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arXiv:quant-ph/0309094 · Physical Review A

Model study on the photoassociation of a pair of trapped atoms into an ultralong-range molecule

Bimalendu Deb, Li You

Published Sep 22, 2003• 11 citations
arXivHTMLPDF

Abstract

Using the method of quantum-defect theory, we calculate the ultra-long-range molecular vibrational states near the dissociation threshold of a diatomic molecular potential which asymptotically varies as $\ensuremath{-}{1/R}^{3}.$ The properties of these states are of considerable interest as they can be formed by photoassociation (PA) of two ground-state atoms. The Franck-Condon overlap integrals between the harmonically trapped atom-pair states and the ultra-long-range molecular vibrational states are estimated and compared with their values for a pair of untrapped free atoms in the low-energy scattering state. We find that the binding between a pair of ground-state atoms by a harmonic trap has significant effect on the Franck-Condon integrals and thus can be used to influence PA. Trap-induced binding between two ground-state atoms may facilitate coherent PA dynamics between the two atoms and the photoassociated diatomic molecule.

DOI
10.1103/physreva.68.033408

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Photoassociation spectroscopy

J. Weiner

Introduction If, while approaching on an unbound ground-state potential, two atoms absorb a photon and couple to an excited bound molecular state, they are said to undergo photoassociation. Figure 5.1 illustrates the process. At long range electrostatic dispersion forces give rise to the ground-state molecular potential varying as C 6 / R 6 . If the two atoms are homonuclear, then a resonant dipole–dipole interaction sets up ± C 3 / R 3 excited-state repulsive and attractive potentials. Figure 5.2 shows the actual long-range excited potential curves for the sodium dimer, originating from the 2 S ½ + 2 P 3/2 and 2 S ½ + 2 P ½ separated atom states. For cold and ultracold photoassociation processes the long-range attractive potentials play the key role; the repulsive potentials figure importantly in optical shielding and suppression, the subject of Chapter 6. In the presence of a photon with frequency ω p the colliding pair with kinetic energy k B T couples from the ground-state to the attractive molecular state in a free–bound transition near the Condon point R C , the point at which the difference potential just matches ћω p . Scanning the probe laser ω p excites population of vibration–rotation states in the excited bound potential and generates a free–bound spectrum. This general class of measurements is called photoassociative spectroscopy (PAS) and can be observed in several different ways. The observation may consist of bound-state decay by spontaneous emission, most probably as the nuclei move slowly around the outer turning point, to some distribution of continuum states on the ground potential controlled by bound–free nuclear Franck–Condon overlap factors.

Cambridge University Press eBooks•Dec 4, 2003•0 citations

Formation of deeply bound LiRb molecules via photoassociation to near asymptotic states

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We present the results of a spectroscopic study LiRb molecules created via photoassociation (PA) to vibration levels of the 4(1) potential. Atoms are first cooled and trapped in a dual species 7Li/ 85Rb magneto-optical trap (MOT) at temperatures of ≈ 1 mK or less. In a cold sample of sufficient density, PA occurs when a resonant laser field induces a free-bound transition to create molecules in an excited electronic potential. After spontaneous emission the molecules decay to a mixture of free atoms and bound molecules depending on the Franck-Condon factors (FCFs) of the excited and ground state vibrational wavefunctions. While excited LiRb * has been previously detected by trap loss fluorescence detection, ionization spectroscopy is required to determine the population of ground state levels after decay. We detect ground state molecules via resonantly enhanced multiphoton ionization (REMPI) where a two photon ionization transition is enhanced by an intermediate resonance. The intermediate resonances match progressions from the D1Π and possibly B1&Pgr; potentials, many of which have known energies obtained from previous heat pipe experiments. This is contrary to the expectation that weakly bound LiRb * should primarily decay to weakly bound levels of the ground state and could point to a possible path for creating molecules in the rovibronic ground state.

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We study the photoassociative collisional loss of laser-cooled Rb atoms from a far-off resonance optical dipole force atom trap. We obtain a well-resolved photoassociation spectrum from 50 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ to 980 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ below the first excited dissociation limit of the ${\mathrm{Rb}}_{2}$ molecule. Two vibrational series associated with excited ${\mathrm{Rb}}_{2}$ $^{3}\mathrm{\ensuremath{\Sigma}}_{\mathit{g}}^{+}$ states are clearly visible. Oscillations in the associated Franck-Condon factors reflect the structure of the triplet ground state wave function. Our results clearly demonstrate the potential of photoassociation spectroscopy as a new probe of molecular structure.

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This work explores the vibrational state-selective photoassociation (PA) in the ground state of the HX (X = F, Cl, I) molecule by solving the time-dependent Schrödinger equation. For the three systems, the vibrational level of [Formula: see text] is set to be the target state and the PA probability of the target state is calculated and compared by considering different initial collision momentums. It is found that the PA probabilities are in accordance with Franck–Condon overlap integral for the HI and HCl systems, but it is not the case for the HF system. Moreover, for the HF system, it is shown that the PA probability of the target state is largest and the multiphoton transition is more likely to occur.

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Photoassociation, the bound←free absorption of a photon by a colliding pair of atoms, has been studied experimentally in the Kr–F and Xe–I systems and is demonstrated to be an effective tool for deducing molecular interaction potentials and for determining the dependence of the relative electronic transition moment on internuclear separation (R) in small molecules having dissociative ground states. Specifically, the excitation (‘‘action’’) spectrum for the photoassociation of thermalized Kr(4p6 1S0)–F(2p5 2P) collision pairs, measured at 300 K in the 208–250 nm wavelength region, reveals deeply modulated Franck–Condon structure associated with transitions of Kr–F pairs from the ground state’s thermal and vibrational continua to the lowest 27 bound vibrational states (v′=0–26) of the KrF(B 2Σ) excited state. Under these conditions, photoassociation occurs in a narrow (ΔR=0.7–0.8 Å) Franck–Condon region in which the difference potential is a single valued function of R. Similar spectra have been observed for Xe(1S0)–I(2P) pairs in the 208–258 nm spectral region that arise from bound←free transitions to the lowest ∼40 vibrational levels of the XeI(B) state. Since the Kr–F and Xe–I collision pairs are photoexcited from the vibrational continuum of the ground state, the atomic pair energy distribution is thermalized and the envelope of the excitation spectrum can be interpreted directly in terms of the relative B–X transition moment, μ(R). Consequently, the behavior of μ(R) has been determined over a limited range in R and, for XeI, μ is found to fall by a factor of 2 in the ∼0.4 Å region extending from R−ReB≊0.25–0.62 Å. The XeI ground state (X 2Σ1/2+) potential in the 3.0≤R≤5.0 Å interval, derived from photoassociation spectra, is similar to that deduced from scattering experiments. Excited and ground state structural constants derived from numerical quantum simulations of the experimental spectra are presented.

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Ultracold photoassociative spectroscopy of heteronuclear alkali-metal diatomic molecules

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We have examined and identified the excited long-range Hund’s case (c) molecular states of the ten heteronuclear alkali metal diatomic molecules which support bound states and can be probed by ultracold photoassociative spectroscopy. Analytical expressions for the heteronuclear long-range free-bound Franck–Condon factors as a function of the internuclear distance R and the vibrational quantum number v are derived and discussed. The KRb system has considerably stronger excited long-range interactions than any other heteronuclear alkali diatomic molecule and has very favorable Franck–Condon factors for the photoassociation process. The heteronuclear photoassociative spectroscopy will provide spectroscopic measurements of the binary elastic scattering lengths of heteronuclear cold collisions which are the crucial parameters for sympathetic cooling of mixed atomic gases.

The Journal of Chemical Physics•Apr 8, 1998•123 citations
Using the method of quantum-defect theory, we calculate the ultra-long-range molecular vibrational states near the dissociation threshold of a diatomic molecular potential which asymptotically varies as \ensuremath−1/R3.\ensuremath{-}{1/R}^{3}.\ensuremath−1/R3. The properties of these states are of considerable interest as they can be formed by photoassociation (PA) of two ground-state atoms. The Franck-Condon overlap integrals between the harmonically trapped atom-pair states and the ultra-long-range molecular vibrational states are estimated and compared with their values for a pair of untrapped free atoms in the low-energy scattering state. We find that the binding between a pair of ground-state atoms by a harmonic trap has significant effect on the Franck-Condon integrals and thus can be used to influence PA. Trap-induced binding between two ground-state atoms may facilitate coherent PA dynamics between the two atoms and the photoassociated diatomic molecule.
Introduction If, while approaching on an unbound ground-state potential, two atoms absorb a photon and couple to an excited bound molecular state, they are said to undergo photoassociation. Figure 5.1 illustrates the process. At long range electrostatic dispersion forces give rise to the ground-state molecular potential varying as C 6 / R 6 . If the two atoms are homonuclear, then a resonant dipole–dipole interaction sets up ± C 3 / R 3 excited-state repulsive and attractive potentials. Figure 5.2 shows the actual long-range excited potential curves for the sodium dimer, originating from the 2 S ½ + 2 P 3/2 and 2 S ½ + 2 P ½ separated atom states. For cold and ultracold photoassociation processes the long-range attractive potentials play the key role; the repulsive potentials figure importantly in optical shielding and suppression, the subject of Chapter 6. In the presence of a photon with frequency ω p the colliding pair with kinetic energy k B T couples from the ground-state to the attractive molecular state in a free–bound transition near the Condon point R C , the point at which the difference potential just matches ћω p . Scanning the probe laser ω p excites population of vibration–rotation states in the excited bound potential and generates a free–bound spectrum. This general class of measurements is called photoassociative spectroscopy (PAS) and can be observed in several different ways. The observation may consist of bound-state decay by spontaneous emission, most probably as the nuclei move slowly around the outer turning point, to some distribution of continuum states on the ground potential controlled by bound–free nuclear Franck–Condon overlap factors.
We present the results of a spectroscopic study LiRb molecules created via photoassociation (PA) to vibration levels of the 4(1) potential. Atoms are first cooled and trapped in a dual species 7Li/ 85Rb magneto-optical trap (MOT) at temperatures of ≈ 1 mK or less. In a cold sample of sufficient density, PA occurs when a resonant laser field induces a free-bound transition to create molecules in an excited electronic potential. After spontaneous emission the molecules decay to a mixture of free atoms and bound molecules depending on the Franck-Condon factors (FCFs) of the excited and ground state vibrational wavefunctions. While excited LiRb * has been previously detected by trap loss fluorescence detection, ionization spectroscopy is required to determine the population of ground state levels after decay. We detect ground state molecules via resonantly enhanced multiphoton ionization (REMPI) where a two photon ionization transition is enhanced by an intermediate resonance. The intermediate resonances match progressions from the D1Π and possibly B1&Pgr; potentials, many of which have known energies obtained from previous heat pipe experiments. This is contrary to the expectation that weakly bound LiRb * should primarily decay to weakly bound levels of the ground state and could point to a possible path for creating molecules in the rovibronic ground state.
We study the photoassociative collisional loss of laser-cooled Rb atoms from a far-off resonance optical dipole force atom trap. We obtain a well-resolved photoassociation spectrum from 50 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ to 980 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ below the first excited dissociation limit of the Rb2{\mathrm{Rb}}_{2}Rb2​ molecule. Two vibrational series associated with excited Rb2{\mathrm{Rb}}_{2}Rb2​ $^{3}\mathrm{\ensuremath{\Sigma}}_{\mathit{g}}^{+}$ states are clearly visible. Oscillations in the associated Franck-Condon factors reflect the structure of the triplet ground state wave function. Our results clearly demonstrate the potential of photoassociation spectroscopy as a new probe of molecular structure.
This work explores the vibrational state-selective photoassociation (PA) in the ground state of the HX (X = F, Cl, I) molecule by solving the time-dependent Schrödinger equation. For the three systems, the vibrational level of [Formula: see text] is set to be the target state and the PA probability of the target state is calculated and compared by considering different initial collision momentums. It is found that the PA probabilities are in accordance with Franck–Condon overlap integral for the HI and HCl systems, but it is not the case for the HF system. Moreover, for the HF system, it is shown that the PA probability of the target state is largest and the multiphoton transition is more likely to occur.
Photoassociation, the bound←free absorption of a photon by a colliding pair of atoms, has been studied experimentally in the Kr–F and Xe–I systems and is demonstrated to be an effective tool for deducing molecular interaction potentials and for determining the dependence of the relative electronic transition moment on internuclear separation (R) in small molecules having dissociative ground states. Specifically, the excitation (‘‘action’’) spectrum for the photoassociation of thermalized Kr(4p6 1S0)–F(2p5 2P) collision pairs, measured at 300 K in the 208–250 nm wavelength region, reveals deeply modulated Franck–Condon structure associated with transitions of Kr–F pairs from the ground state’s thermal and vibrational continua to the lowest 27 bound vibrational states (v′=0–26) of the KrF(B 2Σ) excited state. Under these conditions, photoassociation occurs in a narrow (ΔR=0.7–0.8 Å) Franck–Condon region in which the difference potential is a single valued function of R. Similar spectra have been observed for Xe(1S0)–I(2P) pairs in the 208–258 nm spectral region that arise from bound←free transitions to the lowest ∼40 vibrational levels of the XeI(B) state. Since the Kr–F and Xe–I collision pairs are photoexcited from the vibrational continuum of the ground state, the atomic pair energy distribution is thermalized and the envelope of the excitation spectrum can be interpreted directly in terms of the relative B–X transition moment, μ(R). Consequently, the behavior of μ(R) has been determined over a limited range in R and, for XeI, μ is found to fall by a factor of 2 in the ∼0.4 Å region extending from R−ReB≊0.25–0.62 Å. The XeI ground state (X 2Σ1/2+) potential in the 3.0≤R≤5.0 Å interval, derived from photoassociation spectra, is similar to that deduced from scattering experiments. Excited and ground state structural constants derived from numerical quantum simulations of the experimental spectra are presented.
We have examined and identified the excited long-range Hund’s case (c) molecular states of the ten heteronuclear alkali metal diatomic molecules which support bound states and can be probed by ultracold photoassociative spectroscopy. Analytical expressions for the heteronuclear long-range free-bound Franck–Condon factors as a function of the internuclear distance R and the vibrational quantum number v are derived and discussed. The KRb system has considerably stronger excited long-range interactions than any other heteronuclear alkali diatomic molecule and has very favorable Franck–Condon factors for the photoassociation process. The heteronuclear photoassociative spectroscopy will provide spectroscopic measurements of the binary elastic scattering lengths of heteronuclear cold collisions which are the crucial parameters for sympathetic cooling of mixed atomic gases.