Physical Review A

Observation of the last bound levels near the Na2 ground-state asymptote

M. Elbs, H. Knöckel, T. Laue, Christian Samuelis, E. Tiemann

Published May 1, 1999• 23 citations

Abstract

A multistep laser excitation scheme was used to access the last, least bound levels close to the lowest asymptote $3s+3s$ with the molecular states $X{}^{1}{\ensuremath{\Sigma}}_{g}^{+}$ and $a{}^{3}{\ensuremath{\Sigma}}_{u}^{+}$ of ${\mathrm{Na}}_{2}$. All singlet levels within the last $10 {\mathrm{cm}}^{\ensuremath{-}1}$, and some triplet levels with sufficient singlet admixture, were observed. The level energies were determined with uncertainties of less than 22 MHz with respect to the dissociation limit. The hyperfine structure was resolved, and asymmetric line shapes due to predissociation by tunneling through the rotational barrier or electronic state coupling were recorded for levels above the dissociation limit.

DOI: 10.1103/physreva.59.3665

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Physical Review A

Observation of the last bound levels near the Na2 ground-state asymptote

M. Elbs, H. Knöckel, T. Laue, Christian Samuelis, E. Tiemann

Published May 1, 1999• 23 citations

Publisher

Abstract

A multistep laser excitation scheme was used to access the last, least bound levels close to the lowest asymptote

3s+3s

with the molecular states

X{}^{1}{\ensuremath{\Sigma}}_{g}^{+}

and

a{}^{3}{\ensuremath{\Sigma}}_{u}^{+}

{\mathrm{Na}}_{2}

. All singlet levels within the last

10 {\mathrm{cm}}^{\ensuremath{-}1}

, and some triplet levels with sufficient singlet admixture, were observed. The level energies were determined with uncertainties of less than 22 MHz with respect to the dissociation limit. The hyperfine structure was resolved, and asymmetric line shapes due to predissociation by tunneling through the rotational barrier or electronic state coupling were recorded for levels above the dissociation limit.

DOI: 10.1103/physreva.59.3665

Related papers

Molecular beam study of the a3Σ+ state of NaK up to the dissociation limit

Ivo I. Temelkov, H. Knöckel, A. Pashov +1 more

We provide spectroscopic data for the $a{\phantom{\rule{0.16em}{0ex}}}^{3}{\ensuremath{\Sigma}}^{+}$ state of the $^{23}\mathrm{Na}^{39}\mathrm{K}$ molecule. The experiment is done in an ultrasonic beam apparatus, starting from the ground state $X{\phantom{\rule{0.16em}{0ex}}}^{1}{\ensuremath{\Sigma}}^{+}$ and driving the population to the $a{\phantom{\rule{0.16em}{0ex}}}^{3}{\ensuremath{\Sigma}}^{+}$ state, using a $\ensuremath{\Lambda}$ scheme with fixed pump and scanning dump laser. The signals are observed as dips of the total fluorescence. The intermediate level is chosen to be strongly perturbed by the $B{\phantom{\rule{0.16em}{0ex}}}^{1}\ensuremath{\Pi}/c{\phantom{\rule{0.16em}{0ex}}}^{3}{\ensuremath{\Sigma}}^{+}$ states mixing to overcome the singlet-triplet transfer prohibition. We observed highly resolved hyperfine spectra of various rovibrational levels of the $a{\phantom{\rule{0.16em}{0ex}}}^{3}{\ensuremath{\Sigma}}^{+}$ state from ${v}_{a}=2$ up to the highest vibrational levels for rotational quantum numbers ${N}_{a}=4,6,8$ . By the typical experimental linewidth of 17 MHz, the vibrational dependence of the hyperfine splitting is clearly revealed for NaK. The absolute frequency measurements of the vibrational levels are used for improvement of the $a{\phantom{\rule{0.16em}{0ex}}}^{3}{\ensuremath{\Sigma}}^{+}$ potential curve and of the derived scattering length of all natural isotope combinations. Applying the $\ensuremath{\Lambda}$ scheme in the reverse direction can provide a pathway for efficient transfer of ultracold $^{23}\mathrm{Na}^{39}\mathrm{K}$ molecules from the $\text{Na}(3s)+\text{K}(4s)$ asymptote to the lowest levels of the ground state. We show spectra that couple the absolute ground state ${v}_{X}=0,J=0$ with an appropriate intermediate state for direct realization of the reverse path. The refined theoretical model of the coupled excited states of the $\text{Na}(3s)+\text{K}(4p)$ asymptote allows predictions of efficient paths for $^{23}\mathrm{Na}^{40}\mathrm{K}$ ; one example is calculated.We provide spectroscopic data for the $a{\phantom{\rule{0.16em}{0ex}}}^{3}{\ensuremath{\Sigma}}^{+}$ state of the $^{23}\mathrm{Na}^{39}\mathrm{K}$ molecule. The experiment is done in an ultrasonic beam apparatus, starting from the ground state $X{\phantom{\rule{0.16em}{0ex}}}^{1}{\ensuremath{\Sigma}}^{+}$ and driving the population to the $a{\phantom{\rule{0.16em}{0ex}}}^{3}{\ensuremath{\Sigma}}^{+}$ state, using a $\ensuremath{\Lambda}$ scheme with fixed pump and scanning dump laser. The signals are observed as dips of the total fluorescence. The intermediate level is chosen to be strongly perturbed by the $B{\phantom{\rule{0.16em}{0ex}}}^{1}\ensuremath{\Pi}/c{\phantom{\rule{0.16em}{0ex}}}^{3}{\ensuremath{\Sigma}}^{+}$ states mixing to overcome the singlet-triplet transfer prohibition. We observed highly resolved hyperfine spectra of various rovibrational levels of the $a{\phantom{\rule{0.16em}{0ex}}}^{3}{\ensuremath{\Sigma}}^{+}$ state from ${v}_{a}=2$ up to the highest vibrational levels for rotational quantum numbers ${N}_{a}=4,6,8$. By the typical experimental linewidth of 17 MHz, the vibrational dependence of the hyperfine splitting is clearly revealed for NaK. The absolute frequency measurements of the vibrational levels are used for improvement of the $a{\phantom{\rule{0.16em}{0ex}}}^{3}{\ensuremath{\Sigma}}^{+}$ potential curve and of the derived scattering length of all natural isotope combinations. Applying the $\ensuremath{\Lambda}$ scheme in the reverse direction can provide a pathway for efficient transfer of ultracold $^{23}\mathrm{Na}^{39}\mathrm{K}$ molecules from the $\text{Na}(3s)+\text{K}(4s)$ asymptote to the lowest levels of the ground state. We show spectra that couple the absolute ground state ${v}_{X}=0,J=0$ with an appropriate intermediate state for direct realization of the reverse path. The refined theoretical model of the coupled excited states of the $\text{Na}(3s)+\text{K}(4p)$ asymptote allows predictions of efficient paths for $^{23}\mathrm{Na}^{40}\mathrm{K}$; one example is calculated.

Physical Review AMar 23, 201517 citations

Cold atomic collisions studied by molecular spectroscopy

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Hyperfine and vibrational structure of weakly bound levels of the lowest 1g state of molecular 87 Rb 2

Chin‐Chun Tsai, T. H. Bergeman, Eite Tiesinga +2 more

Photoassociation resonances in the ${}^{87}$ Rb ${}_{2}$ ${1}_{g}$ state dissociating to $5{\phantom{\rule{0.16em}{0ex}}}^{2}S+5{}^{2}{P}_{1/2}$ were produced by the excitation of colliding ${}^{87}$ Rb atoms in a far-off resonance trap. Levels down to 31 cm${}^{\ensuremath{-}1}$ below the dissociation limit were measured with resonance linewidths of 15 to 20 MHz, and have been located to a one-sigma combined systematic and statistical uncertainty of 50 MHz relative to the $5{\phantom{\rule{0.16em}{0ex}}}^{2}S+5{}^{2}{P}_{1/2}$ limit. Electron and nuclear spins were fixed to a space-fixed axis by circularly polarized optical pumping, so that only states with total nuclear spin $I=3$ were excited, thereby greatly simplifying the spectrum. The analysis of the data yielded hyperfine coupling parameters $A(v)$ , vibrational $G(v)$ , and rotational $B(v)$ parameters. The $G(v)$ parameters could be fit to an rms accuracy of about 0.01 cm${}^{\ensuremath{-}1}$ to a potential constructed from current ${C}_{3}$ and ${C}_{6}$ long-range dispersion parameters plus an ab initio potential that was adjusted in depth and with quadratic terms in the internuclear distance added to the inner wall.Photoassociation resonances in the ${}^{87}$Rb${}_{2}$ ${1}_{g}$ state dissociating to $5{\phantom{\rule{0.16em}{0ex}}}^{2}S+5{}^{2}{P}_{1/2}$ were produced by the excitation of colliding ${}^{87}$Rb atoms in a far-off resonance trap. Levels down to 31 cm${}^{\ensuremath{-}1}$ below the dissociation limit were measured with resonance linewidths of 15 to 20 MHz, and have been located to a one-sigma combined systematic and statistical uncertainty of 50 MHz relative to the $5{\phantom{\rule{0.16em}{0ex}}}^{2}S+5{}^{2}{P}_{1/2}$ limit. Electron and nuclear spins were fixed to a space-fixed axis by circularly polarized optical pumping, so that only states with total nuclear spin $I=3$ were excited, thereby greatly simplifying the spectrum. The analysis of the data yielded hyperfine coupling parameters $A(v)$, vibrational $G(v)$, and rotational $B(v)$ parameters. The $G(v)$ parameters could be fit to an rms accuracy of about 0.01 cm${}^{\ensuremath{-}1}$ to a potential constructed from current ${C}_{3}$ and ${C}_{6}$ long-range dispersion parameters plus an ab initio potential that was adjusted in depth and with quadratic terms in the internuclear distance added to the inner wall.

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Simple determination of Na

A. Crubellier, Olivier Dulieu, Françoise Masnou-Seeuws +3 more

\n A simple model is developed to determine a scattering length from the\nexperimental values of the energy of the last, least bound, vibrational\nlevels of the ground state, either $^1\\Sigma _g^{+}$ or $^3\\Sigma _u^{+}$ ,\nof an alkali dimer. It is based on an extrapolation of the positions of the\nfew outermost nodes of the bound vibrational wave functions towards the\ndissociation threshold. It uses the asymptotic part of the molecular\npotential only. The method is applied to recently measured levels at the\nasymptote (3s+3s) of Na2. We obtain precise values for the two scattering\nlengths respectively associated to the dissociation limits $F_1=F_2=1,F=2$ \n(55.1±1.6 a0) and $F_1=F_2=1,F=0$ (50.0±1.6 a0); the first\nvalue corresponds to the $a_{1,-1}$ scattering length usually considered in\ncold collisions. The extrapolation procedure is also applied to Li2,\nusing existing experimental data.\n\n\n A simple model is developed to determine a scattering length from the\nexperimental values of the energy of the last, least bound, vibrational\nlevels of the ground state, either $^1\\Sigma _g^{+}$ or $^3\\Sigma _u^{+}$,\nof an alkali dimer. It is based on an extrapolation of the positions of the\nfew outermost nodes of the bound vibrational wave functions towards the\ndissociation threshold. It uses the asymptotic part of the molecular\npotential only. The method is applied to recently measured levels at the\nasymptote (3s+3s) of Na2. We obtain precise values for the two scattering\nlengths respectively associated to the dissociation limits $F_1=F_2=1,F=2$\n(55.1±1.6 a0) and $F_1=F_2=1,F=0$ (50.0±1.6 a0); the first\nvalue corresponds to the $a_{1,-1}$ scattering length usually considered in\ncold collisions. The extrapolation procedure is also applied to Li2,\nusing existing experimental data.\n\n

The European Physical Journal DJan 1, 199952 citations

Ultracold ground-state molecule production in sodium

Fredrik K. Fatemi, K. M. Jones, Paul D. Lett +1 more

We have observed the formation of ground-state ${\mathrm{Na}}_{2}$ molecules via the spontaneous decay of excited molecules created by the photoassociation of ultracold atoms. We measure the binding energies of molecules created in three hyperfine components of the lowest singlet and triplet potentials of ${\mathrm{Na}}_{2}$ by two different methods. Two of the features are purely triplet a ${}^{3}{\ensuremath{\Sigma}}_{u}^{+}$ $(v=15)$ (quasibound) states that have not been previously observed, while the third is a mixed X ${}^{1}{\ensuremath{\Sigma}}_{g}^{+}--a$ ${}^{3}{\ensuremath{\Sigma}}_{u}^{+}$ state. The molecules are detected with high-resolution cw laser ionization techniques and binding energies are measured to within 10 MHz.We have observed the formation of ground-state ${\mathrm{Na}}_{2}$ molecules via the spontaneous decay of excited molecules created by the photoassociation of ultracold atoms. We measure the binding energies of molecules created in three hyperfine components of the lowest singlet and triplet potentials of ${\mathrm{Na}}_{2}$ by two different methods. Two of the features are purely triplet a ${}^{3}{\ensuremath{\Sigma}}_{u}^{+}$ $(v=15)$ (quasibound) states that have not been previously observed, while the third is a mixed X ${}^{1}{\ensuremath{\Sigma}}_{g}^{+}--a$ ${}^{3}{\ensuremath{\Sigma}}_{u}^{+}$ state. The molecules are detected with high-resolution cw laser ionization techniques and binding energies are measured to within 10 MHz.

Physical Review ANov 11, 200253 citations

A multistep laser excitation scheme was used to access the last, least bound levels close to the lowest asymptote

3s+3s

with the molecular states

X{}^{1}{\ensuremath{\Sigma}}_{g}^{+}

and

a{}^{3}{\ensuremath{\Sigma}}_{u}^{+}

{\mathrm{Na}}_{2}

. All singlet levels within the last

10 {\mathrm{cm}}^{\ensuremath{-}1}

We provide spectroscopic data for the $a{\phantom{\rule{0.16em}{0ex}}}^{3}{\ensuremath{\Sigma}}^{+}$ state of the

^{23}\mathrm{Na}^{39}\mathrm{K}

molecule. The experiment is done in an ultrasonic beam apparatus, starting from the ground state $X{\phantom{\rule{0.16em}{0ex}}}^{1}{\ensuremath{\Sigma}}^{+}$ and driving the population to the $a{\phantom{\rule{0.16em}{0ex}}}^{3}{\ensuremath{\Sigma}}^{+}$ state, using a $\ensuremath{\Lambda}$ scheme with fixed pump and scanning dump laser. The signals are observed as dips of the total fluorescence. The intermediate level is chosen to be strongly perturbed by the $B{\phantom{\rule{0.16em}{0ex}}}^{1}\ensuremath{\Pi}/c{\phantom{\rule{0.16em}{0ex}}}^{3}{\ensuremath{\Sigma}}^{+}$ states mixing to overcome the singlet-triplet transfer prohibition. We observed highly resolved hyperfine spectra of various rovibrational levels of the $a{\phantom{\rule{0.16em}{0ex}}}^{3}{\ensuremath{\Sigma}}^{+}$ state from

{v}_{a}=2

up to the highest vibrational levels for rotational quantum numbers

{N}_{a}=4,6,8

. By the typical experimental linewidth of 17 MHz, the vibrational dependence of the hyperfine splitting is clearly revealed for NaK. The absolute frequency measurements of the vibrational levels are used for improvement of the $a{\phantom{\rule{0.16em}{0ex}}}^{3}{\ensuremath{\Sigma}}^{+}$ potential curve and of the derived scattering length of all natural isotope combinations. Applying the $\ensuremath{\Lambda}$ scheme in the reverse direction can provide a pathway for efficient transfer of ultracold

^{23}\mathrm{Na}^{39}\mathrm{K}

molecules from the

\text{Na}(3s)+\text{K}(4s)

asymptote to the lowest levels of the ground state. We show spectra that couple the absolute ground state

{v}_{X}=0,J=0

with an appropriate intermediate state for direct realization of the reverse path. The refined theoretical model of the coupled excited states of the

\text{Na}(3s)+\text{K}(4p)

asymptote allows predictions of efficient paths for

^{23}\mathrm{Na}^{40}\mathrm{K}

; one example is calculated.

{a}_{\mathrm{singlet}}{=19.20(30)a}_{0},

and

{a}_{\mathrm{triplet}}{=62.51(50)a}_{0},

where

{1a}_{0}=0.0529177

nm.

We have observed the spectrum of long range molecular states of singly excited

{\mathrm{Na}}_{2}

formed by photoassociation during ultracold associative ionization collisions of laser-cooled Na atoms. The low kinetic energy of the collision allows us to obtain very high resolution spectra and to observe states close to the dissociation limit. The spectrum shows regular vibrational series characteristic of the 1/

{\mathit{R}}^{3}

long range portion of the

{1}_{\mathit{g}}

potential (asymptotically

{\mathit{S}}_{1/2}

{\mathit{P}}_{3/2}

) as well as molecular hyperfine structure within these peaks. We extract potential parameters and compare with recent theory.

Photoassociation resonances in the

{}^{87}

{}_{2}

{1}_{g}

state dissociating to

5{\phantom{\rule{0.16em}{0ex}}}^{2}S+5{}^{2}{P}_{1/2}

were produced by the excitation of colliding

{}^{87}

Rb atoms in a far-off resonance trap. Levels down to 31 cm${}^{\ensuremath{-}1}$ below the dissociation limit were measured with resonance linewidths of 15 to 20 MHz, and have been located to a one-sigma combined systematic and statistical uncertainty of 50 MHz relative to the

5{\phantom{\rule{0.16em}{0ex}}}^{2}S+5{}^{2}{P}_{1/2}

limit. Electron and nuclear spins were fixed to a space-fixed axis by circularly polarized optical pumping, so that only states with total nuclear spin

I=3

were excited, thereby greatly simplifying the spectrum. The analysis of the data yielded hyperfine coupling parameters

A(v)

, vibrational

G(v)

, and rotational

B(v)

parameters. The

G(v)

parameters could be fit to an rms accuracy of about 0.01 cm${}^{\ensuremath{-}1}$ to a potential constructed from current

{C}_{3}

and

{C}_{6}

long-range dispersion parameters plus an ab initio potential that was adjusted in depth and with quadratic terms in the internuclear distance added to the inner wall.

\n A simple model is developed to determine a scattering length from the\nexperimental values of the energy of the last, least bound, vibrational\nlevels of the ground state, either

^1\\Sigma _g^{+}

^3\\Sigma _u^{+}

,\nof an alkali dimer. It is based on an extrapolation of the positions of the\nfew outermost nodes of the bound vibrational wave functions towards the\ndissociation threshold. It uses the asymptotic part of the molecular\npotential only. The method is applied to recently measured levels at the\nasymptote (3s+3s) of Na2. We obtain precise values for the two scattering\nlengths respectively associated to the dissociation limits

F_1=F_2=1,F=2

\n(55.1±1.6 a0) and

F_1=F_2=1,F=0

(50.0±1.6 a0); the first\nvalue corresponds to the

a_{1,-1}

scattering length usually considered in\ncold collisions. The extrapolation procedure is also applied to Li2,\nusing existing experimental data.\n\n

We have observed the formation of ground-state

{\mathrm{Na}}_{2}

molecules via the spontaneous decay of excited molecules created by the photoassociation of ultracold atoms. We measure the binding energies of molecules created in three hyperfine components of the lowest singlet and triplet potentials of

{\mathrm{Na}}_{2}

by two different methods. Two of the features are purely triplet a ${}^{3}{\ensuremath{\Sigma}}_{u}^{+}$

(v=15)

(quasibound) states that have not been previously observed, while the third is a mixed X ${}^{1}{\ensuremath{\Sigma}}_{g}^{+}--a$ ${}^{3}{\ensuremath{\Sigma}}_{u}^{+}$ state. The molecules are detected with high-resolution cw laser ionization techniques and binding energies are measured to within 10 MHz.