Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:physics/0407109 · Physical Review A

Photoassociation spectroscopy of cold alkaline-earth-metal atoms near the intercombination line

R. Ciuryło, Eite Tiesinga, Svetlana Kotochigova, Paul S. Julienne

Published Dec 13, 2004• 57 citations
arXivHTMLPDF

Abstract

The properties of photoassociation (PA) spectra near the intercombination line (the weak transition between and states) of group II atoms are theoretically investigated. As an example, we have carried out a calculation for calcium atoms colliding at ultralow temperatures of , , and . Unlike in most current photoassociation spectroscopy, the Doppler effect can significantly affect the shape of the investigated lines. Spectra are obtained using and short-range potentials and long-range van der Waals and resonance dipole potentials. The similar van der Waals coefficients of ground and excited states cause the PA to differ greatly from those of strong, allowed transitions with resonant dipole interactions. The density of spectral lines is lower, the Condon points are at relatively short range, the reflection approximation for the Franck-Condon factors is not applicable, and the spontaneous decay to bound ground-state molecules is efficient. Finally, the possibility of efficient production of cold molecules is discussed.

DOI
10.1103/physreva.70.062710

Related papers

Photoassociation Spectroscopy of Cold Alkaline Earth Atoms near the Intercombination Line

Eite Tiesinga, R. Ciuryło, Svetlana Kotochigova +1 more

The properties of photoassociation spectra near the intercombination line of group II atoms are theoretically investigated. Unlike in most current photoassociation spectroscopy the Doppler effect can significantly affect the shape of the investigated lines

Quantum Electronics and Laser Science Conference•Dec 10, 2005•2 citations

Photoassociation spectroscopy

J. Weiner

Introduction If, while approaching on an unbound ground-state potential, two atoms absorb a photon and couple to an excited bound molecular state, they are said to undergo photoassociation. Figure 5.1 illustrates the process. At long range electrostatic dispersion forces give rise to the ground-state molecular potential varying as C 6 / R 6 . If the two atoms are homonuclear, then a resonant dipole–dipole interaction sets up ± C 3 / R 3 excited-state repulsive and attractive potentials. Figure 5.2 shows the actual long-range excited potential curves for the sodium dimer, originating from the 2 S ½ + 2 P 3/2 and 2 S ½ + 2 P ½ separated atom states. For cold and ultracold photoassociation processes the long-range attractive potentials play the key role; the repulsive potentials figure importantly in optical shielding and suppression, the subject of Chapter 6. In the presence of a photon with frequency ω p the colliding pair with kinetic energy k B T couples from the ground-state to the attractive molecular state in a free–bound transition near the Condon point R C , the point at which the difference potential just matches ћω p . Scanning the probe laser ω p excites population of vibration–rotation states in the excited bound potential and generates a free–bound spectrum. This general class of measurements is called photoassociative spectroscopy (PAS) and can be observed in several different ways. The observation may consist of bound-state decay by spontaneous emission, most probably as the nuclei move slowly around the outer turning point, to some distribution of continuum states on the ground potential controlled by bound–free nuclear Franck–Condon overlap factors.

Cambridge University Press eBooks•Dec 4, 2003•0 citations

Influence of ground-state scattering properties on photoassociation spectra near the intercombination line of bosonic ytterbium

Mateusz Borkowski, R. Ciuryło, Paul S. Julienne +5 more

We study theoretically the properties of photoassociation spectra near the 1S0‐3P1 inter‐combination line of bosonic ytterbium. We construct a mass scaled model of the excited state interaction potential that well describes bound state energies obtained in a previous photoassociation experiment. We then use it to calculate theoretical photoassociation spectra in a range of ultracold temperatures using semianalytical theory developed by Bohn and Julienne.Photoassociation spectra not only give us the energies of excited bound states, but also provide information about the behavior of the ground state wavefunction. In fact, it can be shown that within the so‐called reflection approximation the line intensity is proportional to the ground state wavefunction at the transition’s Condon point. We show that in the case of ytterbium, the rotational structure of the photoassociation spectra depends heavily on the behavior of the ground‐state wavefunction. The change of the scattering length from one isotope to another and the resulting occurence of shape resonances in higher partial waves determines the appearance and disapperance of rotational components, especially in the deeper lying states, whose respective Condon points lie near the ground state centrifugal barrier. Thus, photoassociation spectra differ qualitatively between isotopes.

AIP conference proceedings•Jan 1, 2010•0 citations

Line shapes of optical Feshbach resonances near the intercombination transition of bosonic ytterbium

Mateusz Borkowski, R. Ciuryło, Paul S. Julienne +3 more

The properties of bosonic ytterbium photoassociation spectra near the intercombination transition ${^{1}S}_{0}\ensuremath{-}{^{3}P}_{1}$ are studied theoretically at ultralow temperatures. We demonstrate how the shapes and intensities of rotational components of optical Feshbach resonances are affected by mass tuning of the scattering properties of the two colliding ground-state atoms. Particular attention is given to the relationship between the magnitude of the scattering length and the occurrence of shape resonances in higher partial waves of the van der Waals system. We develop a mass-scaled model of the excited-state potential that represents the experimental data for different isotopes. The shape of the rotational photoassociation spectrum for various bosonic Yb isotopes can be qualitatively different.

arXiv:0905.0958•Physical Review A•Jul 29, 2009•38 citations

Photoassociative Spectroscopy and Formation of Cold Molecules

P. Pillet, Cyril Drag, B. Laburthe-Tolra +7 more

In the molecular photoassociation process, two free cold atoms absorb one photon by a resonant way, to create an excited molecule in a well defined ro-vibrational state. The photoassociative spectroscopy of alkaline dimers yields accurate determinations for the long-range parts of molecular potential curves correlated to the first s + p asymptote. In contrast to atoms, laser cooling of molecules is very difficult because of the lack of a closed two-level scheme for recycling the population. The molecular photoassociation of cold atoms opens also a promising alternative for the formation of cold ground state molecules. Photoassociation of cold cesium atoms has permitted the first observation of translationally cold ground state molecules. The case of the cesium atom is very favorable because the 0 g - and 1 u purely long-range states below the dissociation limit 6s 1/2 +6p 3/2 present Condon points at intermediate distances. Such configurations offer rather efficient channels for the creation of singlet or triplet ground state Cs 2 molecules after spontaneous decay.

Physica Scripta•Jan 1, 2000•0 citations

Photoassociation of cold calcium atoms through the AΣu+1(1D1+1S1),cΠu3(1P3+1S1) , and aΣu+3(1P3+1S1) states: Anab initiononadiabatic treatment

Béatrice Bussery‐Honvault, Jean–Michel Launay, Robert Moszyński

A nonadiabatic theory of photoassociation spectra and spontaneous emission processes in diatomic molecules is presented. This theory was applied in nearly exact nonadiabatic calculations of the photoassociation intensities to the $A\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{u}^{+}(1\phantom{\rule{0.2em}{0ex}}^{1}S+1\phantom{\rule{0.2em}{0ex}}^{1}D),\phantom{\rule{0.2em}{0ex}}c\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Pi}_{u}(1\phantom{\rule{0.2em}{0ex}}^{3}P+1\phantom{\rule{0.2em}{0ex}}^{1}S)$, and $a\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Sigma}_{u}^{+}(1\phantom{\rule{0.2em}{0ex}}^{3}P+1\phantom{\rule{0.2em}{0ex}}^{1}S)$ manifold of states for two colliding calcium atoms at ultralow temperatures and of the spontaneous emission coefficients to the ground $X\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{g}^{+}$ electronic state. The calculations were based on most recent state-of-the-art ab initio results for the potential energy curves for the ground $X\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{g}^{+}$ and excited $A\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{u}^{+}(1\phantom{\rule{0.2em}{0ex}}^{1}S+1\phantom{\rule{0.2em}{0ex}}^{1}D),\phantom{\rule{0.2em}{0ex}}c\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Pi}_{u}(1\phantom{\rule{0.2em}{0ex}}^{3}P+1\phantom{\rule{0.2em}{0ex}}^{1}S)$, and $a\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Sigma}_{u}^{+}(1\phantom{\rule{0.2em}{0ex}}^{3}P+1\phantom{\rule{0.2em}{0ex}}^{1}S)$ states, for the spin-orbit and nonadiabatic coupling matrix elements, and for the transition dipole moment governing the $A\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{u}^{+}\ensuremath{\leftarrow}X\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{g}^{+}$ transitions. The computed photoassociation spectrum shows several transitions in the detuning frequency range up to $\ensuremath{-}3000\phantom{\rule{0.3em}{0ex}}\mathrm{GHz}$. This frequency range corresponds to vibrational levels of the ${J}^{\ensuremath{'}}=1$ state of ${\mathrm{Ca}}_{2}$ that can mostly be assigned to the $c\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Pi}_{u}$ state. The two by far most intense lines at a detuning frequency around $\ensuremath{-}800\phantom{\rule{0.3em}{0ex}}\mathrm{GHz}$ correspond to the last two bound rovibrational levels lying below the $1\phantom{\rule{0.2em}{0ex}}^{3}P+1\phantom{\rule{0.2em}{0ex}}^{1}S$ asymptote which are heavily mixed and can partly be assigned to the $A\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{u}^{+}$ state. The corresponding lifetimes and Franck-Condon factors suggest that these levels can be detected experimentally and should show a relatively efficient spontaneous emission to the ground state. An analysis of the branching ratios describing the probability of the decay from these two levels to bound vibrational levels of the ground electronic state shows that the decay will end in the levels with the vibrational quantum number between 10 and 16 with a total probability well over 90%.

Physical Review A•Jul 1, 2005•16 citations
The properties of photoassociation (PA) spectra near the intercombination line (the weak transition between and states) of group II atoms are theoretically investigated. As an example, we have carried out a calculation for calcium atoms colliding at ultralow temperatures of , , and . Unlike in most current photoassociation spectroscopy, the Doppler effect can significantly affect the shape of the investigated lines. Spectra are obtained using and short-range potentials and long-range van der Waals and resonance dipole potentials. The similar van der Waals coefficients of ground and excited states cause the PA to differ greatly from those of strong, allowed transitions with resonant dipole interactions. The density of spectral lines is lower, the Condon points are at relatively short range, the reflection approximation for the Franck-Condon factors is not applicable, and the spontaneous decay to bound ground-state molecules is efficient. Finally, the possibility of efficient production of cold molecules is discussed.
Introduction If, while approaching on an unbound ground-state potential, two atoms absorb a photon and couple to an excited bound molecular state, they are said to undergo photoassociation. Figure 5.1 illustrates the process. At long range electrostatic dispersion forces give rise to the ground-state molecular potential varying as C 6 / R 6 . If the two atoms are homonuclear, then a resonant dipole–dipole interaction sets up ± C 3 / R 3 excited-state repulsive and attractive potentials. Figure 5.2 shows the actual long-range excited potential curves for the sodium dimer, originating from the 2 S ½ + 2 P 3/2 and 2 S ½ + 2 P ½ separated atom states. For cold and ultracold photoassociation processes the long-range attractive potentials play the key role; the repulsive potentials figure importantly in optical shielding and suppression, the subject of Chapter 6. In the presence of a photon with frequency ω p the colliding pair with kinetic energy k B T couples from the ground-state to the attractive molecular state in a free–bound transition near the Condon point R C , the point at which the difference potential just matches ћω p . Scanning the probe laser ω p excites population of vibration–rotation states in the excited bound potential and generates a free–bound spectrum. This general class of measurements is called photoassociative spectroscopy (PAS) and can be observed in several different ways. The observation may consist of bound-state decay by spontaneous emission, most probably as the nuclei move slowly around the outer turning point, to some distribution of continuum states on the ground potential controlled by bound–free nuclear Franck–Condon overlap factors.
We study theoretically the properties of photoassociation spectra near the 1S0‐3P1 inter‐combination line of bosonic ytterbium. We construct a mass scaled model of the excited state interaction potential that well describes bound state energies obtained in a previous photoassociation experiment. We then use it to calculate theoretical photoassociation spectra in a range of ultracold temperatures using semianalytical theory developed by Bohn and Julienne.Photoassociation spectra not only give us the energies of excited bound states, but also provide information about the behavior of the ground state wavefunction. In fact, it can be shown that within the so‐called reflection approximation the line intensity is proportional to the ground state wavefunction at the transition’s Condon point. We show that in the case of ytterbium, the rotational structure of the photoassociation spectra depends heavily on the behavior of the ground‐state wavefunction. The change of the scattering length from one isotope to another and the resulting occurence of shape resonances in higher partial waves determines the appearance and disapperance of rotational components, especially in the deeper lying states, whose respective Condon points lie near the ground state centrifugal barrier. Thus, photoassociation spectra differ qualitatively between isotopes.
The properties of bosonic ytterbium photoassociation spectra near the intercombination transition ${^{1}S}_{0}\ensuremath{-}{^{3}P}_{1}$ are studied theoretically at ultralow temperatures. We demonstrate how the shapes and intensities of rotational components of optical Feshbach resonances are affected by mass tuning of the scattering properties of the two colliding ground-state atoms. Particular attention is given to the relationship between the magnitude of the scattering length and the occurrence of shape resonances in higher partial waves of the van der Waals system. We develop a mass-scaled model of the excited-state potential that represents the experimental data for different isotopes. The shape of the rotational photoassociation spectrum for various bosonic Yb isotopes can be qualitatively different.
In the molecular photoassociation process, two free cold atoms absorb one photon by a resonant way, to create an excited molecule in a well defined ro-vibrational state. The photoassociative spectroscopy of alkaline dimers yields accurate determinations for the long-range parts of molecular potential curves correlated to the first s + p asymptote. In contrast to atoms, laser cooling of molecules is very difficult because of the lack of a closed two-level scheme for recycling the population. The molecular photoassociation of cold atoms opens also a promising alternative for the formation of cold ground state molecules. Photoassociation of cold cesium atoms has permitted the first observation of translationally cold ground state molecules. The case of the cesium atom is very favorable because the 0 g - and 1 u purely long-range states below the dissociation limit 6s 1/2 +6p 3/2 present Condon points at intermediate distances. Such configurations offer rather efficient channels for the creation of singlet or triplet ground state Cs 2 molecules after spontaneous decay.
A nonadiabatic theory of photoassociation spectra and spontaneous emission processes in diatomic molecules is presented. This theory was applied in nearly exact nonadiabatic calculations of the photoassociation intensities to the $A\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{u}^{+}(1\phantom{\rule{0.2em}{0ex}}^{1}S+1\phantom{\rule{0.2em}{0ex}}^{1}D),\phantom{\rule{0.2em}{0ex}}c\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Pi}_{u}(1\phantom{\rule{0.2em}{0ex}}^{3}P+1\phantom{\rule{0.2em}{0ex}}^{1}S)$, and $a\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Sigma}_{u}^{+}(1\phantom{\rule{0.2em}{0ex}}^{3}P+1\phantom{\rule{0.2em}{0ex}}^{1}S)$ manifold of states for two colliding calcium atoms at ultralow temperatures and of the spontaneous emission coefficients to the ground $X\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{g}^{+}$ electronic state. The calculations were based on most recent state-of-the-art ab initio results for the potential energy curves for the ground $X\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{g}^{+}$ and excited $A\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{u}^{+}(1\phantom{\rule{0.2em}{0ex}}^{1}S+1\phantom{\rule{0.2em}{0ex}}^{1}D),\phantom{\rule{0.2em}{0ex}}c\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Pi}_{u}(1\phantom{\rule{0.2em}{0ex}}^{3}P+1\phantom{\rule{0.2em}{0ex}}^{1}S)$, and $a\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Sigma}_{u}^{+}(1\phantom{\rule{0.2em}{0ex}}^{3}P+1\phantom{\rule{0.2em}{0ex}}^{1}S)$ states, for the spin-orbit and nonadiabatic coupling matrix elements, and for the transition dipole moment governing the $A\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{u}^{+}\ensuremath{\leftarrow}X\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{g}^{+}$ transitions. The computed photoassociation spectrum shows several transitions in the detuning frequency range up to $\ensuremath{-}3000\phantom{\rule{0.3em}{0ex}}\mathrm{GHz}$. This frequency range corresponds to vibrational levels of the ${J}^{\ensuremath{'}}=1$ state of Ca2{\mathrm{Ca}}_{2}Ca2​ that can mostly be assigned to the $c\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Pi}_{u}$ state. The two by far most intense lines at a detuning frequency around $\ensuremath{-}800\phantom{\rule{0.3em}{0ex}}\mathrm{GHz}$ correspond to the last two bound rovibrational levels lying below the 13P+11S1\phantom{\rule{0.2em}{0ex}}^{3}P+1\phantom{\rule{0.2em}{0ex}}^{1}S13P+11S asymptote which are heavily mixed and can partly be assigned to the $A\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{u}^{+}$ state. The corresponding lifetimes and Franck-Condon factors suggest that these levels can be detected experimentally and should show a relatively efficient spontaneous emission to the ground state. An analysis of the branching ratios describing the probability of the decay from these two levels to bound vibrational levels of the ground electronic state shows that the decay will end in the levels with the vibrational quantum number between 10 and 16 with a total probability well over 90%.