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Physical Review A

Measurement and modeling of hyperfine- and rotation-induced state mixing in large weakly bound sodium dimers

Eite Tiesinga, K. M. Jones, Paul D. Lett, Udo Volz, Carl J. Williams, Paul S. Julienne

Published May 5, 2005• 32 citations
Publisher

Abstract

We present high-precision trap loss spectroscopy of excited molecules obtained by the photoassociation of ultracold sodium atoms. Near the dissociation limit, hyperfine and rotational (Coriolis-type) interactions cause significant mixing of states of different nominal Hund's case (c) symmetry resulting in a complex pattern of spectral lines. We construct a theoretical model of the large, slowly rotating molecule starting from a long-range, atomic viewpoint. Interaction potentials are derived from the known long-range resonant dipole and van der Waals forces between atoms, supplemented at short range by the results of electronic-structure calculations. Spin-dependent interactions coupling the various angular momenta---nuclear spin, electron spin, electron orbit, and the mechanical rotation of the molecule as a whole---are derived from known atomic parameters. We avoid imposing approximate symmetries or coupling schemes and consequently include all nonadiabatic mixing of different degrees of freedom. Quantitative agreement between experiment and theory for both line positions and intensities is found. Specifically, we observe and calculate mixing of levels of , , and symmetry bound by below the asymptote.

DOI
10.1103/physreva.71.052703

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The work presented in this dissertation represents a comprehensive study on long-range interactions between alkali Rydberg atoms. As a consequence of their size, Rydberg atoms possess very large dipole moments, making them highly sensitive to external fields and to other Rydberg atoms. The strong dipole-dipole interaction between two Rydberg atoms results in a mixing of their angular momentum characters, which is the cornerstone of the work presented here. We describe the ℓ-mixing between various local molecular asymptotes through a residual Coulomb potential, assuming no electron cloud overlap. We then directly diagonalize an interaction Hamiltonian consisting of these Rydberg-Rydberg interactions and spin-orbit (fine structure) coupling in the Hund's case (c). In this manner, we calculate potential energy curves for various molecular symmetries and find that some of these curves exhibit deep potential wells, capable of supporting very extended bound molecular states ( macrodimers). We analyze the specific structure of the ℓ-mixing for these potential wells and derive convenient n-scaling relations for both their equilibrium separations Re and well depths De. We also explore various properties of the macrodimers, including their response to small electric fields and stability with respect to predissociation. We note throughout the dissertation that the detection of such extended dimers could help progress studies in a variety of areas such as exotic, ultracold chemistry and quantum information and computing. To facilitate detection, we propose a scheme to form and study the macrodimers via photoassociation (PA). We present calculated PA lineshapes from two different electronic ground states based on a harmonic trapping model. We find that both PA signals vary significantly with the laser detunings, indicating that different ℓ-characters could be probed at different equilibrium lengths. Finally, we extend the two-body formalism to the case of three interacting Rydberg atoms and present preliminary results for triply excited 58p rubidium atoms along a common axis. We provide a few examples of surface plots corresponding to different local asymptotes, each with a unique three-dimensional "landscape" and discuss the relevance of the physical features. The highlight of our analysis is the appearance of a potential well, which indicates the formation of a linear trimer. ^

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This thesis is concerned with long range behavior of the interaction potential of two neutral atoms.Two aspects are of special interest: First, how the long range behavior changes if one of the atoms is replaced by another isotope.Second, how to model the influence of a laser field on long range interaction.Several high precision spectroscopy experiments on particle beams are carried out.The transition frequencies of the D lines of 39,40,41 K are measured with frequency comb generated by a self-referenced femtosecond laser, which is locked to a Cs-clock.Discrepancies in the literature are removed and new values for the hyperfine structures of the 4p 1/2 and 4p 3/2 state and the isotope shift of both D lines are derive.On a beam of potassium dimers the A 1 Σ + u state of K 2 is studied up to the dissociation limit complementing and extending photoassociation spectroscopy of ultracold ensembles.Local perturbation due to the spin-orbit coupling with the b 3 Π u state are identified.Molecular hyperfine structure of levels close to the asymptote is observed and modeled by atomic parameter only.Improved values of the atomic radiative lifetime of the states 4p 1/2 and 4p 3/2 are derived from the long range parameter C 3 of the molecule.Also, an improved value for the dissociation energy of the X 1 Σ + g ground state is obtained and recipes for the investigation of cold collision via spectroscopy of the molecular structure at the ground state asymptotes are derived.For the first time asymptotic levels of two isotopomers of K 2 are studied and a comparison of asymptotic spectra of two isotopomers 39 K 2 and 39 K 41 K shows that corrections to the Born-Oppenheimer potential are needed.Optical coupling between asymptotic ground state levels and long range levels of an excited state has been suggested as tool for influencing cold collisions.Here, we model lineshapes for an experiment which investigates such a coupling systematically in Na 2 by laser spectroscopy in a beam.A fit program for the lineshape is used to compare experimental and theoretical values and to check the validity of the applied model from multichannel quantum defect theory.The dependency on the detuning of the coupling laser is reproduced but other details failed.To allow similar studies are reported for alkali metals on the simpler quantum system from alkali earth elements the development of an oven for a continuous beam of Ca 2 for Doppler-free spectroscopy is discussed including a major change of design and first experiences are reported.The heating of the oven is, unlike those for the beams applied above, outside the vacuum tank because of the high temperatures needed for the oven.

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Observation of photoassociation of ultracold sodium and cesium at the asymptote Na (3S1/2) + Cs (6P1/2)

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We report on the production of ultracold heteronuclear NaCs* molecules in a dual-species magneto-optical trap through photoassociation. The electronically excited molecules are formed below the Na (3S1/2) + Cs (6P1/2) dissociation limit. 12 resonance lines are detected using trap-loss spectroscopy based on a highly sensitive modulation technique. The highest observed rovibrational level exhibits clear hyperfine structure, which is detected for the first time. This structure is simulated within a simplified model consisting of 4 coupled levels belonging to the initially unperturbed Hund’s case “a” electronic states, which have been explored in our previous work that dealt with the Na (3S1/2) + Cs (6P3/2) asymptote [W. Liu et al., Phys. Rev. A 94, 032518 (2016)].

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We present high-precision trap loss spectroscopy of excited molecules obtained by the photoassociation of ultracold sodium atoms. Near the dissociation limit, hyperfine and rotational (Coriolis-type) interactions cause significant mixing of states of different nominal Hund's case (c) symmetry resulting in a complex pattern of spectral lines. We construct a theoretical model of the large, slowly rotating molecule starting from a long-range, atomic viewpoint. Interaction potentials are derived from the known long-range resonant dipole and van der Waals forces between atoms, supplemented at short range by the results of electronic-structure calculations. Spin-dependent interactions coupling the various angular momenta---nuclear spin, electron spin, electron orbit, and the mechanical rotation of the molecule as a whole---are derived from known atomic parameters. We avoid imposing approximate symmetries or coupling schemes and consequently include all nonadiabatic mixing of different degrees of freedom. Quantitative agreement between experiment and theory for both line positions and intensities is found. Specifically, we observe and calculate mixing of levels of , , and symmetry bound by below the asymptote.
We report photoassociation (PA) of ultracold Na and Cs atoms in a dual-species magneto-optical trap. Trap loss spectroscopy of the ultracold polar NaCs molecules formed by PA, which carries information about relative PA transition strengths, has been experimentally obtained by using highly sensitive modulation spectroscopy technique. The fine and hyperfine effects at near-dissociation levels of NaCs molecular $c\phantom{\rule{0.16em}{0ex}}^{3}\mathrm{\ensuremath{\Sigma}}^{+}$ state are observed and modeled. The interaction Hamiltonian is described in terms of the Hund's case (aaa) coupling scheme. The molecular hyperfine structure of near-dissociation levels is simulated within a simplified model of four interacting vibrational levels belonging to different initially unperturbed electronic states. The results of the simulation infer that the interaction parameters of the observed near-dissociation levels are close to the asymptotic parameters of the pair of atoms. The coupling of the electronic states is essential for forming the hyperfine structure.
The work presented in this dissertation represents a comprehensive study on long-range interactions between alkali Rydberg atoms. As a consequence of their size, Rydberg atoms possess very large dipole moments, making them highly sensitive to external fields and to other Rydberg atoms. The strong dipole-dipole interaction between two Rydberg atoms results in a mixing of their angular momentum characters, which is the cornerstone of the work presented here. We describe the ℓ-mixing between various local molecular asymptotes through a residual Coulomb potential, assuming no electron cloud overlap. We then directly diagonalize an interaction Hamiltonian consisting of these Rydberg-Rydberg interactions and spin-orbit (fine structure) coupling in the Hund's case (c). In this manner, we calculate potential energy curves for various molecular symmetries and find that some of these curves exhibit deep potential wells, capable of supporting very extended bound molecular states ( macrodimers). We analyze the specific structure of the ℓ-mixing for these potential wells and derive convenient n-scaling relations for both their equilibrium separations Re and well depths De. We also explore various properties of the macrodimers, including their response to small electric fields and stability with respect to predissociation. We note throughout the dissertation that the detection of such extended dimers could help progress studies in a variety of areas such as exotic, ultracold chemistry and quantum information and computing. To facilitate detection, we propose a scheme to form and study the macrodimers via photoassociation (PA). We present calculated PA lineshapes from two different electronic ground states based on a harmonic trapping model. We find that both PA signals vary significantly with the laser detunings, indicating that different ℓ-characters could be probed at different equilibrium lengths. Finally, we extend the two-body formalism to the case of three interacting Rydberg atoms and present preliminary results for triply excited 58p rubidium atoms along a common axis. We provide a few examples of surface plots corresponding to different local asymptotes, each with a unique three-dimensional "landscape" and discuss the relevance of the physical features. The highlight of our analysis is the appearance of a potential well, which indicates the formation of a linear trimer. ^
We report a high-resolution spectroscopic investigation of the long-range states of the 23Na87Rb^{23}\mathrm{Na}^{87}\mathrm{Rb}23Na87Rb molecule near its Na(32S1/2)+Rb(52P3/2)\mathrm{Na}(3{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2})+\mathrm{Rb}(5{\phantom{\rule{0.16em}{0ex}}}^{2}{P}_{3/2})Na(32S1/2​)+Rb(52P3/2​) asymptote. This study was performed with weakly bound ultracold molecules produced via magnetoassociation with an interspecies Feshbach resonance. We observed several regular vibrational series, which are assigned to the five attractive long-range states correlated with this asymptote. The vibrational levels of two of these states have sharp but complex structures due to hyperfine and Zeeman interactions. For the other states we observed significant linewidth broadenings due to strong predissociation caused by spin-orbit couplings with states correlated to the lower Na(32S1/2)+Rb(52P1/2)\mathrm{Na}(3{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2})+\mathrm{Rb}(5{\phantom{\rule{0.16em}{0ex}}}^{2}{P}_{1/2})Na(32S1/2​)+Rb(52P1/2​) asymptote. The long-range C6{C}_{6}C6​ van der Waals coefficients extracted from our spectrum are in good agreement with theoretical values.
We have performed high precision photoassociation spectroscopy of ultracold cesium gas. Using trap-loss fluorescence detection and controlling the background cesium pressure we were able to photoassociate atoms into excited states of ultracold molecules with large detunings up to 56 cm(-1) below the Cs(6S(1/2)) + Cs(6P(1/2)) atomic asymptote. Vibrational progressions are assigned to 0(g)(-), 0(u)(+), and 1(g) long-range states. By fitting the spectral data to the LeRoy-Bernstein expression, the effective coefficients of the leading long-range interactions and the vibrational quantum number at dissociation are obtained. In addition we have observed spectral perturbations between states of the same symmetry belonging to different asymptotes (6P(1/2) and 6P(3/2)). The perturbations are manifested through irregular vibrational level spacings and are especially pronounced in the 0(u)(+) symmetry. Many observed rotational levels indicate d- and higher partial wave contributions to the photoassociation cross section in the presence of trapping laser light, while spectral regions with only weak features suggest nodes in the lower state wave functions corresponding to the two ground state atoms asymptote.
This thesis is concerned with long range behavior of the interaction potential of two neutral atoms.Two aspects are of special interest: First, how the long range behavior changes if one of the atoms is replaced by another isotope.Second, how to model the influence of a laser field on long range interaction.Several high precision spectroscopy experiments on particle beams are carried out.The transition frequencies of the D lines of 39,40,41 K are measured with frequency comb generated by a self-referenced femtosecond laser, which is locked to a Cs-clock.Discrepancies in the literature are removed and new values for the hyperfine structures of the 4p 1/2 and 4p 3/2 state and the isotope shift of both D lines are derive.On a beam of potassium dimers the A 1 Σ + u state of K 2 is studied up to the dissociation limit complementing and extending photoassociation spectroscopy of ultracold ensembles.Local perturbation due to the spin-orbit coupling with the b 3 Π u state are identified.Molecular hyperfine structure of levels close to the asymptote is observed and modeled by atomic parameter only.Improved values of the atomic radiative lifetime of the states 4p 1/2 and 4p 3/2 are derived from the long range parameter C 3 of the molecule.Also, an improved value for the dissociation energy of the X 1 Σ + g ground state is obtained and recipes for the investigation of cold collision via spectroscopy of the molecular structure at the ground state asymptotes are derived.For the first time asymptotic levels of two isotopomers of K 2 are studied and a comparison of asymptotic spectra of two isotopomers 39 K 2 and 39 K 41 K shows that corrections to the Born-Oppenheimer potential are needed.Optical coupling between asymptotic ground state levels and long range levels of an excited state has been suggested as tool for influencing cold collisions.Here, we model lineshapes for an experiment which investigates such a coupling systematically in Na 2 by laser spectroscopy in a beam.A fit program for the lineshape is used to compare experimental and theoretical values and to check the validity of the applied model from multichannel quantum defect theory.The dependency on the detuning of the coupling laser is reproduced but other details failed.To allow similar studies are reported for alkali metals on the simpler quantum system from alkali earth elements the development of an oven for a continuous beam of Ca 2 for Doppler-free spectroscopy is discussed including a major change of design and first experiences are reported.The heating of the oven is, unlike those for the beams applied above, outside the vacuum tank because of the high temperatures needed for the oven.
We report on the production of ultracold heteronuclear NaCs* molecules in a dual-species magneto-optical trap through photoassociation. The electronically excited molecules are formed below the Na (3S1/2) + Cs (6P1/2) dissociation limit. 12 resonance lines are detected using trap-loss spectroscopy based on a highly sensitive modulation technique. The highest observed rovibrational level exhibits clear hyperfine structure, which is detected for the first time. This structure is simulated within a simplified model consisting of 4 coupled levels belonging to the initially unperturbed Hund’s case “a” electronic states, which have been explored in our previous work that dealt with the Na (3S1/2) + Cs (6P3/2) asymptote [W. Liu et al., Phys. Rev. A 94, 032518 (2016)].