Photoassociation of Ultracold Atoms: A New Spectroscopic Technique

Effect of light-assisted tunable interaction on the position response function of cold atoms

The position response of a particle subjected to a perturbation is of general interest in physics. We study the modification of the position response function of an ensemble of cold atoms in a magneto-optical trap (MOT) in the presence of tunable light-assisted interactions. We subject the cold atoms to an intense laser light tuned near the photoassociation (PA) resonance and observe the position response of the atoms subjected to a sudden displacement. Surprisingly, we observe that the entire cold atomic cloud undergoes collective oscillations. We use a generalized quantum Langevin approach to theoretically analyze the results of the experiments and find good agreement.

Quantum Molecular Devices

Miniaturization has been the driving force in contemporary technologies. However, two main obstacles limit further progress: additional reduction in size has reached its quantum limit, and lithography has reached its threshold. Future progress requires tackling three challenges: chemical synthesis of a complete device, active cooling for exploiting quantum characteristics, and quantum coherent control for operation. Chemical synthesis replaces the current top-bottom approach to manufacturing with bottom-up synthesis from elementary building blocks. New ultracold synthetic methods should be developed. An additional challenge is the active cooling of molecules, where the bottleneck is entropy removal. Notably, the current solution, namely, diffusion, is too slow. A coherent approach offers a possible solution; specifically, quantum coherent control is the method of choice for manipulating ultracold matter. Finally, the many degrees of freedom of molecules should be an asset that allows the design and implementation of complex tasks such as sensing communication and computing.

Observation of Photoassociation Resonances in Ultracold Atom-Molecule Collisions

We report on the observation of photoassociation resonances in ultracold collisions between ^{23}Na^{40}K molecules and ^{40}K atoms. We perform photoassociation in a long-wavelength optical dipole trap to form deeply bound triatomic molecules in electronically excited states. The atom-molecule Feshbach resonance is used to enhance the free-bound Franck-Condon overlap. The photoassociation into well-defined quantum states of excited triatomic molecules is identified by observing resonantly enhanced loss features. These loss features depend on the polarization of the photoassociation lasers, allowing us to assign rotational quantum numbers. The observation of ultracold atom-molecule photoassociation resonances paves the way toward preparing ground-state triatomic molecules, provides a new high-resolution spectroscopy technique for polyatomic molecules, and is also important to atom-molecule Feshbach resonances.

Modeling Photoassociative Spectra of Ultracold NaK + K

A model for photoassociation of ultracold atoms and molecules is presented and applied to the case of 39K and 23Na39K bosonic particles. The model relies on the assumption that photoassociation is dominated by long-range atom-molecule interactions well outside the chemical bond region. The frequency of the photoassociation laser is chosen close to a bound-bound rovibronic transition from the X1Σ+ ground state toward the metastable b3Π lowest excited state of 23Na39K, allowing us to neglect any other excitation, which could hinder the photoassociation detection. The energy level structure of the long-range 39K···23Na39K excited super-dimer is computed in the space-fixed frame by solving coupled-channel equations, involving the coupling between the 23Na39K internal rotation and the mechanical rotation of the super-dimer complex. A quite rich structure is obtained, and the corresponding photoassociation rates are presented. Other possible photoassociation transitions are discussed in the context of the proposed model.

Quantum control of reactions and collisions at ultralow temperatures

At temperatures close to absolute zero, the molecular reactions and collisions are dominantly governed by quantum mechanics. Remarkable quantum phenomena such as quantum tunneling, quantum threshold behavior, quantum resonances, quantum interference, and quantum statistics are expected to be the main features in ultracold reactions and collisions. Ultracold molecules offer great opportunities and challenges in the study of these intriguing quantum phenomena in molecular processes. In this article, we review the recent progress in the preparation of ultracold molecules and the study of ultracold reactions and collisions using ultracold molecules. We focus on the controlled ultracold chemistry and the scattering resonances at ultralow temperatures. The challenges in understanding the complex ultracold reactions and collisions are also discussed.

Nonlinear photoassociation through exotic orbits

We investigate the effects of a particular kind of orbits, which we call exotic orbits, on the process of classical molecular photoassociation. As a starting model system, we consider the process described by the Morse potential with a time-dependent perturbation consisting of the interaction of an external laser field with the molecular dipole. When the external perturbation is turned off, the bound molecular states are classically represented by librational motion, whereas the unbound, the collisional states, are represented by unbound motion, and in both cases, the energy is a constant of motion. When the perturbation is turned on, the total energy is no longer a constant of motion and initial conditions in the unbound region can reach the bound region, and vice versa, through chaotic orbits. Alternatively, we have found that the connection between the bound and unbound sectors can be achieved through exotic orbits, which are comprised by librationlike parts, a localized chaotic region, and an unbounded constant-energy part. Thus, if a colliding atomic pair is in an exotic orbit, it penetrates a chaotic region coming from the unbound sector, subsequently performing librationlike motion, during which the molecule with constant bound energy is formed. Afterwards, the molecule returns to the chaotic region and from this region, it can either access a distinct bound energy or dissociate. We call this phenomenon, in which a metastable molecule is formed, intermittent photoassociation. We show that the key for the emergence of exotic orbits is the relatively short range of the dipole as compared to the interacting potential range. In order to further verify our results, we have considered realistic forms for the potentials and dipole functions of several molecules and found the emergence of exotic orbits, and consequently of intermittent photoassociation, for the MgLi and SrLi molecular parameters.

Modelling interactions of cationic dimers in He droplets: microsolvation trends in HenK2+ clusters

We report the results of a detailed theoretical investigation of small K₂⁺-doped He clusters. The structural characteristics and stabilities of such cations are determined from ab initio electronic structure calculations at the MRCI+Q level of theory. The underlying interactions show a multireference character and such effects are analyzed. The interaction potentials are constructed employing an interpolation technique within the inverse problem theory method, while the nuclear quantum effects are computed for the trimers, their spatial arrangements are discussed, and information was extracted on the orientational anisotropy of the forces. We found that energetically the most stable conformer corresponds to linear arrangements that are taking place under large amplitude vibrations, with high zero-point energy. We have further looked into the behavior of higher-order species with various He atoms surrounding the cationic dopant. By using a sum of potentials approach and an evolutionary programming method, we analyzed the structural stability of clusters with up to six He atoms in comparison with interactions energies obtained from MRCI+Q quantum chemistry computations. Structures containing He_n motifs that characterize pure rare gas clusters, appear for the larger K₂⁺-doped He clusters, showing selective growth during the microsolvation process of the alkali-dimer cation surrounded by He atoms. Such results indicate the existence of local solvation microstructures in these aggregates, where the cationic impurity could get trapped for a short time, contributing to the slow ionic mobility observed experimentally in ultra-cold He-droplets.

Formation of ultracold 39K133Cs molecules via Feshbach optimized photoassociation

A Feshbach optimized photoassociation (FOPA) process for preparing ultracold excited-state ³⁹K¹³³Cs molecules is studied theoretically. Under the joint action of the magnetic field and short laser pulse, the colliding atoms in a superposition state composed of eight hyperfine components are converted into a molecule in the vibrational level of the excited state via two transition processes, the transition between singlet states and the transition between triplet states. The association efficiency can be significantly enhanced by taking advantage of Feshbach resonance. At different resonance positions, different hyperfine components of the superposition state dominate over the FOPA process, and the quantum interference displays different behaviors. Compared with the FOPA process only including a single hyperfine component, the quantum interference in the FOPA process containing all hyperfine components has a visible effect on the association efficiency.

Time-resolved double-resonance spectroscopy: Lifetime measurement of the 6 1 Σ g + ( 7,31 ) electronic state of molecular sodium

We report on the lifetime measurement of the 6   1 Σ g + ( 7,31 ) state of Na₂ molecules, produced in a heat-pipe oven, using a time-resolved spectroscopic technique. The 6   1 Σ g + ( 7,31 ) level was populated by two-step two-color double resonance excitation via the intermediate A   1 Σ u + ( 8,30 ) state. The excitation scheme was done using two synchronized pulsed dye lasers pumped by a Nd:YAG laser operating at the second harmonics. The fluorescence emitted upon decay to the final state was measured using a time-correlated photon counting technique, as a function of argon pressure. From this, the radiative lifetime was extracted by extrapolating the plot to collision-free zero pressure. We also report the calculated radiative lifetimes of the N a 2   6   1 Σ g + ro-vibrational levels in the range of v = 0-200 with J = 1 and J = 31 using the LEVEL program for bound-bound and the BCONT program for bound-free transitions. Our calculations reveal the importance of the bound-free transitions on the lifetime calculations and a large difference of about a factor of three between the J = 1 and J = 31 for the v = 40 and v = 100, respectively, due to the wavefunction alternating between having predominantly inner and outer well amplitude.

Three-Body Dispersion Potentials Involving Electric Octupole Coupling

Non-pairwise additive three-body dispersion potentials dependent upon one or more electric octupole moments are evaluated using the theory of molecular quantum electrodynamics. To simplify the perturbation theory calculations, an effective two-photon interaction Hamiltonian operator is employed. This leads to only third-order theory being required to evaluate energy shifts instead of the usual sixth-order formula, and the summation over six time-ordered sequences of virtual photon creation and annihilation events. Specific energy shifts computed include DD-DD-DO, DD-DO-DO, DO-DO-DO, and DD-DO-OO terms, where D and O are electric dipole and octupole moments, respectively. The formulae obtained are applicable to an arbitrary arrangement of the three particles, and we present explicit results for the equilateral triangle and collinear configurations, which complements the recently published DD-DD-OO potential. In this last case it was found that the contribution from the octupole weight-1 term could be viewed as a higher-order correction to the triple-dipole dispersion potential DD-DD-DD. In a similar fashion the octupole moment is decomposed into its irreducible components of weights-1 and -3, enabling insight to be gained into the potentials obtained in this study. Dispersion interaction energies proportional to mixed dipole-octupole polarisabilities, for example, are found to depend only on the weight-1 octupole moment for isotropic species and are retarded. Additional approximations are necessary in the evaluation of wave vector integrals for these cases in order to yield energy shifts that are valid in the near-zone.

Measurement-Based Entanglement of Noninteracting Bosonic Atoms

We demonstrate the ability to extract a spin-entangled state of two neutral atoms via postselection based on a measurement of their spatial configuration. Typically, entangled states of neutral atoms are engineered via atom-atom interactions. In contrast, in our Letter, we use Hong-Ou-Mandel interference to postselect a spin-singlet state after overlapping two atoms in distinct spin states on an effective beam splitter. We verify the presence of entanglement and determine a bound on the postselected fidelity of a spin-singlet state of (0.62±0.03). The experiment has direct analogy to creating polarization entanglement with single photons and hence demonstrates the potential to use protocols developed for photons to create complex quantum states with noninteracting atoms.

Photoassociation of ultracold NaLi

We perform photoassociation spectroscopy in an ultracold ²³Na-⁶Li mixture to study the c³Σ⁺ excited triplet molecular potential. We observe 50 vibrational states and their substructure to an accuracy of 20 MHz, and provide line strength data from photoassociation loss measurements. An analysis of the vibrational line positions using near-dissociation expansions and a full potential fit is presented. This is the first observation of the c³Σ⁺ potential, as well as photoassociation in the NaLi system.

Efficient Formation of Ultracold Molecules with Chirped Nanosecond Pulses

We describe experiments and associated quantum simulations involving the production of ultracold (87)Rb2 molecules with nanosecond pulses of frequency-chirped light. With appropriate chirp parameters, the formation is dominated by coherent processes. For a positive chirp, excited molecules are produced by photoassociation early in the chirp, and then transferred into high vibrational levels of the lowest triplet state by stimulated emission later in the chirp. Generally good agreement is seen between the data and the simulations. Shaping of the chirp can lead to a significant enhancement of the formation rate. Further improvements using higher intensities and different intermediate states are predicted.

Observations and analysis with the spline-based Rydberg-Klein-Rees approach for the 3(1)Σg(+) state of Rb2

Ro-vibrational term values of the 3(1)Σg (+) state of (85,85)Rb2 and (85,87)Rb2 and resolved fluorescence spectra to the A(1)Σu (+) state are recorded following optical-optical double resonance excitation. The experimental data are heavily perturbed, and as a result, the standard analysis based on Dunham series representation of the energy levels fails. The analysis is done via modeling the adiabatic potential function with the Rydberg-Klein-Rees potential constructed from the generalized smoothing spline interpolation of the vibrational energies Gv and rotational constants Bv.

Control of laser-induced frequency shift in ultracold cesium molecules by an external magnetic field

We investigate an effective control of the laser-induced frequency shift of ultracold cesium molecules formed by photoassociation (PA) in a magnetically levitated crossed dipole trap via an external magnetic field. A series of molecular PA spectra have been measured with increasing the PA laser intensity at different bias fields. We find that the slope of laser-induced frequency shift is strongly dependent on the external magnetic field: the slope can be increased up to a maximum of ∼6 times compared with a slope without an external magnetic field. A qualitatively theoretical explanation has been offered by considering the external magnetic field that can be used to manipulate the interaction between ultracold atoms.

Binding energies of the ground triplet state a(3) Σ(u)(+) of Rb2 and Cs2 in terms of the generalized Le Roy-Bernstein near-dissociation expansion

Formulae of Le Roy-Bernstein near-dissociation theory are derived in a general isotope-invariant form, applicable to any term in the rotational expansion of a diatomic ro-vibrational term value. It is proposed to use the generalized Le Roy-Bernstein expansion to describe the binding energies (ro-vibrational term values) of the ground triplet state a(3) Σ(u)(+) of alkali metal dimers. The parameters of this description are determined for Rb2 and Cs2 molecules. This approach gives a recipe to calculate the whole variety of the binding energies with characteristic accuracies from ∼1 × 10(-3) to 1 × 10(-2) cm(-1) using a relatively simple algebraic equation.

An ab initio study of the ground and low-lying excited states of KBe with the effect of inner-shell electrons

The potential energy curves (PECs) of 1(2)Σ(+), 2(2)Σ(+), 1(2)Π, and 2(2)Π states of KBe are calculated using multireference configuration interaction method and large all-electron basis sets. Four sets of frozen core orbitals (FCOs) are considered to examine the effect of inner-shell correlation electrons on the molecular properties. The ro-vibrational energy levels are obtained by solving the Schrödinger equation of nuclear motion based on the ab initio PECs. The spectroscopic parameters are determined from the ro-vibrational levels with Dunham expansion. The PECs are fitted into analytical potential energy functions using the Morse long-range potential function. The dipole moment functions of the states for KBe calculated with different FCOs are presented. The transition dipole moments for KBe between 1(2)Σ(+) and 2(2)Σ(+) states, 1(2)Π and 1(2)Σ(+) states, and 2(2)Π and 1(2)Σ(+) states are also obtained.

Formation of ultracold Rb2 molecules in the v'' = 0 level of the a(3)Σ+(u) state via blue-detuned photoassociation to the 1(3)Π(g) state

We report on the observation of blue-detuned photoassociation in Rb(2), in which vibrational levels are energetically above the corresponding excited atomic asymptote. (85)Rb atoms in a MOT were photoassociated at short internuclear distance to levels of the 1(3)Π(g) state at a rate of approximately 5 × 10(4) molecules s(-1). We have observed most of the predicted vibrational levels for all four spin-orbit components; 0(+)(g), 0(-)(g), 1(g), and 2(g), including levels of the 0(+)(g) outer well. These molecules decay to the metastable a(3)Σ(+)(u) state, some preferentially to the v'' = 0 level, as we have observed for photoassociation to the v' = 8 level of the 1(g) component.

Experimental long range potential of the BΠ1 state in NaRb

The long range potential of the B 1Pi state in NaRb has been investigated by observation of rovibrational levels that it supports, including the high lying ones, with the technique of polarization labeling spectroscopy. This has allowed us to characterize the potential energy curve up to 1.9 cm(-1) from the dissociation limit. The highest observed rovibrational level v=49, J=10 has the outer turning point at R=16.48 A.

Direct deperturbation analysis of the AΠ2∼BΣ+2 complex of LiAr7,6 isotopomers

Direct deperturbation analysis of the highly accurate experimental rovibronic term values of the A (2)Pi approximately B (2)Sigma(+) complex of LiAr [R. Bruhl and D. Zimmermann, J. Chem. Phys. 114, 3035 (2001)] has been performed in the framework of inverted close-coupling approach implicitly adjusted to the unified treatment of the overall A approximately B coupling effect without reducing the rovibrational dimensionality. The nonlinear fitting procedure was supported by the ab initio calculations on the spin-orbit and angular coupling matrix elements between the lowest X (2)Sigma(+), A (2)Pi, and B (2)Sigma(+) states. The analytical grid mapping based on the reduced variable representation of the radial coordinate r was used to improve the efficiency of the solution of the close-coupling radial equations near the dissociation limit. The mutual A approximately X perturbation effect on the A (2)Pi term values and spin-rotation splitting of the ground state were evaluated for both (7,6)LiAr isotopomers. The resulting empirical potential-energy curves for the adiabatic A (2)Pi and B (2)Sigma(+) states, along with the refined r-dependent nonadiabatic matrix elements, reproduce the total rovibronic structure of the (7)LiAr complex with the standard deviation of 0.003 cm(-1). The mass invariance of the deperturbed electronic parameters was confirmed by the calculation of the rovibronic term values of the (6)LiAr isotopomer which coincided with their experimental counterparts within 0.004 cm(-1).

Ultracold molecule production via a resonant oscillating magnetic field

A novel atom-molecule conversion technique has been investigated. Ultracold 85Rb atoms sitting in a dc magnetic field near the 155 G Feshbach resonance are associated by applying a small sinusoidal oscillation to the magnetic field. There is resonant atom to molecule conversion when the modulation frequency closely matches the molecular binding energy. We observe that the atom to molecule conversion efficiency depends strongly on the frequency, amplitude, and duration of the applied modulation and on the phase space density of the sample. This technique offers high conversion efficiencies without the necessity of crossing or closely approaching the Feshbach resonance and allows precise spectroscopic measurements. Efficiencies of 55% have been observed for pure Bose-Einstein condensates.

Improved dissociation energy of the K39Rb85 molecule

The predissociation data for the 1 (1)Pi state of (39)K(85)Rb of Kasahara et al. [J. Chem. Phys. 111, 8857 (1999)] are combined with the recent determination of the long range C(6) coefficients of the predissociating 2 (3)Sigma(+) approximately 2(0(-)), 2(1) states [Wang et al., Eur. Phys. J. D31, 165 (2004) ] molecule: to infer a more precise dissociation energy of the (39)K(85)Rb molecule D(0)=4180.06+/-0.42 cm(-1) and D(e)=4217.91+/-0.42 cm(-1).

Photoassociative production and trapping of ultracold KRb molecules

We have produced ultracold heteronuclear KRb molecules by the process of photoassociation in a two-species magneto-optical trap. Following decay of the photoassociated KRb*, the molecules are detected using two-photon ionization and time-of-flight mass spectroscopy of KRb+. A portion of the metastable triplet molecules thus formed are magnetically trapped. Photoassociative spectra down to 91 cm(-1) below the K(4s)+Rb(5p(1/2)) asymptote have been obtained. We have made assignments to all eight of the attractive Hund's case (c) KRb* potential curves in this spectral region.

Photoassociation spectroscopy of ultracold Cs below the 6P(3/2) limit

High precision photoassociation spectroscopy is performed in ultracold cesium gas, with detunings as large as 51 cm(-1) below the Cs(6S(1/2))+Cs(6P(3/2)) asymptote. Trap-loss fluorescence detection is used for detecting the photoassociation to excited state ultracold molecules. Long vibrational progressions are assigned to electronic states of 0(g) (-), 0(u) (+), and 1(g) symmetry. The spectral data are fitted to a LeRoy-Bernstein equation, in order to obtain the effective coefficients of the leading long-range interaction term (C(3)/R(3)) and the relative vibrational quantum numbers measured down from dissociation. Additionally we present evidence for perturbations between the 0(g) (-) state and the dark 2(u) state.

Photoassociation spectroscopy of laser-cooled ytterbium atoms

We report the photoassociation spectroscopy of laser-cooled ytterbium atoms in an optical trap. We observed more than 90 photoassociation resonances of vibrational levels in the (1)Sigma(+)(u) state, including 80 consecutive series, up to 490 GHz detuning with respect to the atomic resonance. From the resonance frequencies we derived the atomic radiative lifetime of the (6s6p) 1P1 state to be 5.464+/-0.005 ns, which is about 2 orders of magnitude improvement over previous results. We also observed line broadening of resonances, which is ascribed to the predissociation to the triplet states, and estimated the transition probability to be 0.2. Furthermore, we observed the decrease of the photoassociation signal intensity, from which the scattering length is estimated to be equal to or less than 3 nm.

Photoassociation spectroscopy of ultracold Cs below the 6P1/2 limit

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.

Collisions and reactions of ultracold molecules

It is argued that collision dynamics of atoms and molecules at ultracold temperatures (below 1 mK) are not readily predictable from knowledge of collision dynamics above 100 K. In the case of elastic collisions, it is well known that the collision cross section is constant as T → 0 K but mass and symmetry effects are dramatic. The cases of inelastic and reactive collisions are less studied, but a T–1/2 dependence of the cross section as T → 0 K is expected. It seems that extrapolations of high-temperature inelastic and reactive behavior normally greatly underestimate ultracold-temperature rates. The prospects for experimental observation of ultracold collision dynamics are rapidly improving.Key words: ultracold molecules, collisions, reactions, hydrogen, scattering length.