Time-dependent analysis of tunneling effect in the formation of ultracold molecules via photoassociation of laser-cooled atoms

The paper contains a time-dependent investigation of the tunneling effect observed in the photoassociation spectrum of Cs₂ and attributed to the 0_g ^-(6s, 6p _3/2) double well. When by photoassociation of two cold cesium atoms a vibrational level of the outer well is populated, tunneling is an efficient mechanism for transferring the population to the inner well (R < 15a ₀), where spontaneous emission may lead to formation of cold molecules in low vibrational levels of the a ³Σ⁺ _u(6s, 6s) electronic state. This tunneling effect is analyzed by wavepackets propagation, first considering the double well potential alone, and following a packet made by a superposition of states initially located at large distances. Characteristic times for the vibration dynamics, corresponding to a beating phenomenon between the two wells, to partial “revival” at large distances, and to maxima in the population localized in the inner well are reported and discussed. Second, we simulate the two-channels a ³Σ⁺ _u(6s, 6s)↦0_g ^-(6s, 6p _3/2) photoassociation at detunings around 2.9 cm^-1: the inner well can be populated either by the excitation of a vibrational level of the external well (resonant excitation), or by tuning the photoassociation laser at the energy of the inner well level which displays tunneling (“off-resonance excitation”). In the first case the photoassociation is efficient, while the tunneling probability is small; in the second, the tunneling probability is large, so that despite the poor efficiency of the photoassociation process, more population can be transferred to the inner well. This second choice is shown to be very sensitive to the laser intensity, which could be used to control the population of the inner well and hence the formation of ultracold molecules in low vibrational levels. Received 19 April 2002 Published online 1st October 2002 RID="a" ID="a"e-mail: francoise.masnou@lac.u-psud.fr     

Spectroscopy of the a3Σu + state and the coupling to the X1Σg + state of K2

We report on high resolution Fourier-transform spectroscopy of fluorescence to the a³Σ_u ⁺ state induced by two-photon or two-step excitation from the X¹Σ_g ⁺ state to the 2³Π_g state in the molecule K₂. These spectroscopic data are combined with recent results of Feshbach resonances and two-color photoassociation spectra for deriving the potential curves of X¹Σ_g ⁺ and a³Σ_u ⁺ up to the asymptote. The precise relative position of the triplet levels with respect to the singlet levels was achieved by including the excitation energies from the X¹Σ_g ⁺ state to the 2³Π_g state and the frequencies of the fluorescence down to the a³Σ_u ⁺ state in the simultaneous fit of both potentials. The derived precise potential curves allow for reliable modeling of cold collisions of pairs of potassium atoms in their ²S ground state. Electronic supplementary material Supplementary Online Material     

Temperature dependence of Rb2 molecule formation rate constant in a magneto-optical trap

In this paper, we report the measurement of Rb₂ molecule formation rate constant due to a two body process in a magneto-optical trap as a function of the sample temperature. The ground state molecules are detected by two-photon ionization, through the intermediate a ³Σ _u ⁺ → 2³Π _g molecular band. Our results show that the Rb₂ molecules formed in the MOT could be due to a wave shape resonance, which enhances the molecule formation rate. This effect may be used to enhance the molecule production; and therefore it maybe important to future experiments involving production and trapping of cold ground state molecules.     

Detection by two-photon ionization and magnetic trapping of cold Rb2 triplet state molecules

We present detailed experimental spectra and accurate theoretical interpretation of resonance-enhanced two-photon ionization of ultracold rubidium molecules in the 14000–17000 cm^-1 transition energy range. The dimers are formed in a magneto-optical trap by photoassociation followed by radiative decay into the a ³Σ_u⁺ lowest triplet state. The theoretical treatment of the process, which reproduces the main features of the spectra, takes into account the photoassociation and decay steps as well as the resonant ionization through the manifold of intermediate gerade states correlated to the 5S + 4D limit. In particular, the energy of the v=1 level of the potential well has been determined for the first time. In addition, a tight constraint has been put on the position of the a ³Σ_u⁺ repulsive wall. Finally, magnetic trapping of rubidium molecules in the a ³Σ_u⁺ state is demonstrated. Electronic supplementary material Online Material     

Formation of ultracold RbCs molecules by photoassociation

The formation of ultracold metastable RbCs molecules is observed in a double species magneto-optical trap through photoassociation below the ⁸⁵Rb(5S_1/2) + ¹³³Cs(6P_3/2) dissociation limit followed by spontaneous emission. The molecules are detected by resonance enhanced two-photon ionization. Using accurate quantum chemistry calculations of the potential energy curves and transition dipole moment, we interpret the observed photoassociation process as occurring at short internuclear distance, in contrast with most previous cold atom photoassociation studies. The vibrational levels excited by photoassociation belong to the 5th 0⁺ or the 4th 0^? electronic states correlated to the Rb(5P_{1/2, 3/2}) + Cs(6S_1/2) dissociation limit. The computed vibrational distribution of the produced molecules shows that they are stabilized in deeply bound vibrational states of the lowest triplet state. We also predict that a noticeable fraction of molecules is produced in the lowest level of the electronic ground state.     

Research on ultracold cesium molecule long-range states by high-resolution photoassociative spectroscopy

In this paper, an ultra-high resolution photoassociation spectroscopy study on photoassociation of cesium atoms is reported. The cold cesium gas in the magneto-optical trap is illuminated by a photoassociation laser with red-tuning as large as 40 cm⁻¹ below the 6S _1/2 + 6P _3/2 dissociation limit, and the photoassociation to the excited state ultracold molecule is detected. High signal-to-noise ratio is obtained by using the lock-in detection of the fluorescence from the modulated cold Cs atoms. The 0 _g ⁻ , 1_g and 0 _u ⁺ long-range states which correspond to 6S _1/2 + 6P _3/2 dissociation limit are present in the photoassociation spectrum. The effective coefficients of leading long-range interactions and the corresponding vibrational quantum number are obtained using LeRoy-Bernstein Law. It is found that photoassociation process creates rotating molecules and the high J value is a hint that higher partial waves participate in the PA process in the presence of trapping laser. Supported by 973 Program of China (Grant. No. 2006CB921603), the National Natural Science Foundation of China (Grant Nos. 10574084, 60678003, and 60778008), the Special Foundation for State Major Basic Research Program of China (Grant No. 2005CCA06300), and the Youth Science Foundation of Shanxi Province of China (Grant No. 20041013)     

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. Received 1st March 2001     

High sensitive photoassociation spectroscopy based on modulated ultra-cold Cs atoms

In this paper, a high sensitive photoassociation spectroscopy based on modulated ultra-cold cesium atoms is reported. The cold cesium gas in the magneto-optical trap is illuminated by a photoassociation laser with red detuning 40 cm^-1 below the 6S _1/2+6P _3/2 dissociation limit and photoassociation to the excited state ultra-cold molecules is observed. The rotationally bound levels of 0_g ^- state are well resolved using the lock-in detection. The 0_g ^-, 1_g and 0_u ⁺ long range states which connect to this dissociation limit are measured. The long-range dipole–dipole interaction constants are determined through a fit of the experimental energy levels. PACS 33.15.Mt; 33.20.Vq; 32.80.Pj     

CARS study of the vibrational kinetics of nitrogen molecules in the burning and afterglow stages of a pulsed discharge

The vibrational kinetics of the nitrogen molecule in the ground state X ¹Σ _g ⁺ in the burning and afterglow stages of a pulsed discharge are investigated by coherent anti-Stokes Raman spectroscopy (CARS). The total cross section for vibrational excitation of the nitrogen molecule by electron impact to the first eight vibrational levels is determined. The rate constant for the associative ionization reaction involving nitrogen atoms in the metastable states ² P and ² D is estimated. It is found that the best agreement between the calculated and measured populations of the nitrogen molecules in the ground state X ¹Σ _g ⁺ in the afterglow stage of a pulsed discharge is obtained when the rate constant for VV exchange K ₀₁ ¹⁰ has the value predicted by the quantum-classical Billing-Fisher model. Zh. Tekh. Fiz. 67, 34–42 (May 1997)     

Determination of the helium-4 mass in a Penning trap

The determination of the rotational quadrupole alignment of diatomic molecules via REMPI detection is investigated. In this process a high focal intensity usually increases the detection probability. At high intensities the AC Stark effect may cause a splitting of the normally degenerate m_J sublevels of a rotational state J beyond the spectral width of the exciting radiation. This leads to a selective detection of only certain m_J states with the consequence that deduced alignment factors can be misleading. From the theoretical considerations line profiles are explicitly calculated for dynamic polarizabilities which represent the B ¹Σ⁺ _u←X ¹Σ⁺ _g transition of H₂, in order to fit an experimental (3+1) REMPI spectrum and to predict (1+1') line shapes as a function of laser intensity. It is further shown that the deduced quadrupole alignment factor A ₀ ⁽²⁾ is significantly changed by the second order AC Stark effect when the intensities are chosen high enough to observe asymmetric broadened line profiles. Different combinations of relative linear polarizations of the exciting and ionizing laser beams are discussed. Received 1st August 2000 and Received in final form 2 May 2001     

Studies on the full vibrational energy spectra for some electronic states of diatomic molecular ions XY+

The first accurate studies on the vibrational spectroscopic constants and the corresponding full vibrational energy spectra of some electronic states of diatomic molecular ions XY⁺ were performed using algebraic method(AM). The AM is applied on the X¹Σ⁺ state of BeH⁺, the X²Σ⁺ state of CO⁺, the X²Π_g state of F ₂ ⁺ , the A²Π_u state of O ₂ ⁺ and the X²Σ _g ⁺ state of Li ₂ ⁺ . The results show that AM can generate accurate vibrational spectroscopic constants as well as accurate full vibrational energy spectra by using some accurate experimental vibrational energies, and that the AM vibrational energies are better than other theoretical data. __________ Translated from Chinese Journal of Atomic and Molecular Physics, 2005, 22 (4) (in Chinese)     

Combined analysis of the PFOODR data on the a 3Σ u+ , 23Πg, 23Σ g+ , 33Πg, and 43Σ g+ states of the K2 molecule

The known and new heterogeneous spectral data on the triplet states a ³Σ _u ⁺ , 2³Π_g, 2³Σ _g ⁺ , 3³Π_g, and 4³Σ _g ⁺ of the K₂ dimer are simultaneously fitted. The data published in J. Mol. Spectrosc. 234, 41 (2005) are refined. The new information used in the analysis contains the data on the 2³Σ _g ⁺ state, which have not been considered previously. The range of internuclear distances where the potential function of the lowest triplet state a ³Σ _u ⁺ is defined is extended. Original Russian Text ? V.B. Sovkov, V.S. Ivanov, D. Li, F. Xie, Li Li, 2007, published in Optika i Spektroskopiya, 2007, Vol. 103, No. 5, pp. 747–751.     

Molecular relaxations in mixtures of O2 with CO2 observed on?laser-induced gratings

Laser-induced gratings in mixtures of O₂ with CO₂ were formed by excitation of the O₂ molecules to the singlet state b ¹ Σ _g ⁺(v′=0). Density changes from heat release and from electrostriction, and variation of electric polarizability by excitation of molecules contribute to the grating. For modeling the relaxation of the excited O₂ molecules, a three-step process is assumed: Fast heat release with respect to the rotational states first, then medium fast electronic de-activation with excitation of vibrational states of the O₂ and CO₂ molecules, and then the final slow heat release processes. The observed temporal evolution of the diffraction efficiency of the grating agrees rather well with modeling. Average rates of the final relaxations and the value of the polarizability of the singlet state b ¹ Σ _g ⁺(v′=0) are determined in this way.     

Formation of cold Cs ground state molecules through photoassociation in the pure long-range state

We report on the formation of translationally cold Cs₂ ground state molecules through photoassociation in the 1_u attractive molecular state below the 6 s _1/2 +6 p _3/2 dissociation limit. The cold molecules are obtained after spontaneous decay of photoassociated molecules in a MOT and in a dark SPOT. We also used polarized atoms, in the f =3, m f =+3Zeeman ground state. Purely asymptotic and adiabatic calculations including hyperfine interaction and rotation are in excellent agreement with observed structures. As expected, the 1_u state is actually a pure long-range state, consisting of paired atoms, uniquely linked by the first terms of the multipole expansion of the electrostatic interaction. A temperature of 20 K has been measured for the molecular cloud. Received 19 July 1999     

Tunable KrF laser-induced fluorescence of C2 in a sooting flame

2 in a flame, excited by a tunable KrF laser near 248 nm. The first comprises several P and R lines of the (1,0) band of the e ³Π_g-a ³Π_u Fox–Herzberg system, with fluorescence bands extending past 350 nm. The second is the band head region of the (7,1) band of the D ¹Σ_u ⁺←B^′ 1Σ_g ⁺ system, with fluorescence at 232 nm from D to the X ¹Σ_g ⁺ ground state. Neither band has been previously observed in any environment. The flame in these experiments is highly sooting, and the C₂ seen here is likely produced by laser vaporization of the soot with subsequent laser photolysis of a C₂ precursor. In a rich flame, this fluorescence could cause interferences in other studies such as KrF laser Raman scattering. Moreover, signal level calculations suggest native C₂ near 10 ppm could be readily observed using the Fox–Herzberg excitation. Raman measurements of major species (X≥0.01) in the same flame, using the KrF laser, are in good agreement with a model prediction. Received: 2 April 1998/Revised version: 8 June 1998     

Kinetics of processes in the middle atmosphere during the laser excitation of O2 molecules

Kinetic processes taking place in the atomic-molecular system O-O₂-O₃ in the middle atmosphere with the participation of oxygen molecules in the excited electronic states O₂(a ¹Δ_g) and O₂(b ¹Σ _g ⁺ ) are analyzed in detail. The possibility of increased ozone production under the influence of solar radiation during the laser excitation of O₂ molecules in the a ¹Δ_g state is demonstrated on the basis of numerical modeling. Upper and lower bounds are determined for the densities of O₂(a ¹Δ_g) molecules at which the ozone concentration increases in the irradiated zone. Zh. Tekh. Fiz. 68, 15–23 (August 1998)     

Laser-initiated ignition of hydrogen-air mixtures

The subject of investigation is the kinetic mechanisms intensifying chain reactions that proceed in a hydrogen-air mixture when O₂ molecules dissociate under the action of laser radiation with wavelength λ _I = 193.3 nm and are excited into the b ¹Σ _g ⁺ electron state by radiation with λ _I = 762.346 nm. The efficiencies of both methods to initiate ignition are compared. Numerical simulation shows that the ignition temperature for the laser-induced excitation of O₂ molecules into theb ¹Σ _g ⁺ state is lower than for the dissociation of O₂ molecules by UV laser radiation, with the energy supplied to the mixture being the same. However, both photochemical methods are much more efficient than mere heating of the mixture by laser radiation or another source of heat.     

Ab initio calculation of excited state dipole polarizability - Application to the first 1, 3 Σ + g,u states of Li 2

Firstly, imaginary frequency-dependent dipole polarizabilities of Li in its ² S ground state and the first ² P excited state are calculated from a time-dependent gauge-invariant method using effective core pseudo-potentials and the multi-configuration one-electron wave function. C₆ dispersion coefficients of the 2 s + 2 s and 2 s + 2 p dissociations are deduced and also compared with all-electron values. Then, static polarizabilities of Li₂ in its ground and first excited ^{1, 3} Σ ⁺ _g,u states are obtained at interatomic distance corresponding to the energy minimum of each state. Received 10 May 2001 and Received in final form 14 September 2001     

Application of CI expansion techniques to the computation of two-photon absorptivities

Summary We show how conventional linear expansion techniques for both electronic and vibrational wave functions can be used for the computation of matrix elements governing the two-photon absorption probability in molecules. In particular, the²Σ⁺ A←²∏X transition matrix elements of OH and the¹Σ _g ⁺ E,F←¹Σ _g ⁺ X of H₂are computed using 1) the sum over states in the Born-Oppenheimer approximation with inclusion of vibrational wave functions, 2) solution of perturbation theory equations by expansion in the CI basis at fixed nuclei, followed by a kind of vibrational averaging. The results are compared with experiment and discussed. To speed up publication, the authors of this paper have agreed to not receive the proofs for correction.