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Physical Review A

Two-photon Raman transition channels of NaCs predicted from ab initio calculations

Jingbo Wei, Peng Li, Jizhou Wu, V. B. Sovkov, Wenliang Liu, Yuqing Li, Yongming Fu, Feng Xie, Jie Ma

Published Jun 22, 2022• 3 citations
Publisher

Abstract

Obtaining effective spontaneous radiative transition channels is a fundamental topic in the preparation of ultracold rovibrational ground states of molecules. Herein, the ranges of prospective transition channels in the NaCs dimer are predicted via exploring the complex energy level structure and transition properties. The potential energy curves of \ensuremath{\Lambda}-$S$ states and \ensuremath{\Omega} states, spectroscopy constants, absolute energies of bound states, and transition information (Frank-Condon factors, lifetimes, transition dipole moments) have been researched. With this purpose, the results of our experiment on binding energies of the ${b}^{3}{\mathrm{\ensuremath{\Pi}}}_{0}{}^{+}$ rovibrational states are analyzed; the transition from the higher (photoassociated) ${}^{1}\mathrm{\ensuremath{\Pi}}$ state to the ground ${X}^{1}{\mathrm{\ensuremath{\Sigma}}}^{+}$ state is discussed. The wavelengths of the two lasers are predicted as 622.8-656.7 nm and 896.3-969.8 nm with the ${B}^{1}{\mathrm{\ensuremath{\Pi}}}_{1}$ and ${c}^{3}{\mathrm{\ensuremath{\Sigma}}}_{1}^{+}$ states, respectively, for the stimulated raman adiabatic passage method.

DOI
10.1103/physreva.105.063322

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Formation and analysis of ultracold polar molecules

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Alkali hydride molecules are polar, exhibiting large ground-state dipole moments. As ultracold sources of alkali atoms, as well as hydrogen, have been created in the laboratory, we explore theoretically the feasibility of forming such molecules from a mixture of the ultracold atomic gases, employing various photoassociation schemes. In this work we use lithium and sodium hydride as benchmark systems to calculate molecule formation rates through stimulated one-photon radiative association directly from the continuum as well as two-photon stimulated radiative association (Raman transfer) and excitation to bound levels of an excited state followed by spontaneous emission to the ground state. Using accurate molecular potential energy curves and dipole transition moments and with laser intensities and MOT densities that are easily attainable experimentally, we have found that substantial molecule formation rates can be realized even after the effect of back-stimulation has been accounted for. We examine the spontaneous emission cascade which takes place from the upper vibrational levels of the singlet ground state on a time scale of milliseconds. Because photon emission in the cascade process does not contribute to trap loss, a sizable population of molecules in the lowest vibrational level can be achieved. The triplet ground electronic state is of particular interest for experimental efforts since, although it has never been observed experimentally, molecular structure calculations of the a3Σ+ state for LiH and NaH predict a small van der Waals attraction, with a potential energy well so shallow that it can support only one bound rotational-vibrational level. Any molecule formed in the triplet ground state would then be immediately in the lowest and most stable level of that state and would be quite long-lived, unlike molecules in high vibrational levels which have significantly shorter lifetimes. As an analysis of our method of calculating molecule formation rates, we investigate more thoroughly the two-photon stimulated photoassociation process by employing the exact treatment of Dalgarno & Lewis to solve the Raman scattering problem. ^

•Jan 1, 2007•1 citation
Obtaining effective spontaneous radiative transition channels is a fundamental topic in the preparation of ultracold rovibrational ground states of molecules. Herein, the ranges of prospective transition channels in the NaCs dimer are predicted via exploring the complex energy level structure and transition properties. The potential energy curves of \ensuremath{\Lambda}-SSS states and \ensuremath{\Omega} states, spectroscopy constants, absolute energies of bound states, and transition information (Frank-Condon factors, lifetimes, transition dipole moments) have been researched. With this purpose, the results of our experiment on binding energies of the b3\ensuremathΠ0+{b}^{3}{\mathrm{\ensuremath{\Pi}}}_{0}{}^{+}b3\ensuremathΠ0​+ rovibrational states are analyzed; the transition from the higher (photoassociated) 1\ensuremathΠ{}^{1}\mathrm{\ensuremath{\Pi}}1\ensuremathΠ state to the ground X1\ensuremathΣ+{X}^{1}{\mathrm{\ensuremath{\Sigma}}}^{+}X1\ensuremathΣ+ state is discussed. The wavelengths of the two lasers are predicted as 622.8-656.7 nm and 896.3-969.8 nm with the B1\ensuremathΠ1{B}^{1}{\mathrm{\ensuremath{\Pi}}}_{1}B1\ensuremathΠ1​ and c3\ensuremathΣ1+{c}^{3}{\mathrm{\ensuremath{\Sigma}}}_{1}^{+}c3\ensuremathΣ1+​ states, respectively, for the stimulated raman adiabatic passage method.
Calculations of the adiabatic potential energy curves and the transition dipole moments between the ground (A 1 Σ + ) and the first excited (A 1 Σ + ) states have been determined for the LiCs and NaCs molecules. The calculations are performed using an ab initio approach based on non-empirical pseudopotentials for Cs + , Li + and Na + cores, parameterized l -dependent polarization potentials and full configuration interaction calculations. The potential energy curves and the transition dipole moment are used to estimate the radiative lifetimes of the vibrational levels of the A + Σ + state using the Franck–Condon (FC) approximation and the approximate sum rule method. The radiative lifetimes associated with the A + Σ + state are presented here for the first time. These data can help experimentalists to optimize photoassociative formation of ultracold molecules and their longevity in a trap or in an optical lattice.
Abstract We present a study of two-photon pathways for the transfer of NaCs molecules to their rovibrational ground state. Starting from NaCs Feshbach molecules, we perform bound-bound excited state spectroscopy in the wavelength range from 900 nm to 940 nm, covering more than 30 vibrational states of the c 3 Σ + , b 3 Π , and B 1 Π electronic states. Analyzing the rotational substructure, we identify the highly mixed c 3 Σ 1 + | v = 22 ⟩ ∼ b 3 Π 1 | v = 54 ⟩ state as an efficient bridge for stimulated Raman adiabatic passage. We demonstrate transfer into the NaCs ground state with an efficiency of up to 88(4)%. Highly efficient transfer is critical for the realization of many-body quantum phases of strongly dipolar NaCs molecules and high fidelity detection of single molecules, for example, in spin physics experiments in optical lattices and quantum information experiments in optical tweezer arrays.
In this thesis properties of ultracold alkali dimers are studied both theoretically and experimentally. In the first, theoretical, part, the prospects for the formation of ultracold LiCs dimers in deeply bound vibrational levels using photoassociation (PA) are investigated. Furthermore a previous systematic investigation of the structure of all alkali dimers is extended by the ab initio calculation of static dipole polarizabilities. An extensive comparison with other published results supports the reliability of the chosen method. Based on these results an experimental scheme for the creation of an sample of oriented ultracold dipolar molecules is developed. In the second, experimental part the formation of LiCs ground state molecules by PA is investigated. PA spectroscopy is used to improve the accuracy of the potential energy curve for the B1P and the value of the dissociation energy of the X1S+ state significantly. The rovibrational distribution of ground state molecules is probed in a combination of resonance-enhanced multi-photon ionization and depletion spectroscopy. A simple scheme is found to form ultracold polar LiCs molecules in the absolute ground state X1S+,v''=0,J''=0. In a quasi-electrostatic trap created by a CO2 laser, LiCs molecules are formed and stored. A lifetime of 24(3)s, limited by collisions with background gas, is observed and rate coefficients for inelastic collisions between LiCs in high vibrational states and Cs atoms are determined. The long storage time facilitates the observation of radiative decay of polar molecules towards lower vibrational levels.
This dissertation presents the study of how two laser pulses can bind sodium and cesium atoms at ultracold temperature (T=200muKT=200\\mu KT=200muK) into an ultracold, polar, diatomic molecule with a definite quantum state. \nA single-channel scattering model represents the initial continuum state, and two different models represent the intermediate state: one excluding spin-orbit coupling effects in the intermediate state, the other accounting for such effects. \nWe calculate the A1Sigma+−b3PiA^1\\Sigma^+-b^3\\PiA1Sigma+−b3Pi spin-orbit coupled wave functions using a basis expansion technique, and validate the results by comparing to experimentally obtained, spin-orbit coupled energy levels. \nThe computation of photoassociation rates between the continuum state and the intermediate states reveals the crucial importance of spin-orbit coupling. \nFurthermore, this study shows how the spectral bandwidth (narrow \\vs broad), the chirping (chirped vs. unchirped), the detunings, the intensities, and the pulse delay (intuitive \\vs counter-intuitive sequence) of the lasers affect the transfer of population from the continuum scattering state to a comparatively low-lying (vX=32,JX=0v_X=32, J_X=0vX​=32,JX​=0) rovibrational state of the X1Sigma+X^1\\Sigma^+X1Sigma+ ground electronic state of NaCs. \nThe transfer process relies either on a sequence of pi\\pipi-pulses, or uses stimulated Raman adiabatic passage (STIRAP). \nLasers with narrow spectral bandwidth (0.5GHz0.5\\GHz0.5GHz) always yield a final population in ketX1Sigma+,vX=32,JX=0\\ket{X^1\\Sigma^+, v_X=32, J_X=0}ketX1Sigma+,vX​=32,JX​=0 higher than 95\\% in less than 4 ns.
We recently reported the formation of ultracold LiCs molecules in the rovibrational ground state X1sigma+, v" = 0,J" = 0 (J. Deiglmayr et al., Phys. Rev. Lett., 2008, 101, 133004). Here we discuss details of the experimental setup and present a thorough analysis of the photoassociation step including the photoassociation line shape. We predict the distribution of produced ground state molecules using accurate potential energy curves combined with an ab initio dipole transition moment and compare this prediction with experimental ionization spectra. Additionally we improve the value of the dissociation energy for the X1sigma+ state by high resolution spectroscopy of the vibrational ground state.
Alkali hydride molecules are polar, exhibiting large ground-state dipole moments. As ultracold sources of alkali atoms, as well as hydrogen, have been created in the laboratory, we explore theoretically the feasibility of forming such molecules from a mixture of the ultracold atomic gases, employing various photoassociation schemes. In this work we use lithium and sodium hydride as benchmark systems to calculate molecule formation rates through stimulated one-photon radiative association directly from the continuum as well as two-photon stimulated radiative association (Raman transfer) and excitation to bound levels of an excited state followed by spontaneous emission to the ground state. Using accurate molecular potential energy curves and dipole transition moments and with laser intensities and MOT densities that are easily attainable experimentally, we have found that substantial molecule formation rates can be realized even after the effect of back-stimulation has been accounted for. We examine the spontaneous emission cascade which takes place from the upper vibrational levels of the singlet ground state on a time scale of milliseconds. Because photon emission in the cascade process does not contribute to trap loss, a sizable population of molecules in the lowest vibrational level can be achieved. The triplet ground electronic state is of particular interest for experimental efforts since, although it has never been observed experimentally, molecular structure calculations of the a3Σ+ state for LiH and NaH predict a small van der Waals attraction, with a potential energy well so shallow that it can support only one bound rotational-vibrational level. Any molecule formed in the triplet ground state would then be immediately in the lowest and most stable level of that state and would be quite long-lived, unlike molecules in high vibrational levels which have significantly shorter lifetimes. As an analysis of our method of calculating molecule formation rates, we investigate more thoroughly the two-photon stimulated photoassociation process by employing the exact treatment of Dalgarno & Lewis to solve the Raman scattering problem. ^