phase wavefunctions. Taking the (1)1Πg state as the target state, it is found that although these three methods can present the same population on the (1)1Πg state, the computation efficiency of method A increases dramatically with the increase in temperature. With this efficient method A, we find that the PA process at 1000 K can also induce rotational coherence, i.e., the molecular field-free alignment in the excited electronic states.
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Affiliation(s)
- Jin-Wei Hu
- Department of Physics, Dalian University of Technology, Dalian 116024, China
| | - Yong-Chang Han
- Department of Physics, Dalian University of Technology, Dalian 116024, China
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Carini JL, Kallush S, Kosloff R, Gould PL. Efficient Formation of Ultracold Molecules with Chirped Nanosecond Pulses. J Phys Chem A 2016; 120:3032-41. [PMID: 26652642 DOI: 10.1021/acs.jpca.5b10088] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We describe experiments and associated quantum simulations involving the production of ultracold (87)Rb2 molecules with nanosecond pulses of frequency-chirped light. With appropriate chirp parameters, the formation is dominated by coherent processes. For a positive chirp, excited molecules are produced by photoassociation early in the chirp, and then transferred into high vibrational levels of the lowest triplet state by stimulated emission later in the chirp. Generally good agreement is seen between the data and the simulations. Shaping of the chirp can lead to a significant enhancement of the formation rate. Further improvements using higher intensities and different intermediate states are predicted.
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Affiliation(s)
- J L Carini
- Department of Physics, University of Connecticut , Storrs, Connecticut 06269, United States
| | - S Kallush
- Department of Physics and Optical Engineering, ORT Braude , P.O. Box 78, Karmiel, Israel.,Department of Physical Chemistry and the Fritz Haber Research Center for Molecular Dynamics, The Hebrew University , 91094 Jerusalem, Israel
| | - R Kosloff
- Department of Physical Chemistry and the Fritz Haber Research Center for Molecular Dynamics, The Hebrew University , 91094 Jerusalem, Israel
| | - P L Gould
- Department of Physics, University of Connecticut , Storrs, Connecticut 06269, United States
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Carini JL, Kallush S, Kosloff R, Gould PL. Enhancement of Ultracold Molecule Formation Using Shaped Nanosecond Frequency Chirps. PHYSICAL REVIEW LETTERS 2015; 115:173003. [PMID: 26551111 DOI: 10.1103/physrevlett.115.173003] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/17/2015] [Indexed: 06/05/2023]
Abstract
We demonstrate that judicious shaping of a nanosecond-time-scale frequency chirp can dramatically enhance the formation rate of ultracold (87)Rb(2) molecules. Starting with ultracold (87)Rb atoms, we apply pulses of frequency-chirped light to first photoassociate the atoms into excited molecules and then, later in the chirp, deexcite these molecules into a high vibrational level of the lowest triplet state a (3)Σ(u)(+). The enhancing chirp shape passes through the absorption and stimulated emission transitions relatively slowly, thus increasing their adiabaticity, but jumps quickly between them to minimize the effects of spontaneous emission. Comparisons with quantum simulations for various chirp shapes support this enhancement mechanism.
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Affiliation(s)
- J L Carini
- Department of Physics, University of Connecticut, Storrs, Connecticut 06269, USA
| | - S Kallush
- Department of Physics and Optical Engineering, ORT Braude, P.O. Box 78, Karmiel, Israel
- Department of Physical Chemistry and the Fritz Haber Research Center for Molecular Dynamics, The Hebrew University, 91094 Jerusalem, Israel
| | - R Kosloff
- Department of Physical Chemistry and the Fritz Haber Research Center for Molecular Dynamics, The Hebrew University, 91094 Jerusalem, Israel
| | - P L Gould
- Department of Physics, University of Connecticut, Storrs, Connecticut 06269, USA
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Amaran S, Kosloff R, Tomza M, Skomorowski W, Pawłowski F, Moszynski R, Rybak L, Levin L, Amitay Z, Berglund JM, Reich DM, Koch CP. Femtosecond two-photon photoassociation of hot magnesium atoms: A quantum dynamical study using thermal random phase wavefunctions. J Chem Phys 2013; 139:164124. [DOI: 10.1063/1.4826350] [Citation(s) in RCA: 27] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Yan M, DeSalvo BJ, Huang Y, Naidon P, Killian TC. Rabi oscillations between atomic and molecular condensates driven with coherent one-color photoassociation. PHYSICAL REVIEW LETTERS 2013; 111:150402. [PMID: 24160581 DOI: 10.1103/physrevlett.111.150402] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/19/2013] [Indexed: 06/02/2023]
Abstract
We demonstrate coherent one-color photoassociation of a Bose-Einstein condensate, which results in Rabi oscillations between atomic and molecular condensates. We attain atom-molecule Rabi frequencies that are comparable to decoherence rates by driving photoassociation of atoms in an ^{88}Sr condensate to a weakly bound level of the metastable 1S0+3P1 molecular potential, which has a long lifetime and a large Franck-Condon overlap integral with the ground scattering state. Transient shifts and broadenings of the excitation spectrum are clearly seen at short times, and they create an asymmetric excitation profile that only displays Rabi oscillations for blue detuning from resonance.
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Affiliation(s)
- Mi Yan
- Department of Physics and Astronomy, Rice University, Houston, Texas 77251, USA
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Tomza M, Skomorowski W, Musiał M, González-Férez R, Koch CP, Moszynski R. Interatomic potentials, electric properties and spectroscopy of the ground and excited states of the Rb2 molecule: ab initio calculations and effect of a non-resonant field*. Mol Phys 2013. [DOI: 10.1080/00268976.2013.793835] [Citation(s) in RCA: 51] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
Affiliation(s)
- Michał Tomza
- a Faculty of Chemistry , University of Warsaw , Warsaw , Poland
- b Theoretische Physik , Universität Kassel , Kassel , Germany
| | | | - Monika Musiał
- c Institute of Chemistry , University of Silesia , Katowice , Poland
| | - Rosario González-Férez
- d Instituto Carlos I de Física Teórica y Computacional and Departamento de Física Atómica, Molecular y Nuclear , Universidad de Granada , Granada , Spain
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Ulmanis J, Deiglmayr J, Repp M, Wester R, Weidemüller M. Ultracold Molecules Formed by Photoassociation: Heteronuclear Dimers, Inelastic Collisions, and Interactions with Ultrashort Laser Pulses. Chem Rev 2012; 112:4890-927. [PMID: 22931226 DOI: 10.1021/cr300215h] [Citation(s) in RCA: 33] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Juris Ulmanis
- Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Philosophenweg
12, 69120 Heidelberg, Germany
| | - Johannes Deiglmayr
- Laboratorium für Physikalische
Chemie, ETH Zürich, Wolfgang-Pauli-Strasse
10, 8093 Zürich, Switzerland
| | - Marc Repp
- Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Philosophenweg
12, 69120 Heidelberg, Germany
| | - Roland Wester
- Institut für Ionenphysik
und Angewandte Physik, Universität Innsbruck, Technikerstrasse 25/3, 6020 Innsbruck, Austria
| | - Matthias Weidemüller
- Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Philosophenweg
12, 69120 Heidelberg, Germany
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Affiliation(s)
- Christiane P. Koch
- Theoretische Physik, Universität Kassel, Heinrich-Plett-Strasse 40,
34132 Kassel, Germany
| | - Moshe Shapiro
- Department
of Chemistry, University of British Columbia, Vancouver, Canada V6T
1Z1, and Department of Chemical Physics, The Weizmann Institute, Rehovot, Israel 76100
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Rybak L, Amaran S, Levin L, Tomza M, Moszynski R, Kosloff R, Koch CP, Amitay Z. Generating molecular rovibrational coherence by two-photon femtosecond photoassociation of thermally hot atoms. PHYSICAL REVIEW LETTERS 2011; 107:273001. [PMID: 22243308 DOI: 10.1103/physrevlett.107.273001] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/24/2011] [Indexed: 05/31/2023]
Abstract
The formation of diatomic molecules with rotational and vibrational coherence is demonstrated experimentally in free-to-bound two-photon femtosecond photoassociation of hot atoms. In a thermal gas at a temperature of 1000 K, pairs of magnesium atoms, colliding in their electronic ground state, are excited into coherent superpositions of bound rovibrational levels in an electronically excited state. The rovibrational coherence is probed by a time-delayed third photon, resulting in quantum beats in the UV fluorescence. A comprehensive theoretical model based on ab initio calculations rationalizes the generation of coherence by Franck-Condon filtering of collision energies and partial waves, quantifying it in terms of an increase in quantum purity of the thermal ensemble. Our results open the way to coherent control of a binary reaction.
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Affiliation(s)
- Leonid Rybak
- The Shirlee Jacobs Femtosecond Laser Research Laboratory, Schulich Faculty of Chemistry, Technion-Israel Institute of Technology, Haifa, Israel
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Rybak L, Amitay Z, Amaran S, Kosloff R, Tomza M, Moszynski R, Koch CP. Femtosecond coherent control of thermal photoassociation of magnesium atoms. Faraday Discuss 2011; 153:383-94; discussion 395-413. [DOI: 10.1039/c1fd00052g] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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Koch CP, Ndong M, Kosloff R. Two-photon coherent control of femtosecond photoassociation. Faraday Discuss 2010; 142:389-402; discussion 429-61. [PMID: 20151555 DOI: 10.1039/b818458e] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Photoassociation with short laser pulses has been proposed as a technique to create ultracold ground state molecules. A broad-band excitation seems the natural choice to drive the series of excitation and deexcitation steps required to form a molecule in its vibronic ground state from two scattering atoms. First attempts at femtosecond photoassociation were, however, hampered by the requirement to eliminate the atomic excitation leading to trap depletion. On the other hand, molecular levels very close to the atomic transition are to be excited. The broad bandwidth of a femtosecond laser then appears to be rather an obstacle. To overcome the ostensible conflict of driving a narrow transition by a broad-band laser, we suggest a two-photon photoassociation scheme. In the weak-field regime, a spectral phase pattern can be employed to eliminate the atomic line. When the excitation is carried out by more than one photon, different pathways in the field can be interfered constructively or destructively. In the strong-field regime, a temporal phase can be applied to control dynamic Stark shifts. The atomic transition is suppressed by choosing a phase which keeps the levels out of resonance. We derive analytical solutions for atomic two-photon dark states in both the weak-field and strong-field regime. Two-photon excitation may thus pave the way toward coherent control of photoassociation. Ultimately, the success of such a scheme will depend on the details of the excited electronic states and transition dipole moments. We explore the possibility of two-photon femtosecond photoassociation for alkali and alkaline-earth metal dimers and present a detailed study for the example of calcium.
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Affiliation(s)
- Christiane P Koch
- Institut für Theoretische Physik, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany.
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Petrovic J, McCabe D, England D, Martay H, Friedman M, Dicks A, Dimova E, Walmsley I. A pump-probe study of the photoassociation of cold rubidium molecules. Faraday Discuss 2010; 142:403-13; discussion 429-61. [PMID: 20151556 DOI: 10.1039/b818494a] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The dynamics of the excited state during the photoassociation of cold molecules from cold rubidium atoms is studied in a series of pump-probe experiments. Dipole transitions similar to those of the atoms are observed in the molecular signal. While such behaviour is characteristic of the long-range molecules, the photoassociation of bound molecules is confirmed in additional experiments. The pump-probe signal observed on a 250 ps time scale did not, however, reveal wavepacket oscillations predicted by theory. This result is discussed using numerical simulations of photoassociation and a modification to the current experiments that could lead to the detection of wavepacket dynamics is suggested.
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Koch CP, Kosloff R. Pump-probe spectroscopy of two-body correlations in ultracold gases. PHYSICAL REVIEW LETTERS 2009; 103:260401. [PMID: 20366296 DOI: 10.1103/physrevlett.103.260401] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/20/2009] [Indexed: 05/29/2023]
Abstract
We suggest pump-probe spectroscopy to study pair correlations that determine the many-body dynamics in weakly interacting, dilute ultracold gases. A suitably chosen, short laser pulse depletes the pair density locally, creating a "hole" in the electronic ground state. The dynamics of this nonstationary pair density is monitored by a time-delayed probe pulse. The resulting transient signal allows us to spectrally decompose the hole and to map out the pair correlation function.
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Affiliation(s)
- Christiane P Koch
- Institut für Theoretische Physik, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany.
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Abstract
This review summarizes progress in coherent control as well as relevant recent achievements, highlighting, among several different schemes of coherent control, wave-packet interferometry (WPI). WPI is a fundamental and versatile scenario used to control a variety of quantum systems with a sequence of short laser pulses whose relative phase is finely adjusted to control the interference of electronic or nuclear wave packets (WPs). It is also useful in retrieving quantum information such as the amplitudes and phases of eigenfunctions superposed to generate a WP. Experimental and theoretical efforts to retrieve both the amplitude and phase information are recounted. This review also discusses information processing based on the eigenfunctions of atoms and molecules as one of the modern and future applications of coherent control. The ultrafast coherent control of ultracold atoms and molecules and the coherent control of complex systems are briefly discussed as future perspectives.
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Affiliation(s)
- Kenji Ohmori
- Institute for Molecular Science, National Institutes of Natural Sciences; The Graduate University for Advanced Studies (SOKENDAI); and CREST, Japan Science and Technology Agency, Myodaiji, Okazaki 444-8585, Japan
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Beser B, Sovkov VB, Bai J, Ahmed EH, Tsai CC, Xie F, Li L, Ivanov VS, Lyyra AM. Experimental investigation of the [sup 85]Rb[sub 2] a [sup 3]Σ[sub u][sup +] triplet ground state: Multiparameter Morse long range potential analysis. J Chem Phys 2009; 131:094505. [DOI: 10.1063/1.3194290] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Thorpe MJ, Adler F, Cossel KC, de Miranda MH, Ye J. Tomography of a supersonically cooled molecular jet using cavity-enhanced direct frequency comb spectroscopy. Chem Phys Lett 2009. [DOI: 10.1016/j.cplett.2008.11.064] [Citation(s) in RCA: 34] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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