1. Unconventional Conditions at Ultracold Temperatures 4949 1.

Ultracold molecules under control

The discovery of extrasolar planets is one of the major scientific advances of the last two decades. Hundreds of planets have now been detected and astronomers are beginning to characterize their composition and physical characteristics. To do this requires a huge quantity of spectroscopic data most of which are not available from laboratory studies. The ExoMol project will offer a comprehensive solution to this problem by providing spectroscopic data on all the molecular transitions of importance in the atmospheres of exoplanets. These data will be widely applicable to other problems and will be used for studies on cool stars, brown dwarfs and circumstellar environments. This paper lays out the scientific foundations of this project and reviews previous work in this area. A mixture of first principles and empirically tuned quantum mechanical methods will be used to compute comprehensive and very large rotation–vibration and rotation–vibration– electronic line lists. Methodologies will be developed for treating larger molecules such as methane and nitric acid. ExoMol will rely on these developments and the use of state-of-the-art

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ExoMol: molecular line lists for exoplanet and other atmospheres

▪ Abstract As progressively cooler stellar and substellar objects are discovered, the presence first of molecules and then of condensed particulates greatly complicates the understanding of their physical properties. Accurate model atmospheres that include these processes are the key to establishing their atmospheric parameters. They play a crucial role in determining structural characteristics by setting the surface conditions of model interiors and providing transformations to the various observational planes. They can reveal the spectroscopic properties of brown dwarfs and help establish their detectability. In this paper, we review the current state-of-the-art theory and modeling of the atmospheres of very low mass stars, including the coolest known M dwarfs, M subdwarfs, and brown dwarfs, i.e. Teff ≤ 4,000 K and −4.0 ≤ [M/H] ≤ +0.0. We discuss ongoing efforts to incorporate molecular and grain opacities in cool stellar spectra, as well as the latest progress in (a) deriving the effective temperature ...

Model atmospheres of very low mass stars and brown dwarfs

State-selected rubidium-87 molecules were created at rest in a dilute Bose-Einstein condensate of rubidium-87 atoms with coherent free-bound stimulated Raman transitions. The transition rate exhibited a resonance line shape with an extremely narrow width as small as 1.5 kilohertz. The precise shape and position of the resonance are sensitive to the mean-field interactions between the molecules and the atomic condensate. As a result, we were able to measure the molecule-condensate interactions. This method allows molecular binding energies to be determined with unprecedented accuracy and is of interest as a mechanism for the generation of a molecular Bose-Einstein condensate.

Molecules in a Bose-Einstein condensate

A new bosonic species of ultracold alkali heteromolecule with a considerable electric dipole moment has been cooled to its vibrational ground state.

Creation of an Ultracold Gas of Ground-State Dipolar ^{23}Na^{87}Rb Molecules.

Laser-induced fluorescence (LIF) spectra $(4)\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+}\ensuremath{\rightarrow}A\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+}--b\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Pi}$ and collisionally enhanced $A\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+}--b\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Pi}\ensuremath{\rightarrow}X\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+}$ LIF spectra measured by Fourier transform spectrometer with the resolution of $0.03--0.05\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$ provided about 1160 term values of the $e$-symmetry rovibronic levels of the fully mixed $A\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+}$ and $b\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Pi}$ states of a NaCs molecule. Direct deperturbation treatment of the experimental data field, covering rotational quantum numbers $J∊[5,151]$ of the $A\text{\ensuremath{-}}b$ complex in the energy region $E∊[10577,13668]\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$, was accomplished in the framework of the inverted channel-coupling approach by means of the $4\ifmmode\times\else\texttimes\fi{}4$ Hamiltonian constructed on Hund's coupling case $(a)$ basis functions. The nonequidistant spin-orbit splitting of the $b\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Pi}_{\ensuremath{\Omega}=0,1,2}$ substates and the indirect coupling $A\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+}--b\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Pi}_{\ensuremath{\Omega}=1}$ matrix element were introduced in the Hamiltonian phenomenologically to account for the regular perturbations by remote states manifold. The expanded Morse oscillator model was used to approximate both potential energy curves of the mutually perturbed states and spin-orbit coupling matrix elements as an analytical function of internuclear distance. Overall 31 fitting parameters have been required to reproduce 98% of experimental term values with a standard deviation of $0.006\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$, which is consistent with the uncertainty of the experiment. The term values deperturbation analysis was confirmed by a calculation of relative intensity distributions in the $A--b\ensuremath{\rightarrow}X$ LIF progressions. The predicted probabilities for both weakly and strongly perturbed levels agree with their experimental counterparts within the accuracy of measurements. The evaluated nonadiabatic $A\text{\ensuremath{-}}b$ wave functions were applied for a prediction of radiative lifetimes of the $A\text{\ensuremath{-}}b$ complex as well as transition probabilities of the $a\ensuremath{\rightarrow}A--b\ensuremath{\rightarrow}X$ cycle proposed in Stwalley, Eur. Phys. J. D 31, 221 (2004), for efficient transformation of ultracold molecules to their absolute ground level ${v}_{X}=0$; ${J}_{X}=0$.

Solution of the fully-mixed-state problem: Direct deperturbation analysis of the A Σ + 1 – b Π 3 complex in a NaCs dimer

We present new c 3Σ+→a 3Σ+ laser induced fluorescence spectra of the NaK molecule, which clearly indicate that v0=20 is the first vibrational level of the c 3Σ+ state lying above v=0 of B 1Π state. These spectra are used in a multistep deperturbation (B 1Π∼c 3Σ+∼b 3Π) procedure to obtain improved a 3Σ+, b 3Π and c 3Σ+ potential energy curves. The deperturbation analysis is confirmed by the calculated electronic B 1Π∼c 3Σ+ and c 3Σ+∼b 3Π spin–orbit matrix elements obtained from many-body multipartitioning perturbation theory employing the relativistic effective potential method.

The c 3Σ+,b 3Π, and a 3Σ+ states of NaK revisited

The paper presents the study of the fully mixed A 1Σ+–b 3Π complex of the NaRb molecule based on high-resolution sub-Doppler spectroscopy and intensity measurements, ab initio relativistic calculations of energies, transition moments and spin–orbit interactions, as well as an inverted channel-coupling approach (ICCA) deperturbation analysis A two-laser V-type pump–probe excitation scheme was employed to obtain A←X transition frequencies to 16 A-state vibrational levels from v=6 to v=21 with J from 8 to 23 Additionally, relative intensities in laser-induced A→X fluorescence spectra have been recorded, including progressions with all observable transitions to the ground state vibronic levels, the latter yielding unambiguous v assignment of the A-state levels observed All experimental rovibronic term values and all measured intensity distributions were embedded in a direct simultaneous weighted nonlinear fitting in the framework of an elaborated ICCA allowing us to obtain deperturbed relativistic diabatic

High resolution spectroscopy and channel-coupling treatment of the A 1Σ+–b 3Π complex of NaRb

High resolution Fourier transform spectra (FTS) of laser induced fluorescence (LIF) of $C\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+};D\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Pi}\ensuremath{\rightarrow}A\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+}--b\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Pi}$ and $A\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+}--b\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Pi}\ensuremath{\rightarrow}X\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+}$ transitions in ${\mathrm{Na}}^{85}\mathrm{Rb}$ and ${\mathrm{Na}}^{87}\mathrm{Rb}$ were obtained. An analysis of the direct LIF spectra together with the rotational relaxation satellites provided highly accurate rovibronic term values for $(4\ensuremath{\leqslant}J\ensuremath{\leqslant}163)$ of the $A\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+}--b\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Pi}$ complex, covering about 1950 mostly singlet levels $0\ensuremath{\leqslant}{v}_{A}\ensuremath{\leqslant}49$ and a considerable number $(g360)$ of the predominantly triplet $b\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Pi}_{0,1}$ sublevels. The direct deperturbation analysis of the singlet-triplet $A--b$ complex was performed by means of the inverted channel-coupling approach with Hund's coupling case $\mathbf{a}$ basis functions. The electronic matrix elements of the model $4\ifmmode\times\else\texttimes\fi{}4$ Hamiltonian were defined as piecewise analytical functions of the internuclear distance. Besides the Born-Oppenheimer potential energy curves of the mutually perturbed states and the off-diagonal spin-orbit (SO) $A--b$ coupling function, the SO splitting of the $b\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Pi}$ state was determined due to the pronounced electronic-rotation interaction between the $b\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Pi}_{0}$ and $b\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Pi}_{1}$ components observed for high $J$ levels. Overall, 24 mass-invariant fitting parameters have been required to reproduce about 2300 experimental term values of both isotopomers with a standard deviation of $0.012\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$, which is consistent with the uncertainty of the FTS experiment. An analytical mapping procedure based on a reduced variable representation of the radial coordinate was used to diminish the computational effort for the uniform finite-difference grid solution of the coupled-channel equations. The derived nonadiabatic $A--b$ wave functions were used to evaluate the $A\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+}--b\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Pi}--D\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Pi}$, $a\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Sigma}^{+}$, $X\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+}$ rovibronic transition probabilities. The relative intensity distributions predicted for the $D\ensuremath{\rightarrow}A--b$ and $A--b\ensuremath{\rightarrow}X$ LIF progressions agree with their experimental counterparts within the accuracy of the measurements. The calculated $A--b--a$, $X$ transition probabilities were applied for simulation of the stimulated Raman $a\ensuremath{\rightarrow}A--b\ensuremath{\rightarrow}X$ processes, which can lead to efficient formation of ultracold NaRb molecules in the ground level ${v}_{X}=0$; ${J}_{X}=0$.

E. A. Pazyuk

Papers

Solution of the fully-mixed-state problem: Direct deperturbation analysis of the A Σ + 1 – b Π 3 complex in a NaCs dimer

The c 3Σ+,b 3Π, and a 3Σ+ states of NaK revisited

High resolution spectroscopy and channel-coupling treatment of the A 1Σ+–b 3Π complex of NaRb

Deperturbation treatment of theAΣ+1–bΠ3complex of NaRb and prospects for ultracold molecule formation inXΣ+1(v=0;J=0)

Laser synthesis of ultracold alkali metal dimers: optimization and control