Photoassociation Rate Research Articles

Enhancement of the photoassociation of ultracold atoms via a non-resonant magnetic field**Project supported by the National Key Research and Development Program of China (Grant No. 2017YFA0304203), the National Natural Science Foundation of China (Grant Nos. 61722507, 61675121, and 61705123), PCSIRT, China (Grant No. IRT17R70), 111 Project, China (Grant No. D18001), the Program for the Outstanding Innovative Teams of Higher Learning

We report an effective method for enhancing the photoassociation of ultracold atoms using a non-resonant magnetic field, which enables the manipulation of the coupling between the wavefunctions of the colliding atomic pairs and the excited molecules. A series of photoassociation spectra are measured for different magnetic fields. We show that the photoassociation rate is significantly dependent on the non-resonant magnetic field. A qualitatively theoretical explanation is provided, and shows a good agreement with the experimental result.

Observation of Quantum Interference and Coherent Control in a Photochemical Reaction.

Coherent control of reactants remains a long-standing challenge in quantum chemistry. In particular, we have studied laser-induced molecular formation (photoassociation) in a Raman-dressed spin-orbit-coupled ^{87}Rb Bose-Einstein condensate, whose spin quantum state is a superposition of multiple bare spin components. In contrast to the notably different photoassociation-induced fractional atom losses observed for the bare spin components of a statistical mixture, a superposition state with a comparable spin composition displays the same fractional loss on every spin component. We interpret this as the superposition state itself undergoing photoassociation. For superposition states induced by a large Raman coupling and zero Raman detuning, we observe a nearly complete suppression of the photoassociation rate. This suppression is consistent with a model based upon quantum destructive interference between two photoassociation pathways for colliding atoms with different spin combinations. This model also explains the measured dependence of the photoassociation rate on the Raman detuning at a moderate Raman coupling. Our work thus suggests that preparing atoms in quantum superpositions may represent apowerful new technique to coherently control photochemical reactions.

Theory of Long-Range Ultracold Atom-Molecule Photoassociation.

The creation of ultracold molecules is currently limited to diatomic species. In this Letter, we present a theoretical description of the photoassociation of ultracold atoms and molecules to create ultracold excited triatomic molecules, thus being a novel example of a light-assisted ultracold chemical reaction. The calculation of the photoassociation rate of an ultracold Cs_{2} molecule in its rovibrational ground state with an ultracold Cs atom at frequencies close to its resonant excitation is reported, based on the solution of the quantum dynamics involving the atom-molecule long-range interactions and assuming a model potential for the short-range physics. The rate for the formation of excited Cs_{3} molecules is predicted to be comparable with currently observed atom-atom photoassociation rates. We formulate an experimental proposal to observe this process relying on the available techniques of optical lattices and standard photoassociation spectroscopy.

Feshbach-optimized photoassociation controlled by electric and magnetic fields

We study theoretically the Feshbach-optimized photoassociation of the $^{7}\mathrm{Li}$ and $^{133}\mathrm{Cs}$ atoms driven by electric and magnetic fields. The results show that the combination of electric and magnetic fields can significantly enhance the photoassociation rate by regulating scattering resonance and increasing the probability density of atom pairs at sufficiently short internuclear distance. The electric field can induce the coupling between the $s$ wave and $p$ wave and makes it possible to directly produce ultracold molecules in the lowest rotational state via one-photon stimulated emission photoassociation at ultralow temperature. Moreover, in the presence of a magnetic field, only a relatively weak electric field ($E\ensuremath{\le}100$ kV/cm) is required to realize the scattering resonance for heteronuclear alkali-metal atom pairs.

Photoassociation of ultracold molecules near a Feshbach resonance as a probe of the electron–proton mass ratio variation

We show that the photoassociation (PA) rate of ultracold diatomic molecules in the vicinity of a Feshbach resonance could be used to probe variations of the electron-to-proton mass ratio β=me/mp, a quantity related to other fundamental constants via the ΛQCD scale. The PA rate exhibits two features near a Feshbach resonance, a minimum and a maximum, which are very sensitive to the details of the interactions and the exact mass of the system. The effect and detection threshold are illustrated in the formation rates of ultracold Li2 and LiNa molecules by performing coupled-channel calculations in an external magnetic field. We find that the PA rate is particularly sensitive near narrow Feshbach resonances in heavy molecules, where it might be possible to detect relative variability of β on the order of 10-15–10-16. We also use a two-channel model to derive a proportionality relation between the variation of the PA rate and β applicable to diatomic molecules.

Continuous formation of vibronic ground state RbCs molecules via photoassociation

We demonstrate the direct formation of vibronic ground state RbCs molecules by photoassociation of ultracold atoms followed by radiative stabilization. The photoassociation proceeds through deeply bound levels of the (2)3Π0+ state. From analysis of the relevant free-to-bound and bound-to-bound Franck–Condon factors, we have predicted and experimentally verified a set of photoassociation resonances that lead to efficient creation of molecules in the v = 0 vibrational level of the X1Σ+ electronic ground state. We also compare the observed and calculated laser intensity required to saturate the photoassociation rate. We discuss the prospects for using short-range photoassociation to create and accumulate samples of ultracold polar molecules in their rovibronic ground state.

Feshbach-optimized photoassociation of ultracold6Li87Rb molecules with short pulses

Two-color photoassociation of ground state $^6$Li$^{87}$Rb molecules via the $\mathrm{B}^1\Pi$ electronic state using short pulses near a magnetic Feshbach resonance is studied theoretically. A near-resonant magnetic field is applied to mix the hyperfine singlet and triplet components of the initial wave function and enhance the photoassociation rate, before the population is transferred to the ground state by a second pulse. We show that an increase of up to three orders of magnitude in the absolute number of molecules produced is attainable for deeply bound vibrational levels. This technique can be generalized to other molecules with accessible magnetic Feshbach resonances.

Observation of ap-wave optical Feshbach resonance

We demonstrate a p$-wave optical Feshbach resonance (OFR) using purely long-range molecular states of a fermionic isotope of ytterbium ^{171}Yb, following the proposition made by K. Goyal et al. [Phys. Rev. A 82, 062704 (2010)]. The p-wave OFR is clearly observed as a modification of a photoassociation rate for atomic ensembles at about 5 micro-Kelvins. A scattering phase shift variation of \delta \eta=0.022 rad is observed with an atom loss rate coefficient K=28.0*10^{-12} cm^3/s.

Photoassociation to the21Σg+state in ultracold85Rb2in the presence of a shape resonance

We report the first observation of photoassociation to the 2(1)Sigma(g)(+) state of 85Rb2 . We have observed two vibrational levels (v'=98, 99) below the 5s1/2+5p1/2 atomic limit and eleven vibrational levels (v'=102-112) above it. The photoassociation---and subsequent spontaneous emission---occur predominantly between 15 and 20 Bohr in a region of internuclear distance best described as a transition between Hund's case (a) and Hund's case (c) coupling. The presence of a g-wave shape resonance in the collision of two ground-state atoms affects the photoassociation rate and lineshape of the J'= 3 and 5 rotational levels.

Resonant enhancement of the ultracold photoassociation rate by an electric field-induced anisotropic interaction

We study the effects of a static electric field on the photoassociation of a heteronuclear atom pair into a polar molecule. The interaction of permanent dipole moment with a static electric field largely affects the ground state continuum wavefunction of the atom pair at short separations where photoassociation transitions occur according to the Franck–Condon principle. Electric field-induced anisotropic interaction between two heteronuclear ground state atoms leads to scattering resonances at some specific electric fields. Near such resonances the amplitude of the scattering wavefunction at short separation increases by several orders of magnitude. As a result, the photoassociation rate is enhanced by several orders of magnitude near the resonances. We discuss in detail electric field-modified atom–atom scattering properties and resonances. We calculate the photoassociation rate that shows giant enhancement due to electric field tunable anisotropic resonances. We present selected results among which particularly important are the excitations of higher rotational levels in ultracold photoassociation due to electric field tunable resonances.

Theory of combined photoassociation and Feshbach resonances in a Bose-Einstein condensate

We model combined photoassociation and Feshbach resonances in a Bose-Einstein condensate, where the shared dissociation continuum allows for quantum interference in losses from the condensate, as well as a dispersive-like shift of resonance. A simple analytical model, based on the limit of weakly bound molecules, agrees well with numerical experiments that explicitly include dissociation to noncondensate modes. For a resonant laser and an off-resonant magnetic field, constructive interference enables saturation of the photoassociation rate at user-friendly intensities, at a value set by the interparticle distance. This rate limit is larger for smaller condensate densities and, near the Feshbach resonance, approaches the rate limit for magnetoassociation alone. Also, we find agreement with the unitary limit--set by the condensate size--only for a limited range of near-resonant magnetic fields. Finally, for a resonant magnetic field and an off-resonant laser, magnetoassociation displays similar quantum interference and a dispersive-like shift. Unlike photoassociation, interference and the fieldshift in resonant magnetoassociation is tunable with both laser intensity and detuning. Also, the dispersive-like shift of the Feshbach resonance depends on the size of the Feshbach molecule, and is a signature of non-universal physics in a strongly interacting system.

Influence of a Feshbach resonance on the photoassociation of LiCs

We analyze the formation of ultracold 7Li133Cs molecules in the rovibrational ground state through photoassociation into the B1Π state, which has recently been reported (Deiglmayr et al 2008 Phys. Rev. Lett. 101 133004). Absolute rate constants for photoassociation at large detunings from the atomic asymptote are determined and are found to be surprisingly large. The photoassociation process is modeled using a full coupled-channel calculation for the continuum state, taking all relevant hyperfine states into account. The enhancement of the photoassociation rate is found to be caused by an ‘echo’ of the triplet component in the singlet component of the scattering wave function at the inner turning point of the lowest triplet a3Σ+ potential. This perturbation can be ascribed to the existence of a broad Feshbach resonance at low scattering energies. Our results elucidate the important role of couplings in the scattering wave function for the formation of deeply bound ground state molecules via photoassociation.

Probing ultracold Fermi atoms with a single ion

We show that the recently proposed ionic microscope setup [Kollath et al., Phys. Rev. A 76, 063602 (2007)] could be adapted to measure the local single-particle energy distribution of a degenerate Fermi gas in situ with the resolution on the nanometer scale. We study an ion held in a Paul trap in an atomic Fermi gas and compute the two-photon Raman photo-association rate of the ion and an atom. We show that, as a function of the detunings between the frequencies of the two incident lasers and energies in the atom-ion system, the photoassociation rate directly measures the single-particle energy distribution in the Fermi gas around the ion. We describe an experiment to measure the photoassociation rate of a trapped ion and argue that, as the position of the ion can be scanned through the Fermi gas, this experiment directly probes the local energy and spin-state distribution of the Fermi gas.

Optical Feshbach Resonance Using the Intercombination Transition

We report control of the scattering wave function by an optical Feshbach resonance effect using ytterbium atoms. The narrow intercombination line (1S0-3P1) is used for efficient control as proposed by Ciuryło et al. [Phys. Rev. A 71, 030701(R) (2005)10.1103/PhysRevA.71.030701]. The manipulation of the scattering wave function is monitored with the change of a photoassociation rate caused by another laser. The optical Feshbach resonance is especially efficient for isotopes with large negative scattering lengths such as 172Yb, and we have confirmed that the scattering phase shift divided by the wave number, which gives the scattering length in the zero energy limit, is changed by about 30 nm.

Giant Formation Rates of Ultracold Molecules via Feshbach-Optimized Photoassociation

Ultracold molecules offer a broad variety of applications, ranging from metrology to quantum computing. However, forming "real" ultracold molecules, i.e., in deeply bound levels, is a very difficult proposition. Here, we show how photoassociation in the vicinity of a Feshbach resonance enhances molecular formation rates by several orders of magnitude. We illustrate this effect in heteronuclear systems, and find giant rate coefficients even in deeply bound levels. We also give a simple analytical expression for the photoassociation rate and discuss future applications of the Feshbach-optimized photoassociation technique.

Two-Body Transients in Coupled Atomic-Molecular Bose-Einstein Condensates

We discuss the dynamics of an atomic Bose-Einstein condensate when pairs of atoms are converted into molecules by single-color photoassociation. Three main regimes are found, and it is shown that they can be understood on the basis of time-dependent two-body theory. In particular, the so-called rogue dissociation regime [Phys. Rev. Lett. 88, 090403 (2002)10.1103/PhysRevLett.88.090403], which has a density-dependent limit on the photoassociation rate, is identified with a transient regime of the two-atom dynamics exhibiting universal properties. Finally, we illustrate how these regimes could be explored by photoassociating condensates of alkaline-earth atoms.

Ultra-high resolution trap-loss spectroscopy of ultracold 133Cs atom long-range states in a magnetooptical trap

We present an ultra-high resolution spectroscopic study of the photoassociation of cesium atoms inside a magnetooptical trap using trap-loss detection with photoassociation laser slow scanning. The photoassociation spectra show vibrational levels of three molecular symmetries below the 6S 1/2 + 6P 3/2 dissociation limit. A dynamic model is derived to extract the photoassociation rate from the trap-loss spectrum. Many observed rotational levels are well resolved, which indicate d-wave and higher partial wave contributions to the photoassociation cross section.

Influence of a tight isotropic harmonic trap on photoassociation in ultracold homonuclear alkali-metal gases

The influence of a tight isotropic harmonic trap on photoassociation of two ultracold alkali-metal atoms forming a homonuclear diatomic is investigated using realistic atomic interaction potentials. Confinement of the initial atom pair due to the trap leads to a uniform strong enhancement of the photoassociation rate to most, but also to a strongly suppressed rate for some final states. Thus tighter traps do not necessarily enhance the photoassociation rate. A further massive enhancement of the rate is found for strong interatomic interaction potentials. The details of this interaction play a minor role, except for large repulsive interactions for which a sharp window occurs in the photoassociation spectrum as is known from the trap-free case. A comparison with simplified models describing the atomic interaction like the pseudopotential approximation shows that they often provide reasonable estimates for the trap-induced enhancement of the photoassociation rate even if the predicted rates can be completely erroneous.

Grid methods for cold molecules: Determination of photoassociation line shapes and rate constants

A description of photoassociation by cw laser is formulated in the framework of grid methods. The Hamiltonian describing one or several bound states coupled to a multiple of continuum manifolds via a radiative field is written in the energy representation and diagonalized. The generality of the treatment allows us to compute accurately and efficiently physical properties such as nonlinear high-intensity energy shifts, line shapes, and photoassociation rates both for isolated and nonisolated resonances. Application is given to sodium photoassociation in the experimental conditions of McKenzie et al. [Phys. Rev. Lett. 88, 090403 (2002)]. Inverted regions for the dependency of the rate vs the intensity and nonsymmetric line shapes are predicted to occur above the saturation limit. Comparison with the model of Bohn and Julienne [Phys. Rev. A 60, 414 (1999)] is discussed.

Light forces in ultracold photoassociation

We study the time-resolved photoassociation of ultracold sodium in an optical dipole trap. The photoassociation laser excites pairs of atoms to molecular states of large total angular momentum at high intensities (above 20 kW/cm$^{2}$). Such transitions are generally suppressed at ultracold temperatures by the centrifugal barriers for high partial waves. Time-resolved ionization measurements reveal that the atoms are accelerated by the dipole potential of the photoassociation beam. We change the collision energy by varying the potential depth, and observe a strong variation of the photoassociation rate. These results demonstrate the important role of light forces in cw photoassociation at high intensities.