Photoassociation Experiments Research Articles

FCI calculations of the adiabatic electronic structure of KRb highlighting the K−Rb+ ionic limit effect

A non-relativistic description of the electronic structure for the heteronuclear molecule KRb was developed through the Full Configuration Interaction (FCI) and pseudo-potential method. Below the ionic limit K−Rb+, the ground and all excited singlet and triplet states of different symmetries Σ+, Π and Δ (in the Hund's case (a): 2s + 1Λ±) were intensively investigated. Several adiabatic results including potential energy curves (PECs), permanent and transition electric dipole moments (PEDM, TEDM) were analyzed in short and long-range of internuclear distances. Tables of these properties as functions of separation are presented. The spectroscopic constants with the vibrational levels were derived using the “Numerov” algorithm. These molecular parameters were compared with those published in the literature, feature a good agreement. In the adiabatic representation, strong couplings between successive 1Σ+ states were reached by series of avoided crossing, yielding to the appearance of the ionic character and the good illustration of charge transfer. This description of the KRb molecule was helpful in the design of the prospect photo-association experiments and the obtaining of the quantum-degenerate gas of the polar molecule.

Spectroscopic proprieties of the ground and the higher excited states of the KCs

Potential energy curves, spectroscopic parameters, electric dipole moments (PEDM and TEDM) and vibrational levels’ spacing for 141Σ+, 133Σ+, 81,3Π, and 31,3Δ electronic states, including the ionic limit K−Cs+, are highly computed and presented in adiabatic representation. These properties are determined by the use of an ab initio method involving non-empirical pseudo-potentials, the core polarization potentials, the l-dependent cut-off functions, and the full valence configuration interaction. An important shape where an ionic state behaving as (−1/R), has been clearly pointed out in the 1Σ+ symmetry. This irregularity has been made due to the ionic charge transfer state (K−Cs+), which induces a series of avoided crossings at intermediate and long internuclear ranges. It is interesting to note that the ionic character linked to the ionic charge transfer K−Cs+ state has been clearly illustrated in the PEDM. The current calculations on the KCs molecule are complementary to the published theoretical works, including recently observed electronic states that had not been calculated previously. For the low-lying electric states, spectroscopic constants, PEDM, as well as TEDM are in good agreement with the available experimental data. The relevant data of the KCs molecule are meaningful and useful in several prospective experiments such as photo-association experiments or the manipulation of ultra-cold molecules.

High-intensity two-frequency photoassociation spectroscopy of a weakly bound molecular state: Theory and experiment

We investigate two-frequency photoassociation of a weakly bound molecular state, focusing on a regime where the ac Stark shift is comparable to the halo-state energy. In this "high-intensity" regime, we observe features absent in low-intensity two-frequency photoassociation. We experimentally measure the spectra of $^{86}$Sr atoms coupled to the least bound state of the $^{86}$Sr$_2$ ground electronic channel through an intermediate electronically excited molecular state. We compare the spectra to a simple three-level model that includes a two-frequency drive on each leg of the transition. With numerical solution of the time-dependent Schrodinger equation, we show that this model accurately captures (1) the existence of experimentally observed satellite peaks that arise from nonlinear processes, (2) the locations of the two-photon peak in the spectrum, including ac Stark shifts, and (3) in some cases, spectral lineshapes. To better understand these numerical results, we develop an approximate treatment of this model, based on Floquet and perturbation theory, that gives simple formulas that accurately capture the halo-state energies. We expect these expressions to be valuable tools to analyze and guide future two-frequency photoassociation experiments.

Coherent Control of Bond Making.

We demonstrate coherent control of bond making, a milestone on the way to coherent control of photoinduced bimolecular chemical reactions. In strong-field multiphoton femtosecond photoassociation experiments, we find the yield of detected magnesium dimer molecules to be enhanced for positively chirped pulses and suppressed for negatively chirped pulses. Our abinitio model shows that control is achieved by purification combined with chirp-dependent Raman transitions. Experimental closed-loop phase optimization using a learning algorithm yields an improved pulse that utilizes vibrational coherent dynamics in addition to chirp-dependent Raman transitions. Our results show that coherent control of binary photoreactions is feasible even under thermal conditions.

Weakly bound87Rb2(5s1/2+5p1/2)1gmolecules: Hyperfine interaction and LeRoy-Bernstein analysis including linear and nonlinear terms

Data on the $(5{s}_{1/2}+5{p}_{1/2}){1}_{g}$ ${}^{87}{\text{Rb}}_{2}$ state under the ${D}_{1}$ limit, provided by a photoassociation experiment on cold atoms, have been analyzed by an improved LeRoy-Bernstein (LRB) approach including linear and nonlinear terms and provide a ${c}_{6}$ value of the potential. To do that, using a model for hyperfine structure shifts, we have first subtracted the hyperfine effects in the split lines and deduced the vibrational energies. Then, we have compared three LRB-type models to fit the data. We conclude that the second-order improved LRB is well suited and allows us to deduce an experimental value of ${c}_{6}$ [${c}_{6}=(15.14\ifmmode\pm\else\textpm\fi{}0.05)\ifmmode\times\else\texttimes\fi{}{10}^{4}$ a.u.].

Short-range correlations in dilute atomic Fermi gases with spin-orbit coupling

We study the short-range correlation strength of three dimensional spin half dilute atomic Fermi gases with spin-orbit coupling. The interatomic interaction is modeled by the contact pseudopotential. In the high temperature limit, we derive the expression for the second order virial expansion of the thermodynamic potential via the ladder diagrams. We further evaluate the second order virial expansion in the limit that the spin-orbit coupling constants are small, and find that the correlation strength between the fermions increases as the forth power of the spin-orbit coupling constants. At zero temperature, we consider the cases in which there are symmetric spin-orbit couplings in two or three directions. In such cases, there is always a two-body bound state of zero net momentum. In the limit that the average interparticle distance is much larger than the dimension of the two-body bound state, the system primarily consists of condensed bosonic molecules that fermions pair to form; we find that the correlation strength also becomes bigger compared to that in the absence of spin-orbit coupling. Our results indicate that generic spin-orbit coupling enhances the short-range correlations of the Fermi gases. Measurement of such enhancement by photoassociation experiment is also discussed.

Formation of ultracold SrYb molecules in an optical lattice by photoassociation spectroscopy: theoretical prospects

State-of-the-art ab initio techniques have been applied to compute the potential energy curves for the SrYb molecule in the Born-Oppenheimer approximation for the electronic ground state and the first fifteen excited singlet and triplet states. All the excited state potential energy curves were computed using the equation of motion approach within the coupled-cluster singles and doubles framework and large basis-sets, while the ground state potential was computed using the coupled cluster method with single, double, and noniterative triple excitations. The leading long-range coefficients describing the dispersion interactions at large interatomic distances are also reported. The electric transition dipole moments have been obtained as the first residue of the polarization propagator computed with the linear response coupled-cluster method restricted to single and double excitations. Spin-orbit coupling matrix elements have been evaluated using the multireference configuration interaction method restricted to single and double excitations with a large active space. The electronic structure data were employed to investigate the possibility of forming deeply bound ultracold SrYb molecules in an optical lattice in a photoassociation experiment using continuous-wave lasers. Photoassociation near the intercombination line transition of atomic strontium into the vibrational levels of the strongly spin-orbit mixed b(3)Σ(+), a(3)Π, A(1)Π, and C(1)Π states with subsequent efficient stabilization into the v'' = 1 vibrational level of the electronic ground state is proposed. Ground state SrYb molecules can be accumulated by making use of collisional decay from v'' = 1 to v'' = 0. Alternatively, photoassociation and stabilization to v'' = 0 can proceed via stimulated Raman adiabatic passage provided that the trapping frequency of the optical lattice is large enough and phase coherence between the pulses can be maintained over at least tens of microseconds.

Relativistic calculations of ground and excited states of LiYb molecule for ultracold photoassociation spectroscopy studies

We report a series of quantum-chemical calculations for the ground and some of the low-lying excited states of an isolated LiYb molecule by the spin-orbit multistate complete active space second-order perturbation theory (SO-MS-CASPT2). Potential energy curves, spectroscopic constants, and transition dipole moments (TDMs) at both spin-free and spin-orbit levels are obtained. Large spin-orbit effects especially in the TDMs of the molecular states dissociating to Yb((3)P(0,1,2)) excited states are found. To ensure the reliability of our calculations, we test five types of incremental basis sets and study their effect on the equilibrium distance and dissociation energy of the ground state. We also compare CASPT2 and CCSD(T) results for the ground state spectroscopic constants at the spin-free relativistic level. The discrepancies between the CASPT2 and CCSD(T) results are only 0.01 Å in equilibrium bond distance (R(e)) and 200 cm(-1) in dissociation energy (D(e)). Our CASPT2 calculation in the supermolecular state (R=100 a.u.) with the largest basis set reproduces experimental atomic excitation energies within 3% error. Transition dipole moments of the super molecular state (R=100 a.u.) dissociating to Li((2)P) excited states are quite close to experimental atomic TDMs as compared to the Yb((3)P) and Yb((1)P) excited states. The information obtained from this work would be useful for ultracold photoassociation experiments on LiYb.

Short-range correlations and entropy in ultracold-atom Fermi gases

We relate short-range correlations in ultracold-atom Fermi gases to the entropy of the system over the entire temperature, $T$, vs coupling strength, $\ensuremath{-}1/{k}_{F}a$, plane. In the low-temperature limit the entropy is dominated by phonon excitations and the correlations increase as ${T}^{4}$. In the Bose-Einstein condensate (BEC) limit, we calculate a boson model within the Bogoliubov approximation to show explicitly how phonons enhance the fermion correlations. In the high-temperature limit, we show from the virial expansion that the correlations decrease as $1/T$. The correlations therefore reach a maximum at a finite-temperature. We infer the general structure of the isentropes of the Fermi gas in the $(T,\ensuremath{-}1/{k}_{F}a)$ plane, and the temperature dependence of the correlations in the unitary, BEC, and BCS limits. Our results compare well with measurements of the correlations via photoassociation experiments at higher temperatures.

Stimulating the production of deeply bound RbCs molecules with laser pulses: the role of spin–orbit coupling in forming ultracold molecules

We investigate the possibility of forming deeply bound ultracold RbCs molecules by a two-color photoassociation experiment. We compare the results with those for Rb2 in order to understand the characteristic differences between heteronuclear and homonuclear molecules. The major differences arise from the different long-range potential for excited states. Ultracold 85Rb and 133Cs atoms colliding on the X 1Σ+ potential curve are initially photoassociated to form excited RbCs molecules in the region below the Rb(5S)+Cs(6P1/2) asymptote. We explore the nature of the Ω=0+ levels in this region, which have mixed A 1Σ+ and b 3Π character. We then study the quantum dynamics of RbCs by a time-dependent wavepacket (TDWP) approach. A wavepacket is formed by exciting a few vibronic levels and is allowed to propagate on the coupled electronic potential energy curves. We calculate the time dependence of the overlap between the wavepacket and ground-state vibrational levels. For a detuning of 7.5 cm−1 from the atomic line, the wavepacket for RbCs reaches the short-range region in about 13 ps, which is significantly faster than for the homonuclear Rb2 system; this is mostly because of the absence of an R−3 long-range tail in the excited-state potential curves for heteronuclear systems. We give a simple semiclassical formula that relates the time taken to the long-range potential parameters. For RbCs, in contrast to Rb2, the excited-state wavepacket shows a substantial peak in singlet density near the inner turning point, and this produces a significant probability of de-excitation to form ground-state molecules bound by up to 1500 cm−1. The short-range peak depends strongly on non-adiabatic coupling and is reduced if the strength of the spin–orbit coupling is increased. Our analysis of the role of spin–orbit coupling concerns the character of the mixed states in general and is important for both photoassociation and stimulated Raman de-excitation.

Spinor molecule in atomic Bose–Einstein condensate

We have performed two-photon photoassociation experiments in atomic Bose–Einstein condensate (BEC) of 87Rb with spin degree of freedom which is created by all-optical method with CO2 lasers. The spinor character of the molecules has been revealed by the photoassociation spectrum with a new structure. The hyperfine structure of the molecules near the dissociation limit is identified by observations of the Zeeman and AC-Stark effects of the molecules. The molecules have been spin-selectively probed by the use of the light shift. This result would open the new possibility of research on novel spinor molecular BEC.

Lifetime of weakly bound dimers of ultracold metastable helium studied by photoassociation

We describe two-photon photoassociation (PA) experiments operated in an ultracold gas of metastable $^4$He$^*$ atoms in the $2^3S_1$ state. Atom-molecule dark resonances as well as Raman signals provide information on the exotic molecule in the least bound vibrational J=2, $v=14$ state of the $^5\Sigma_g^+$ interaction potential of two spin-polarized metastable atoms. The physical origin of the various two-photon PA signals is first discussed. Their linewidths are interpreted in term of processes limiting the lifetime $\tau$ of the exotic molecule. A value of $\tau=1.4\pm0.3 \mu$s is found, which is discussed in view of two recent calculations of the Penning ionization rate induced by spin-dipole coupling and of the atom-molecule inelastic collisions.

All-optical formation of molecules with spin degree of freedom in an atomic Bose-Einstein condensate

We have performed a two-photon photoassociation experiment in an atomic Bose-Einstein condensate of 87Rb with the spin degree of freedom, which is created by an all-optical method with CO2 lasers. The spinor character of the created molecules has been revealed by the photoassociation spectrum with a new structure. The hyperfine structure of the created molecules near the dissociation limit is identified by observations of the Zeeman and AC-Stark effects of the molecules. We have also demonstrated the spin-selective creation of molecules. This result would open the new possibility of research on novel molecular spinor BEC.

Photoassociation experiments with ultracold metastable helium

The present article gives a review of various photoassociation (PA) experiments performed at ENS with a gas of ultracold atoms of metastable helium in the 23S1 state, using a PA laser beam red-detuned from the 23S1-23P transitions. Molecular spectra close to the D2 atomic line (23S $_1\leftrightarrow 2^3$ P2) are presented. All the measured lines are identified as a signature of molecular bound states having a strong (if not pure) quintet spin character at short interatomic distance. Close to the D0 atomic line (23S $_1\leftrightarrow 2^3$ P0), giant helium dimers can be produced [see Phys. Rev. Lett. 91, 073203 (2003)]. A laser set-up improved recently allows us to measure very accurately the binding energy of the ro-vibrational ground state of the 0 u + purely long-range potential and the agreement with the theory published previously is excellent. Finally, preliminary results on 2 photon PA spectroscopy are given.

Pair dynamics in the formation of molecules in a Bose-Einstein condensate

We revisit the mean-field treatment of photoassociation and Feshbach resonances in a Bose-Einstein condensate previously used by various authors. Generalizing the Cherny and Shanenko approach (Phys. Rev. E 62, 1646-59 (2000) ) where the finite size of the potentials is explicitly introduced, we develop a two-channel model for a mixed atomic-molecular condensate. Besides the individual dynamics of the condensed and non-condensed atoms, the model also takes into account their pair dynamics by means of pair wave functions. We show that the resulting set of coupled equations can be reduced to the usual coupled Gross-Pitaevskii equations when the time scale of the pair dynamics is short compared to that of the individual dynamics. Such time scales are discussed in the case of typical photoassociation experiments with cw lasers. We show that the individual dynamics plays a minor role, demonstrating the validity of the rates predicted by the usual models describing photoassociation in a nondegenerate gas.

Photoassociation of ultracold K atoms: Observation of high lying levels of the 1g∼1 1Πg molecular state of K2

Very high-lying vibrational levels of the 1g∼1 1Πg electronic state of K2 have been observed in a photoassociation experiment using an ion detection scheme. The photoassociation measurements have been treated together with laser induced fluorescence data recorded by Fourier transform spectrometry to construct a pointwise potential curve for this electronic state. Several vibrational levels were observed by both techniques, so the dissocation energy can be deduced without extrapolation, from the sum of binding energies measured in photoassociation and vibrational energies established with respect to the potential minimum (defined by the fluorescence data), giving De=1290.292±0.002 cm−1 (1 standard deviation). The potential curve reproduces over 2000 term values (up to v=138) with a root mean square error of 0.0025 cm−1. Nevertheless, small differences are found between the rotational constants generated from the potential curve and the effective rotational constants deduced from binding energy measurements at very high v. The smoothness of the outermost part of the pointwise potential energy curve has been investigated through fits to a Hund’s case (c) asymptotic model.

Formation of ultracold molecules via photoassociation with blue detuned laser light

We propose a new possibility to form ultracold molecules, via photoassociation of a pair of cold atoms into vibrational levels of the external well of an excited electronic state located at intermediate interatomic distance ( ≈ 20 Bohr radii), and embedded in the dissociation continuum above its dissociation limit. The existence of such a well is demonstrated by conventional free-free absorption spectroscopy at thermal energies. Estimation for cold atom photoassociation and cold molecule formation rates are obtained within a perturbative approach [Drag et al., IEEE J. Quant. Electr. 36, 1378 (2000)], and are found observable for usual conditions of photoassociation experiments.

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.

Coupled singlet-triplet analysis of two-color cold-atom photoassociation spectra

We describe a method that is well suited to analysis of the bound states of the alkali-metal dimers near their dissociation limit. The method combines inverse perturbation theory, coupled-channel bound-state theory, and the accumulated phase method to treat the short-range part of the molecular potentials. We apply this method to analyze the bound-state energies measured in a two-color photoassociation experiment in an ultracold 85Rb gas. This analysis yields information on the interactions between ultracold 85Rb atoms that is important to the understanding of ultracold Rb collisions and Bose-Einstein condensation.

Mechanism for the Production of6Li2and7Li2Ultracold Molecules

Calculations are presented of the spontaneous emission probabilities and oscillator strengths of transitions between the vibrational energy levels of the ground and excited singlet and triplet states of the molecules6Li2and7Li2. The fractions of transitions into the continuum and the discrete levels are estimated and it is shown that the translationally cold molecules can be produced during photoassociation experiments with high efficiency. The data are used to quantify a scheme by which translationally cold molecules can be created in specific rotational and vibrational levels.