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APS

Photoassociation and Rovibrational Cooling of Sodium Cesium Using Chirped Laser Pulses and Stimulated Raman Adiabatic Passage

Stéphane Valladier, Michael A. Morrison

Published May 1, 2011• 0 citations
OpenAlex

Abstract

This dissertation presents the study of how two laser pulses can bind sodium and cesium atoms at ultracold temperature ($T=200\\mu K$) 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 $A^1\\Sigma^+-b^3\\Pi$ 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 ($v_X=32, J_X=0$) rovibrational state of the $X^1\\Sigma^+$ ground electronic state of NaCs. \nThe transfer process relies either on a sequence of $\\pi$-pulses, or uses stimulated Raman adiabatic passage (STIRAP). \nLasers with narrow spectral bandwidth ($0.5\\GHz$) always yield a final population in $\\ket{X^1\\Sigma^+, v_X=32, J_X=0}$ higher than 95\\% in less than 4 ns.

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This theoretical paper presents numerical calculations for the photoassociation of ultracold cesium atoms with a chirped laser pulse and a detailed analysis of the results. In contrast with earlier work, the initial state is represented by a stationary continuum wave function. In the chosen example, it is shown that an important population transfer is achieved to $\ensuremath{\approx}15$ vibrational levels in the vicinity of the $v=98$ bound level in the external well of the ${0}_{g}^{\ensuremath{-}}(6s+6{p}_{3∕2})$ potential. Such levels lie in the energy range swept by the instantaneous frequency of the pulse, thus defining a ``photoassociation window.'' Levels outside this window may be significantly excited during the pulse, but no population remains there after the pulse. Finally, the population transfer to the last vibrational levels of the ground $a\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\sum}_{u}^{+}(6\mathrm{s}+6\mathrm{s})$ state is significant, making stable molecules. The results are interpreted in the framework of a two-state model as an adiabatic inversion mechanism, efficient only within the photoassociation window. The large value found for the photoassociation rate suggests promising applications. The present chirp has been designed in view of creating in the excited state a vibrational wave packet that is focusing at the barrier of the double-well potential.

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FORMATION OF ULTRACOLD CESIUM MOLECULES IN THE GROUND ELECTRONIC STATE

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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.

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Ultracold NaK2 Trimers: From Photoassociation to Coherent Ground-State Stabilization

Baraa Shammout

The assembly and coherent control of ultracold molecules have opened new horizons in quantum science with applications in ultracold chemistry, quantum information, quantum simulation, precision metrology and fundamental physics. While considerable progress has been achieved in controlling diatomic molecules at ultracold temperatures, extending to atom-diatom collisions and triatomic systems introduces additional internal structure, anisotropy, and interaction complexity, enabling access to many-body phenomena. This dissertation presents a detailed theoretical study on the production and stabilization of ultracold alkali-metal triatomic molecules, with a particular focus on the NaK2 molecular species. First, long-range photoassociation in ultracold NaK(X^1Σ+) + K(4s) mixtures is investigated near the molecular transition X^1Σ+ → b^3Π. Photoassociation rates into weakly bound trimers in the electronically excited 3^2A' state are evaluated under experimentally relevant conditions. The calculated photoassociation rates indicate experimentally feasible and spectrally selective routes for detecting ultracold atom–diatom photoassociation resonances, while suppressing competing diatomic loss channels. Second, a microwave-assisted association mechanism is introduced for coherently binding ultracold atoms and polar molecules into weakly bound triatomic molecules on the ground-state 1^2A' potential energy surface. This process relies on the interaction between the electric component of the microwave field and the permanent electric dipole moment of the NaK molecule. In the presence of the anisotropic atom–diatom potential, which couples the molecular rotation to the relative angular motion, the microwave field can drive transitions from scattering states to weakly bound trimer states entirely in the electronic ground-state of the triatomic molecule, without involving spontaneous emission. This process is therefore intrinsically coherent and particularly suited to closed-shell polar molecules for which magnetically tunable Feshbach resonances are weak or absent. Finally, candidate pathways toward coherent population transfer to the absolute rovibronic ground state of NaK2 are explored using bridge states belonging to the excited 3^2A' electronic state, such as those identified in [Ref.1]. The relevant potential energy surfaces, transition dipole moments, and rovibrational structures are analyzed, revealing favorable conditions for future stimulated Raman adiabatic passage scheme. The theoretical modeling combines high-level electronic-structure calculations with nuclear-motion methods across multiple energy and length scales. Three-dimensional potential energy surfaces and electronic transition dipole moment surfaces were obtained from ab initio multireference configuration interaction calculations employing effective-core pseudopotentials and core-polarization potentials. Nuclear motion was treated using coupled-channel methods for describing weakly bound states and discrete variable representation methods for deeply bound rovibrational states. The resulting wavefunctions were subsequently used to evaluate Franck–Condon factors, photo- and microwave association rates, and transition strengths relevant to experimental implementation. Overall, this dissertation provides an extensive theoretical framework for the formation, detection and ground-state stabilization of ultracold NaK2 trimers. Reference: [1] J. Cao, B.-Y. Wang, H. Yang, Z.-J. Fan, Z. Su, J. Rui, B. Zhao, and J.-W. Pan, “Observation of photoassociation resonances in ultracold atom-molecule collisions,” Phys. Rev. Lett., vol. 132, p. 093403, 2024.

•Jan 1, 2026•0 citations

Pulse sequences in photoassociation via adiabatic passage

Xuan Li, William Dupre, Gregory A. Parker

We perform a detailed study of pulse sequences in a photoassociation via adiabatic passage (PAP) process to transfer population from an ensemble of ultracold atomic clouds to a vibrationally cold molecular state. We show that an appreciable final population of ultracold NaCs molecules can be achieved with optimized pulses in either the 'counter-intuitive' ( t P > t S ) or 'intuitive' ( t P < t S ) PAP pulse sequences, with t P and t S denoting the temporal centers of the pump and Stokes pulses, respectively. By investigating the dependence of the reactive yield on pulse sequences, in a wide range of t P – t S , we show that there is not a fundamental preference to either pulse sequence in a PAP process. We explain this no-sequence-preference phenomenon by analyzing a multi-bound model so that an analogy can be drawn to the conventional stimulated Raman adiabatic passage.

New Journal of Physics•Jul 3, 2012•1 citation
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.
This theoretical paper presents numerical calculations for the photoassociation of ultracold cesium atoms with a chirped laser pulse and a detailed analysis of the results. In contrast with earlier work, the initial state is represented by a stationary continuum wave function. In the chosen example, it is shown that an important population transfer is achieved to $\ensuremath{\approx}15$ vibrational levels in the vicinity of the v=98v=98v=98 bound level in the external well of the ${0}_{g}^{\ensuremath{-}}(6s+6{p}_{3∕2})$ potential. Such levels lie in the energy range swept by the instantaneous frequency of the pulse, thus defining a ``photoassociation window.'' Levels outside this window may be significantly excited during the pulse, but no population remains there after the pulse. Finally, the population transfer to the last vibrational levels of the ground $a\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\sum}_{u}^{+}(6\mathrm{s}+6\mathrm{s})$ state is significant, making stable molecules. The results are interpreted in the framework of a two-state model as an adiabatic inversion mechanism, efficient only within the photoassociation window. The large value found for the photoassociation rate suggests promising applications. The present chirp has been designed in view of creating in the excited state a vibrational wave packet that is focusing at the barrier of the double-well potential.
We investigate theoretically the preparation of ultracold photoassociated Cs 2 molecules in the lowest vibrational level of the ground electronic state via the stimulated Raman adiabatic passage (STIRAP) by solving the time-dependent Schrödinger equation using the mapped Fourier grid method. A negative chirped laser pulse is used to produce the unstable photoassociated molecules in the excited electronic state. A dump pulse is utilized to transfer a partial population of the unstable photoassociated molecules to the vibrational v″ = 18 level of the ground electronic state. This part of population is then transferred to the v″ = 0 level of the ground electronic state by the pump and Stokes laser pulses via an intermediate state which is taken to be the v′ = 7 level of the excited electronic state, forming the stable photoassociated molecules. The population transfer efficiency from v″ = 18 to v″ = 0 in the ground electronic state reaches 96.2% via the STIRAP.
We develop a theoretical description of photoassociative stimulated Raman adiabatic passage (STIRAP) near a Feshbach resonance in a thermal atomic gas. We show that it is possible to use low-intensity laser pulses to directly excite pairs of atoms in the continuum near a Feshbach resonance and to transfer most of the atomic cloud to the lowest rovibrational level of the molecular ground state. For a broad resonance, commonly found in several mixtures of alkali atoms, our model predicts a transfer efficiency up to 97% for a given atom pair, and up to 70% when averaged over an atomic ensemble. The laser intensities and pulse durations needed for such an optimal transfer, 10 2 –10 3 W cm −2 and several microseconds, are easily achievable experimentally. A single pair of STIRAP pulses converts an estimated fraction f ∼10 −6 –10 −4 of atoms in an atomic ensemble, leading to the production of 10–1000 molecules in a large sample of 10 7 atoms. A total of ∼10 4 –10 6 pulse pairs are thus required to transfer most atoms into molecules. Such an efficiency compares with or surpasses currently available techniques for creating stable diatomic molecules, and the versatility of this approach simplifies its potential use for many molecular species.
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 ${b}^{3}{\mathrm{\ensuremath{\Pi}}}_{0}{}^{+}$ 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.
The assembly and coherent control of ultracold molecules have opened new horizons in quantum science with applications in ultracold chemistry, quantum information, quantum simulation, precision metrology and fundamental physics. While considerable progress has been achieved in controlling diatomic molecules at ultracold temperatures, extending to atom-diatom collisions and triatomic systems introduces additional internal structure, anisotropy, and interaction complexity, enabling access to many-body phenomena. This dissertation presents a detailed theoretical study on the production and stabilization of ultracold alkali-metal triatomic molecules, with a particular focus on the NaK2 molecular species. First, long-range photoassociation in ultracold NaK(X^1Σ+) + K(4s) mixtures is investigated near the molecular transition X^1Σ+ → b^3Π. Photoassociation rates into weakly bound trimers in the electronically excited 3^2A' state are evaluated under experimentally relevant conditions. The calculated photoassociation rates indicate experimentally feasible and spectrally selective routes for detecting ultracold atom–diatom photoassociation resonances, while suppressing competing diatomic loss channels. Second, a microwave-assisted association mechanism is introduced for coherently binding ultracold atoms and polar molecules into weakly bound triatomic molecules on the ground-state 1^2A' potential energy surface. This process relies on the interaction between the electric component of the microwave field and the permanent electric dipole moment of the NaK molecule. In the presence of the anisotropic atom–diatom potential, which couples the molecular rotation to the relative angular motion, the microwave field can drive transitions from scattering states to weakly bound trimer states entirely in the electronic ground-state of the triatomic molecule, without involving spontaneous emission. This process is therefore intrinsically coherent and particularly suited to closed-shell polar molecules for which magnetically tunable Feshbach resonances are weak or absent. Finally, candidate pathways toward coherent population transfer to the absolute rovibronic ground state of NaK2 are explored using bridge states belonging to the excited 3^2A' electronic state, such as those identified in [Ref.1]. The relevant potential energy surfaces, transition dipole moments, and rovibrational structures are analyzed, revealing favorable conditions for future stimulated Raman adiabatic passage scheme. The theoretical modeling combines high-level electronic-structure calculations with nuclear-motion methods across multiple energy and length scales. Three-dimensional potential energy surfaces and electronic transition dipole moment surfaces were obtained from ab initio multireference configuration interaction calculations employing effective-core pseudopotentials and core-polarization potentials. Nuclear motion was treated using coupled-channel methods for describing weakly bound states and discrete variable representation methods for deeply bound rovibrational states. The resulting wavefunctions were subsequently used to evaluate Franck–Condon factors, photo- and microwave association rates, and transition strengths relevant to experimental implementation. Overall, this dissertation provides an extensive theoretical framework for the formation, detection and ground-state stabilization of ultracold NaK2 trimers. Reference: [1] J. Cao, B.-Y. Wang, H. Yang, Z.-J. Fan, Z. Su, J. Rui, B. Zhao, and J.-W. Pan, “Observation of photoassociation resonances in ultracold atom-molecule collisions,” Phys. Rev. Lett., vol. 132, p. 093403, 2024.
We perform a detailed study of pulse sequences in a photoassociation via adiabatic passage (PAP) process to transfer population from an ensemble of ultracold atomic clouds to a vibrationally cold molecular state. We show that an appreciable final population of ultracold NaCs molecules can be achieved with optimized pulses in either the 'counter-intuitive' ( t P > t S ) or 'intuitive' ( t P < t S ) PAP pulse sequences, with t P and t S denoting the temporal centers of the pump and Stokes pulses, respectively. By investigating the dependence of the reactive yield on pulse sequences, in a wide range of t P – t S , we show that there is not a fundamental preference to either pulse sequence in a PAP process. We explain this no-sequence-preference phenomenon by analyzing a multi-bound model so that an analogy can be drawn to the conventional stimulated Raman adiabatic passage.