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

Physical Review A

Spin-forbidden c 3Σ+(Ω=1)←X 1Σ+ transition in NaCs: Investigation of the Ω=1 state in hot and cold environments

A. Grochola, Pawel Kowalczyk, J. Szczepkowski, W. Jastrzȩbski, Amy Wakim, Patrick Zabawa, N. P. Bigelow

Published Jul 18, 2011• 21 citations
Publisher

Abstract

Comprehensive spectroscopic studies of hot and ultracold samples of NaCs molecules were combined to complete the investigation of the $(3)\ensuremath{\Omega}=1$ $\ensuremath{\leftarrow}$ $X$ ${}^{1}{\ensuremath{\Sigma}}^{+}$ transition for the NaCs molecule. Polarization labeling, photoassociation, and pulsed laser depletion spectroscopy were used to collect data on rovibrational levels of the $(3)\ensuremath{\Omega}=1$ state [here described as the $c$ ${}^{3}{\ensuremath{\Sigma}}^{+}$ state in Hund's case (a) notation]. The highest observed level was $v=72$ located $~$5 GHz below the atomic asymptote Na($3{ }^{2}{S}_{1/2}$) $+$ Cs($6{ }^{2}{P}_{3/2}$). Approximately 1400 levels were used to construct the potential energy curve of the $(3)\ensuremath{\Omega}=1$ state for the full range of interatomic distances.

DOI
10.1103/physreva.84.012507

Related papers

Theoretical evaluation of the radiative lifetimes of LiCs and NaCs in the A1Σ+ state

Nabil Mabrouk, Hamid Berriche

Calculations of the adiabatic potential energy curves and the transition dipole moments between the ground (A 1 Σ + ) and the first excited (A 1 Σ + ) states have been determined for the LiCs and NaCs molecules. The calculations are performed using an ab initio approach based on non-empirical pseudopotentials for Cs + , Li + and Na + cores, parameterized l -dependent polarization potentials and full configuration interaction calculations. The potential energy curves and the transition dipole moment are used to estimate the radiative lifetimes of the vibrational levels of the A + Σ + state using the Franck–Condon (FC) approximation and the approximate sum rule method. The radiative lifetimes associated with the A + Σ + state are presented here for the first time. These data can help experimentalists to optimize photoassociative formation of ultracold molecules and their longevity in a trap or in an optical lattice.

Russian Journal of Physical Chemistry A•Jul 14, 2017•7 citations

Formation of ultracold, highly polar X1Σ+NaCs molecules

Christopher Haimberger, Jan Kleinert, Patrick Zabawa +2 more

We present photoassociation spectroscopy of ultracold NaCs molecules formed in a dual-species magneto-optical trap. Excited-state molecules are formed in states correlating to the Na(3S 1/2 )+Cs(6P 3/2 ) asymptote. We assign the most prominent observed vibrational progression to the Ω=2 long range state based on a comparison with ab initio potentials. Molecules are secondarily excited before decaying to deeply bound levels of the electronic ground X 1 Σ + state where they are ionized and detected by time-of-flight mass spectroscopy.

New Journal of Physics•May 14, 2009•37 citations

Photoassociation studies of ultracold NaCs from the Cs 62P3/2 asymptote

Amy Wakim, Patrick Zabawa, N. P. Bigelow

A combination of pulsed depletion spectroscopy and photoassociation spectroscopy is utilized to assign photoassociation spectra of NaCs. These methods investigate the ab initio Ω = 2 potential energy curve and indicate a previously unknown avoided crossing between the (3)Ω = 1 and (4)Ω = 1 electronic states. We present rotational assignments of deeply bound singlet ground state molecules, an improved C(6) coefficient for the (4)Ω = 1 and assignments for all twenty-three photoassociation resonances detuned from the Cs 6(2)P(3/2) asymptote.

Physical Chemistry Chemical Physics•Jan 1, 2011•12 citations

Experimental Studies of Interacting Electronic States in NaCs

Carl Faust

This dissertation describes methods and results of spectroscopic studies of the NaCs molecule. NaCs is of particular interest in many labs where experimental studies of ultra-cold molecules are being conducted. Data obtained in the present work will also be useful as benchmarks for various theoretical calculations. Our goals in studying this molecule were to map out high lying electronic states and to understand how these states interact with one another. Sodium and cesium metal were heated in a heat-pipe oven to form a vapor of NaCs molecules. These molecules were excited using narrow band, continuous wave (cw), tunable lasers. We employed the optical-optical double resonance (OODR) technique to obtain Doppler-free spectra of transitions to rotational and vibrational levels of high lying electronic states. One state of particular interest was the 12(0+) electronic state. Rovibrational level energies corresponding to this state were measured and used to generate a potential energy curve using computer programs to implement both the Rydberg-Klein-Rees (RKR) method and the inverted perturbation approach (IPA). By observing fluorescence from the 12(0+) state resolved as a function of wavelength, we determined that this state interacts with the nearby 11(0+) electronic state, which was previously mapped out by Ashman et al. A two-stage coupling model was devised to describe the resolved fluorescence originating from these two interacting states. The electronic states interact via spin-orbit coupling, while the individual rovibrational levels interact via a second mechanism, likely nonadiabatic coupling. This two-stage coupling between the levels of these states causes quantum interference between fluorescence pathways associated with different components of the wavefunctions describing these levels. This interference results in more complicated resolved fluorescence spectra. The model was used to fit parameters describing these interactions so that the resolved fluorescence spectra could be reproduced. The NaCs 43 π electronic state was also studied in this work. Energies of many rovibrational levels belonging to the 43 π electronic state were measured. This state is interesting because it likely has a potential energy curve with a double minimum, which results in a different type of quantum interference, directly observed in resolved spectra. The state also very likely has interactions with the 11(0+) and 12(0+) states. Energies of many rovibrational levels lying above the energy of the barrier between the two minima were measured, and it appears that we also observed a few levels lying below the barrier. Since the laser wavelengths necessary to excite the lowest vibrational levels were not available, an experimental potential curve could not be produced. Therefore, rovibrational level energies and spectroscopic constants are tabulated.

•Aug 1, 2014•0 citations

Double-minimum 3 Σu+1 state in Rb2 : Spectroscopic study and possible applications for cold-physics experiments

A. Pashov, Pawel Kowalczyk, W. Jastrzȩbski

The double-minimum 3 $^{1}\mathrm{\ensuremath{\Sigma}}_{\mathrm{u}}^{\phantom{\rule{0.28em}{0ex}}\phantom{\rule{0.16em}{0ex}}+}$ state in $^{85}\mathrm{Rb}_{2}$ and $^{85}\mathrm{Rb}\phantom{\rule{0.16em}{0ex}}^{87}\mathrm{Rb}$ was investigated by analyzing rotationally resolved spectra of the 3 $^{1}\mathrm{\ensuremath{\Sigma}}_{\mathrm{u}}^{\phantom{\rule{0.28em}{0ex}}\phantom{\rule{0.16em}{0ex}}+}\ensuremath{\longleftarrow}\mathrm{X}^{1}\mathrm{\ensuremath{\Sigma}}_{\mathrm{g}}^{+}$ band system simplified by polarization labeling. A total of 3665 transitions to rovibrational levels located in the inner well and above the internal barrier were identified and an accurate potential energy curve of the state reaching up to $R\ensuremath{\approx}21$ \AA{} was constructed using the inverted perturbation approach, making this state the best characterized double-minimum state in alkali dimers. The possibility of formation of ultracold rubidium dimers in the absolute ground state by photoassociation into levels of the 3 $^{1}\mathrm{\ensuremath{\Sigma}}_{\mathrm{u}}^{\phantom{\rule{0.28em}{0ex}}\phantom{\rule{0.16em}{0ex}}+}$ state above the internal barrier followed by spontaneous or stimulated emission is discussed.

Physical Review A•Jul 9, 2019•13 citations

X Σ1+ and a Σ3+ states of the atom pair K+Cs studied by Fourier-transform spectroscopy

R. Ferber, I. P. Klincare, О. Nikolayeva +4 more

A comprehensive study of the $X\text{ }{^{1}\ensuremath{\Sigma}}^{+}$ and $a\text{ }{^{3}\ensuremath{\Sigma}}^{+}$ electronic states of the K and Cs atom pair is presented. Abundant spectroscopic data include 1937 transitions to the $a\text{ }{^{3}\ensuremath{\Sigma}}^{+}$ state and $13\text{ }724$ transitions to the $X\text{ }{^{1}\ensuremath{\Sigma}}^{+}$ state for ${^{39}\text{K}\text{ }}^{133}\text{Cs}$ which were obtained by Fourier-transform spectroscopy. From these data potential energy curves were constructed simultaneously for both states $X\text{ }{^{1}\ensuremath{\Sigma}}^{+}$ and $a\text{ }{^{3}\ensuremath{\Sigma}}^{+}$ which are coupled by the hyperfine interaction. This allows us to accurately model the potential close to $\text{K}(4s)+\text{Cs}(6s)$ atom-pair asymptote which is required to simulate cold collision processes. Dissociation energies of the $X\text{ }{^{1}\ensuremath{\Sigma}}^{+}$ state as ${D}_{e}^{X}=4069.208(40)\text{ }{\text{cm}}^{\ensuremath{-}1}$ and of the $a\text{ }{^{3}\ensuremath{\Sigma}}^{+}$ state as ${D}_{e}^{a}=267.141(20)\text{ }{\text{cm}}^{\ensuremath{-}1}$ were determined. Scattering lengths are predicted for different KCs isotopologs and Feshbach resonances were calculated for magnetic fields up to 1000 G.

Physical Review A•Dec 1, 2009•43 citations
Comprehensive spectroscopic studies of hot and ultracold samples of NaCs molecules were combined to complete the investigation of the (3)\ensuremathΩ=1(3)\ensuremath{\Omega}=1(3)\ensuremathΩ=1 \ensuremath←\ensuremath{\leftarrow}\ensuremath← XXX 1\ensuremathΣ+{}^{1}{\ensuremath{\Sigma}}^{+}1\ensuremathΣ+ transition for the NaCs molecule. Polarization labeling, photoassociation, and pulsed laser depletion spectroscopy were used to collect data on rovibrational levels of the (3)\ensuremathΩ=1(3)\ensuremath{\Omega}=1(3)\ensuremathΩ=1 state [here described as the ccc 3\ensuremathΣ+{}^{3}{\ensuremath{\Sigma}}^{+}3\ensuremathΣ+ state in Hund's case (a) notation]. The highest observed level was v=72v=72v=72 located  ~ 5 GHz below the atomic asymptote Na(32S1/23{ }^{2}{S}_{1/2}32S1/2​) +++ Cs(62P3/26{ }^{2}{P}_{3/2}62P3/2​). Approximately 1400 levels were used to construct the potential energy curve of the (3)\ensuremathΩ=1(3)\ensuremath{\Omega}=1(3)\ensuremathΩ=1 state for the full range of interatomic distances.
Calculations of the adiabatic potential energy curves and the transition dipole moments between the ground (A 1 Σ + ) and the first excited (A 1 Σ + ) states have been determined for the LiCs and NaCs molecules. The calculations are performed using an ab initio approach based on non-empirical pseudopotentials for Cs + , Li + and Na + cores, parameterized l -dependent polarization potentials and full configuration interaction calculations. The potential energy curves and the transition dipole moment are used to estimate the radiative lifetimes of the vibrational levels of the A + Σ + state using the Franck–Condon (FC) approximation and the approximate sum rule method. The radiative lifetimes associated with the A + Σ + state are presented here for the first time. These data can help experimentalists to optimize photoassociative formation of ultracold molecules and their longevity in a trap or in an optical lattice.
We present photoassociation spectroscopy of ultracold NaCs molecules formed in a dual-species magneto-optical trap. Excited-state molecules are formed in states correlating to the Na(3S 1/2 )+Cs(6P 3/2 ) asymptote. We assign the most prominent observed vibrational progression to the Ω=2 long range state based on a comparison with ab initio potentials. Molecules are secondarily excited before decaying to deeply bound levels of the electronic ground X 1 Σ + state where they are ionized and detected by time-of-flight mass spectroscopy.
A combination of pulsed depletion spectroscopy and photoassociation spectroscopy is utilized to assign photoassociation spectra of NaCs. These methods investigate the ab initio Ω = 2 potential energy curve and indicate a previously unknown avoided crossing between the (3)Ω = 1 and (4)Ω = 1 electronic states. We present rotational assignments of deeply bound singlet ground state molecules, an improved C(6) coefficient for the (4)Ω = 1 and assignments for all twenty-three photoassociation resonances detuned from the Cs 6(2)P(3/2) asymptote.
This dissertation describes methods and results of spectroscopic studies of the NaCs molecule. NaCs is of particular interest in many labs where experimental studies of ultra-cold molecules are being conducted. Data obtained in the present work will also be useful as benchmarks for various theoretical calculations. Our goals in studying this molecule were to map out high lying electronic states and to understand how these states interact with one another. Sodium and cesium metal were heated in a heat-pipe oven to form a vapor of NaCs molecules. These molecules were excited using narrow band, continuous wave (cw), tunable lasers. We employed the optical-optical double resonance (OODR) technique to obtain Doppler-free spectra of transitions to rotational and vibrational levels of high lying electronic states. One state of particular interest was the 12(0+) electronic state. Rovibrational level energies corresponding to this state were measured and used to generate a potential energy curve using computer programs to implement both the Rydberg-Klein-Rees (RKR) method and the inverted perturbation approach (IPA). By observing fluorescence from the 12(0+) state resolved as a function of wavelength, we determined that this state interacts with the nearby 11(0+) electronic state, which was previously mapped out by Ashman et al. A two-stage coupling model was devised to describe the resolved fluorescence originating from these two interacting states. The electronic states interact via spin-orbit coupling, while the individual rovibrational levels interact via a second mechanism, likely nonadiabatic coupling. This two-stage coupling between the levels of these states causes quantum interference between fluorescence pathways associated with different components of the wavefunctions describing these levels. This interference results in more complicated resolved fluorescence spectra. The model was used to fit parameters describing these interactions so that the resolved fluorescence spectra could be reproduced. The NaCs 43 π electronic state was also studied in this work. Energies of many rovibrational levels belonging to the 43 π electronic state were measured. This state is interesting because it likely has a potential energy curve with a double minimum, which results in a different type of quantum interference, directly observed in resolved spectra. The state also very likely has interactions with the 11(0+) and 12(0+) states. Energies of many rovibrational levels lying above the energy of the barrier between the two minima were measured, and it appears that we also observed a few levels lying below the barrier. Since the laser wavelengths necessary to excite the lowest vibrational levels were not available, an experimental potential curve could not be produced. Therefore, rovibrational level energies and spectroscopic constants are tabulated.
The double-minimum 3 $^{1}\mathrm{\ensuremath{\Sigma}}_{\mathrm{u}}^{\phantom{\rule{0.28em}{0ex}}\phantom{\rule{0.16em}{0ex}}+}$ state in 85Rb2^{85}\mathrm{Rb}_{2}85Rb2​ and 85Rb87Rb^{85}\mathrm{Rb}\phantom{\rule{0.16em}{0ex}}^{87}\mathrm{Rb}85Rb87Rb was investigated by analyzing rotationally resolved spectra of the 3 $^{1}\mathrm{\ensuremath{\Sigma}}_{\mathrm{u}}^{\phantom{\rule{0.28em}{0ex}}\phantom{\rule{0.16em}{0ex}}+}\ensuremath{\longleftarrow}\mathrm{X}^{1}\mathrm{\ensuremath{\Sigma}}_{\mathrm{g}}^{+}$ band system simplified by polarization labeling. A total of 3665 transitions to rovibrational levels located in the inner well and above the internal barrier were identified and an accurate potential energy curve of the state reaching up to $R\ensuremath{\approx}21$ \AA{} was constructed using the inverted perturbation approach, making this state the best characterized double-minimum state in alkali dimers. The possibility of formation of ultracold rubidium dimers in the absolute ground state by photoassociation into levels of the 3 $^{1}\mathrm{\ensuremath{\Sigma}}_{\mathrm{u}}^{\phantom{\rule{0.28em}{0ex}}\phantom{\rule{0.16em}{0ex}}+}$ state above the internal barrier followed by spontaneous or stimulated emission is discussed.
A comprehensive study of the $X\text{ }{^{1}\ensuremath{\Sigma}}^{+}$ and $a\text{ }{^{3}\ensuremath{\Sigma}}^{+}$ electronic states of the K and Cs atom pair is presented. Abundant spectroscopic data include 1937 transitions to the $a\text{ }{^{3}\ensuremath{\Sigma}}^{+}$ state and 13 72413\text{ }72413 724 transitions to the $X\text{ }{^{1}\ensuremath{\Sigma}}^{+}$ state for 39K 133Cs{^{39}\text{K}\text{ }}^{133}\text{Cs}39K 133Cs which were obtained by Fourier-transform spectroscopy. From these data potential energy curves were constructed simultaneously for both states $X\text{ }{^{1}\ensuremath{\Sigma}}^{+}$ and $a\text{ }{^{3}\ensuremath{\Sigma}}^{+}$ which are coupled by the hyperfine interaction. This allows us to accurately model the potential close to K(4s)+Cs(6s)\text{K}(4s)+\text{Cs}(6s)K(4s)+Cs(6s) atom-pair asymptote which is required to simulate cold collision processes. Dissociation energies of the $X\text{ }{^{1}\ensuremath{\Sigma}}^{+}$ state as ${D}_{e}^{X}=4069.208(40)\text{ }{\text{cm}}^{\ensuremath{-}1}$ and of the $a\text{ }{^{3}\ensuremath{\Sigma}}^{+}$ state as ${D}_{e}^{a}=267.141(20)\text{ }{\text{cm}}^{\ensuremath{-}1}$ were determined. Scattering lengths are predicted for different KCs isotopologs and Feshbach resonances were calculated for magnetic fields up to 1000 G.