Photoassociation Spectroscopy Research Articles

Autler-Townes splitting in two-color photoassociation of6Li

We report on high-resolution two-color photoassociation spectroscopy in the triplet system of magneto-optically trapped ${}^{6}\mathrm{Li}.$ Photoassociation is induced from the ground-state asymptote to the $v=59$ level of the excited $1{}^{3}{\ensuremath{\Sigma}}_{g}^{+}$ state. This level is coupled to the $v=9$ level of the triplet ground state $a{}^{3}{\ensuremath{\Sigma}}_{u}^{+}$ by the light field of a Raman laser. The absolute transition frequencies are measured with an iodine frequency standard and the binding energy of the ground state is determined to be $24.391\ifmmode\pm\else\textpm\fi{}0.020\mathrm{GHz}.$ Strong coupling of the bound molecular states has been observed as Autler-Townes splitting in the photoassociation signal for different detunings of the Raman laser. From the splitting we determine the spontaneous bound-bound decay rate to be $4.3\ifmmode\times\else\texttimes\fi{}{10}^{5}{\mathrm{s}}^{\ensuremath{-}1}$ and estimate the molecule formation rate. The observed line shapes are in good agreement with the theoretical model.

Two-color photoassociation spectroscopy of the lowest triplet potential of Na2

We have performed a type of Autler–Townes spectroscopy to locate a number of rovibrational-hyperfine levels of the a 3Σu+ potential, the lowest triplet potential of the Na2 dimer. The spectroscopy starts with the photoassociation of ultracold atoms in a magneto-optical trap. We have measured the binding energies of over 100 individual states spanning the vibrational levels v=8–15 of this potential (binding energies up to 27 cm−1). We obtain a typical accuracy of 15 MHz and a typical resolution of 20 MHz, improving on the 10 GHz accuracy and 30 GHz resolution previously available for the vibrational states v<12. Vibrational, rotational, and hyperfine structures are resolved. Additionally, we have been able to resolve the magnetic electron–electron spin–spin dipole splitting of a number of these hyperfine levels. The measured rotational and hyperfine structures show good agreement with theoretical calculations. An analysis of the remaining discrepancies indicates where possible refinements to the potentials can be made. We also observe evidence for the presence of second-order spin–orbit coupling.

Photoassociation spectroscopy of cold calcium atoms

Photoassociation spectroscopy experiments on 40Ca atoms close to the dissociation limit 4s4s 1S0 - 4s4p 1P1 are presented. The vibronic spectrum was measured for detunings of the photoassociation laser ranging from 0.6 GHz to 68 GHz with respect to the atomic resonance. In contrast to previous measurements the rotational splitting of the vibrational lines was fully resolved. Full quantum mechanical numerical simulations of the photoassociation spectrum were performed which allowed us to put constraints on the possible range of the calcium scattering length to between 50 a_0 and 300 a_0.

Photoassociation of Ultracold Sodium Atoms

Using ultra-cold atoms a new technique of photoassociation spectroscopy has been developed. The technique has an unprecedented resolution and can be used to obtain high-resolution data on singly and doubly excited states of diatomic molecules. We describe the principle of the technique and show results for one specific case, namely the Na2 molecule.

Saturation in heteronuclear photoassociation of6Li7Li

We report heteronuclear photoassociation spectroscopy in a mixture of magneto-optically trapped ${}^{6}\mathrm{Li}$ and ${}^{7}\mathrm{Li}.$ The laser-induced decrease in the ${}^{7}\mathrm{Li}$ steady-state particle number, only appearing in the presence of ${}^{6}\mathrm{Li},$ gives clear evidence of photoassociation to form ${}^{6}{\mathrm{Li}}^{7}\mathrm{Li}.$ Hyperfine resolved spectra of the vibrational level $v=83$ of the singlet state ${\mathrm{A}}^{1}{\ensuremath{\Sigma}}_{u}^{+}$ have been taken up to intensities of $1000{\mathrm{W}/\mathrm{c}\mathrm{m}}^{2}.$ The absolute resonance frequencies and the rotational constant have been measured. Saturation of the photoassociation rate has been observed for two hyperfine transitions, which can be shown to be due to saturation of the rate coefficient near the unitarity limit. Saturation intensities on the order of $40{\mathrm{W}/\mathrm{c}\mathrm{m}}^{2}$ can be determined.

Simultaneous trapping of rubidium and metastable argon in a magneto-optical trap

We have simultaneously confined rubidium and metastable argon in a dual-species magneto-optical trap (MOT). Here a binary mixture of atomic species from different groups of the periodic table have been optically confined at ultracold temperatures. We describe the apparatus and characterize the individual, single species MOTs and the dual-species MOT. Both fluorescence and ion production are monitored. With both species trapped, we observe $\ensuremath{\sim}5\ifmmode\times\else\texttimes\fi{}{10}^{6}$ ${}^{85}\mathrm{Rb}$ atoms and $\ensuremath{\sim}2\ifmmode\times\else\texttimes\fi{}{10}^{6}$ ${}^{40}{\mathrm{Ar}}^{*}$ atoms. Realization of the dual-species trap opens the way for detailed studies of Penning and associative ionization, photoassociative spectroscopy, and eventually for the production of bound, ultracold RbAr molecules.

The Cs2 ground electronic state by Fourier transform spectroscopy: Dispersion coefficients

This study presents the derivation of an accurate potential energy curve for the ground electronic state of the Cs2 molecule. High resolution laser induced emission spectra data involving vibrational levels of the ground X 1Σg+ state up to v″=135 (16 900 wave numbers) have been determined. The ground state potential energy curve is constructed by combining the inverted perturbation approach for internuclear distances up to 11 Å, with an analytical expression for longer internuclear distances. This potential curve allows an improved derivation of the dissociation energy and of the Coulombic parameters governing the Cs(6s)+Cs(6s) interaction in the electronic ground state, compared with values derived either by calculations or by recent photoassociative spectroscopy measurements. The main constants are C6=6836 (±100) a.u.=32.945 (±0.49)×106 cm−1 Å6, and De=3649.88 (±0.45) cm−1.

Determination of the87Rb5pstate dipole matrix element and radiative lifetime from the photoassociation spectroscopy of theRb20g−(P3/2)long-range state

We present a detailed study of the ${0}_{g}^{\ensuremath{-}}{(P}_{3/2})$ pure long-range electronic state of the ${}^{87}{\mathrm{Rb}}_{2}$ molecule. The high-resolution spectral data provided by photoassociative spectroscopy of ${}^{87}{\mathrm{Rb}}_{2}$ is analyzed by using the generalized simulated annealing method. The dipole matrix element of the $5p$ ${}^{87}\mathrm{Rb}$ atomic state and other effective asymptotic parameters for the ${0}_{g}^{\ensuremath{-}}{(P}_{3/2})$ long-range state are determined and a complete analytical description of the potential well is obtained. We extract a radiative lifetime of the ${5P}_{3/2}$ and ${5P}_{1/2}$ states equal to 26.25(8) ns and 27.75(8) ns, respectively, with a precision (0.3%) comparable to atomic physics experiment.

Treasure of the Past X: A Spectroscopic Determination of Scattering Lengths for Sodium Atom Collisions.

We report a preliminary value for the zero magnetic field Na 2S(f = 1, m = − 1) + Na 2S(f = 1, m = − 1) scattering length, a1,−1. This parameter describes the low-energy elastic two-body processes in a dilute gas of composite bosons and determines, to a large extent, the macroscopic wavefunction of a Bose condensate in a trap. Our scattering length is obtained from photoassociative spectroscopy with samples of uncondensed atoms. The temperature of the atoms is sufficiently low that contributions from the three lowest partial waves dominate the spectrum. The observed lineshapes for the purely long-range molecular state enable us to establish key features of the ground state scattering wavefunction. The fortuitous occurrence of a p-wave node near the deepest point (Re = 72 a0) of the potential curve is instrumental in determining a1,−1 = (52 ± 5) a0 and a2.2 = (85 ± 3) a0, where the latter is for a collision of two Na 2S(f = 2, m = 2) atoms.

Many-body calculations of electric-dipole amplitudes for transitions between low-lying levels of Mg, Ca, and Sr

To support efforts on cooling and trapping of alkaline-earth atoms and designs of atomic clocks, we performed ab initio relativistic many-body calculations of electric-dipole transition amplitudes between low-lying states of Mg, Ca, and Sr. In particular, we report amplitudes for ^1P_1 --> ^1S_0, ^3S_1, ^1D_2$, for ^3P_1 --> ^1S_0, ^1D_2, and for ^3P_2 --> ^1D_2 transitions. For Ca, the reduced matrix element <4s4p, ^1P_1 ||D|| 4s^2, ^1S_0> is in a good agreement with a high-precision experimental value deduced from photoassociation spectroscopy [Zinner et al., Phys.Rev.Lett., v.85, 2292 (2000)]. An estimated uncertainty of the calculated lifetime of the (3s3p ^1P_1) state of Mg is a factor of three smaller than that of the most accurate experiment. Calculated binding energies reproduce experimental values within 0.1-0.2%.

Reflection approximation in photoassociation spectroscopy

We construct an analytical wave function in the phase-amplitude formalism to describe collisions between two neutral atoms. This wave function is valid from intermediate to asymptotic internuclear distance over a large energy range near zero energy, and is especially suitable for cold and ultracold collisions. We have used this analytic wave function with the reflection approximation formula for calculating Franck-Condon factors for photoassociative spectroscopy. Numerical tests show very satisfactory agreement between the resulting analytic formula and the fully quantum numerical results in most cases investigated. Finally, we show in a model case that our analytical wave function enables us to relate the scattering length directly to a preasymptotic node in the ground-state wave function, which in principle can be measured by photoassociative spectroscopy.

Ground-state scattering lengths for potassium isotopes determined by double-resonance photoassociative spectroscopy of ultracold39K

We use double-resonance photoassociative spectroscopy of ultracold ${}^{39}\mathrm{K}$ atoms to precisely determine the triplet $a{}^{3}{\ensuremath{\Sigma}}_{u}^{+}$ scattering length for the various isotopes of potassium. Photoassociation of free ${}^{39}\mathrm{K}$ atoms to the pure long-range ${0}_{g}^{\ensuremath{-}}{(v}^{\ensuremath{'}}=0,{J}^{\ensuremath{'}}=2)$ level is followed by stimulated emission to high-lying levels of the $a{}^{3}{\ensuremath{\Sigma}}_{u}^{+}$ potential. The binding energies of levels within 5 GHz below the lowest ground-state ${4s}_{1/2}{(f}_{a}{=1)+4s}_{1/2}{(f}_{b}=1)$ hyperfine asymptote are measured by both trap loss and ionization detection. The locations of these near-threshold hyperfine-coupled molecular levels allow us to constrain the triplet potential and thereby determine the triplet scattering length. The result for ${}^{39}\mathrm{K},$ ${a}_{t}=\ensuremath{-}33\ifmmode\pm\else\textpm\fi{}{5a}_{0}$ ${(1a}_{0}=0.0529177 \mathrm{nm}),$ is a factor of $\ensuremath{\sim}5$ improvement over previous determinations and establishes that a large ${}^{39}\mathrm{K}$ Bose-Einstein condensate will not be stable.

Photoassociative spectroscopy as a self-sufficient tool for the determination of the Cs triplet scattering length

In photoassociation spectroscopy, the line intensities of a given vibrational progression exhibit zero-signal modulation reflecting the node structure of the s-wave ground state wave function of two free colliding atoms. This leads to the determination of the scattering length. We performed photoassociation of cold Cs atoms polarized in the Zeeman sublevel f = 4, m(f) = 4. We analyzed the intensities of the lines associated with the Cs2 0(-)(g) state dissociating to the 6s(1/2)+6p(3/2) asymptote. This yields a value of the Cs triplet state scattering length, a(T) = -530a(0), while consistency requirements impose a value of the multipole ground state molecular coefficient, C6 = 6510 a.u.

Spectroscopy of autoionizing doubly excited states in ultracoldNa2molecules produced by photoassociation

We have performed photoassociation spectroscopy to study the doubly excited states of Na2 involved in the associative ionization of colliding Na(3P) atoms. Rovibrational levels of two doubly excited potentials connected to the P3/21P3/2 asymptote, one of 0u 2 and one of 1u symmetry, have been identified. These two doubly excited potentials dominate the route to ionization used in photoassociation experiments of cold Na. Binding energies and rotational constants for all the vibrational levels with binding energies ,50 GHz have been measured. The asymptotic potentials and short-range ionization probabilities are extracted from the data.

Photoassociation spectroscopy of cold He(2 3S) atoms

We observe vibrational states by photoassociation spectroscopy of cold He(2 3S) atoms. Photoassociation resonances are detected as peaks in the Penning ionization rate over a frequency range of 20 GHz below the atomic 2 3S1-2 3P2 transition frequency. We have observed three vibrational series, of which two can be identified. A possible mechanism to explain the observed increase of the Penning ionization rate is discussed.

Photoassociative spectroscopy and formation of cold molecules

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 0g- and 1u purely long-range states below the dissociation limit 6s1/2+6p3/2 present Condon points at intermediate distances. Such configurations offer rather efficient channels for the creation of singlet or triplet ground state Cs2 molecules after spontaneous decay.

Fitting line shapes in photoassociation spectroscopy of ultracold atoms: A useful approximation

Line shapes observed in photoassociation spectroscopy of ultracold $(T&lt;1\mathrm{mK})$ atoms are asymmetric and the peak of the line is shifted by a temperature-dependent amount from the zero-temperature threshold. In principle, calculating the line shape requires a full knowledge of both the ground- and excited-state potentials. We demonstrate here that an approximation based on the Wigner threshold law for scattering yields a relatively simple expression which allows one to extract line positions and linewidths directly from the data. The formula contains a few parameters (threshold frequency, linewidth, temperature, height) and does not require a detailed knowledge of the molecular potentials involved. We illustrate the utility of this approach with examples for Na photoassociation at 500 \ensuremath{\mu}K and also discuss the limitations of the approach.

Highly Excited States of Ultracold Molecules: Photoassociative Spectroscopy ofNa2

We describe the spectroscopy of highly excited states of ultracold ${\mathrm{Na}}_{2}$ molecules using a new photoassociative approach based on resonantly enhanced multiphoton ionization. We excite a remarkable number of ${\mathrm{Na}}_{2}$ rotational states providing a rich rovibrational spectrum. We thereby extract not only the first order quadrupole-quadrupole ( ${C}_{5}$) and the van der Waals constants ( ${C}_{6}$) but also sensitive atom-atom interaction parameters such as spin-spin, spin-orbit, and perturbative constants.

Theoretical study of the absorption spectra of the lithium dimer

For the lithium dimer we calculate cross sections for absorption of radiation from the vibrational-rotational levels of the ground $X{}^{1}{\ensuremath{\Sigma}}_{g}^{+}$ electronic state to the vibrational levels and continua of the excited $A{}^{1}{\ensuremath{\Sigma}}_{u}^{+}$ and $B{}^{1}{\ensuremath{\Pi}}_{u}$ electronic states. Theoretical and experimental data are used to characterize the molecular properties taking advantage of knowledge recently obtained from photoassociation spectroscopy and ultra-cold atom collision studies. The quantum-mechanical calculations are carried out for temperatures in the range from 1000 to 2000 K and are compared with previous calculations and measurements where available.

Long-range potentials for two-species alkali-metal atoms

We address a growing interest in trapping and cooling of mixed-species alkali-metal atoms. Long-range coefficients that arise in the multipole expansion of molecular potentials for unlike alkali-metal dimers are calculated. The coefficients for the heteronuclear alkali-metal dimers corresponding to different molecular symmetries that separate to $\mathrm{nS}\ensuremath{-}{n}^{\ensuremath{'}}S,nS\ensuremath{-}{n}^{\ensuremath{'}}P,nS\ensuremath{-}{n}^{\ensuremath{'}}D,$ and $\mathrm{nP}\ensuremath{-}{n}^{\ensuremath{'}}P$ atomic levels are computed with high precision. We consider cases where in the infinite separation limit, one atom is in the ground state and the other is in one of the lowest S, P, and D excited states and both atoms are in their lowest excited P states. We find the long-range potentials for $\mathrm{Rb}(5S)\ensuremath{-}\mathrm{C}\mathrm{s}(6S),\mathrm{Rb}(6S)\ensuremath{-}\mathrm{C}\mathrm{s}(6S),\mathrm{K}(4S)\ensuremath{-}\mathrm{R}\mathrm{b}(5P){ }^{1,3}\ensuremath{\Sigma},\mathrm{K}(4P)\ensuremath{-}\mathrm{C}\mathrm{s}(6P){ }^{1,3}\ensuremath{\Sigma},$ and $\mathrm{Rb}(5S)\ensuremath{-}\mathrm{N}\mathrm{a}(3D){ }^{1,3}\ensuremath{\Sigma}$ molecules to be the most attractive. The $\mathrm{K}(4S)\ensuremath{-}\mathrm{R}\mathrm{b}(5P)$ dimer represents the best candidate molecule for ultracold photoassociative spectroscopy. We also find the $\mathrm{K}(4P)\ensuremath{-}\mathrm{C}\mathrm{s}(6P)$ and $\mathrm{Rb}(5S)\ensuremath{-}\mathrm{K}(4P)$ dimers to form, respectively, the most attractive and the most repulsive long-range potentials. The present calculation is in good agreement with experimentally determined value for the ${1/R}^{6}$ van der Waals coefficient for the interaction between $\mathrm{Cs}(6S)$ and $\mathrm{Li}(2P)$ atoms.