Rovibrational Ground State Research Articles

Production and Detection of Ultracold Ground State 85Rb133Cs Molecules in the Lowest Vibrational Level by Short-Range Photoassociation**Supported by the National Basic Research Program of China under Grant No 2012CB921603, the National Natural Science Foundation of China under Grant Nos 61275209, 11304189, 61378015 and 11434007, the National Natural Science Foundation for Excellent Research Team under Grant No 61121064, and the Program

We investigate the production of ultracold ground state X1σ+ (v = 0) RbCs molecules in the lowest vibrational level via short-range photoassociation followed by spontaneous emission. The starting point is the laser cooled 85Rb and 133Cs atoms in a dual species, forced dark magneto-optical trap. The special intermediate level (5)0+(v = 10) correlated to the (2)3π electric state is achieved by the photoassociation process. The formed ground state X1σ+ (v = 0) molecule is resonantly excited to the 21π intermediate state by a 651 nm pulse laser and is ionized by a 532 nm pulse laser and then detected by the time-of-flight mass spectrum. Saturation of the photoionization spectroscopy at large ionization laser energy is observed and the ionization efficiency is obtained from the fitting. The production of ultracold ground state 85Rb133Cs molecules is facilitative for the further research about the manipulation of ultracold molecules in the rovibrational ground state.

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.

Two-photon pathway to ultracold ground state molecules of 23Na40K

We report on high-resolution spectroscopy of ultracold fermionic 23Na40K Feshbach molecules, and identify a two-photon pathway to the rovibrational singlet ground state via a resonantly mixed B1Π ∼ c3Σ+intermediate state. Photoassociation in a 23Na–40K atomic mixture and one-photon spectroscopy on 23Na40K Feshbach molecules reveal about 20 vibrational levels of the electronically excited c3Σ+state. Two of these levels are found to be strongly perturbed by nearby B1Π levels via spin–orbit coupling, resulting in additional lines of dominant singlet character in the perturbed complex , or of resonantly mixed character in . The dominantly singlet level is used to locate the absolute rovibrational singlet ground state via Autler–Townes spectroscopy. We demonstrate coherent two-photon coupling via dark state spectroscopy between the predominantly triplet Feshbach molecular state and the singlet ground state. Its binding energy is measured to be 5212.0447(1) cm−1, a thousand-fold improvement in accuracy compared to previous determinations. In their absolute singlet ground state, 23Na40K molecules are chemically stable under binary collisions and possess a large electric dipole moment of 2.72 Debye. Our work thus paves the way towards the creation of strongly dipolar Fermi gases of NaK molecules.

Polarizability of ultracold molecules in the rovibrational ground state of

We study, both theoretically and experimentally, the dynamical polarizability of molecules in the rovibrational ground state of . Taking all relevant excited molecular bound states into account, we compute the complex-valued polarizability for wave numbers up to 20 000 . Our calculations are compared to experimental results at () as well as at (). Here, we discuss the measurements at . The ultracold Rb2 molecules are trapped in the lowest Bloch band of a 3D optical lattice. Their polarizability is determined by lattice modulation spectroscopy which measures the potential depth for a given light intensity. Moreover, we investigate the decay of molecules in the optical lattice, where lifetimes of more than are observed. In addition, the dynamical polarizability for the state is calculated. We provide simple analytical expressions that reproduce the numerical results for for all vibrational levels of as well as . Precise knowledge of the molecular polarizability is essential for designing experiments with ultracold molecules as lifetimes and lattice depths are key parameters. Specifically the wavelength at is of interest, since here, ultrastable high power lasers are available.

Ultracold Dipolar Gas of Fermionic 23Na40 K Molecules in Their Absolute Ground State.

We report on the creation of an ultracold dipolar gas of fermionic 23Na40 K molecules in their absolute rovibrational and hyperfine ground state. Starting from weakly bound Feshbach molecules, we demonstrate hyperfine resolved two-photon transfer into the singlet X 1Σ+|v=0,J=0⟩ ground state, coherently bridging a binding energy difference of 0.65 eV via stimulated rapid adiabatic passage. The spin-polarized, nearly quantum degenerate molecular gas displays a lifetime longer than 2.5 s, highlighting NaK's stability against two-body chemical reactions. A homogeneous electric field is applied to induce a dipole moment of up to 0.8 D. With these advances, the exploration of many-body physics with strongly dipolar Fermi gases of 23Na40K molecules is within experimental reach.

A simple, versatile laser system for the creation of ultracold ground state molecules

A narrow-linewidth, dual-wavelength laser system is vital for the creation of ultracold ground state molecules via stimulated Raman adiabatic passage (STIRAP) from a weakly bound Feshbach state. Here we describe how a relatively simple apparatus consisting of a single fixed-length optical cavity can be used to narrow the linewidth of the two different wavelength lasers required for STIRAP simultaneously. The frequency of each of these lasers is referenced to the cavity and is continuously tunable away from the cavity modes through the use of non-resonant electro-optic modulators. Self-heterodyne measurements suggest the laser linewidths are reduced to several 100 Hz. In the context of 87Rb133Cs molecules produced via magnetoassociation on a Feshbach resonance, we demonstrate the performance of the laser system through one- and two-photon molecular spectroscopy. Finally, we demonstrate transfer of the molecules to the rovibrational ground state using STIRAP.

Formation of ultracold NaRb Feshbach molecules

We report the creation of ultracold bosonic 23Na87Rb Feshbach molecules via magneto-association. By ramping the magnetic field across an interspecies Feshbach resonance (FR), at least 4000 molecules can be produced out of the near degenerate ultracold mixture. Fast loss due to inelastic atom–molecule collisions is observed, which limits the pure molecule number, after residual atoms removal, to 1700. The pure molecule sample can live for 21.8(8) ms in the optical trap, long enough for future molecular spectroscopy studies toward coherently transferring to the singlet ro-vibrational ground state, where these molecules are stable against chemical reaction and have a permanent electric dipole moment of 3.3 Debye. We have also measured the Feshbach molecule’s binding energy near the FR by the oscillating magnetic field method and found these molecules have a large closed-channel fraction.

Creation of ultracold ^{87}Rb^{133}Cs molecules in the rovibrational ground state.

We report the creation of a sample of over 1000 ultracold ^{87}Rb^{133}Cs molecules in the lowest rovibrational ground state, from an atomic mixture of ^{87}Rb and ^{133}Cs, by magnetoassociation on an interspecies Feshbach resonance followed by stimulated Raman adiabatic passage (STIRAP). We measure the binding energy of the RbCs molecule to be hc×3811.576(1) cm^{-1} and the |v^{''}=0,J^{''}=0⟩ to |v^{''}=0,J^{''}=2⟩ splitting to be h×2940.09(6) MHz. Stark spectroscopy of the rovibrational ground state yields an electric dipole moment of 1.225(3)(8)D, where the values in parentheses are the statistical and systematic uncertainties, respectively. We can access a space-fixed dipole moment of 0.355(2)(4)D, which is substantially higher than in previous work.

Extended Fourier-transform spectroscopy studies and deperturbation analysis of the spin-orbit coupled A1Σ+ and b3Π states in RbCs.

The article presents a study of the strongly spin-orbit coupled singlet A(1)Σ(+) and triplet b(3)Π states of the RbCs molecule, which provide an efficient optical path to transfer ultracold molecules to their rovibrational ground state. Fourier-transform A(1)Σ(+) - b(3)Π → X(1)Σ(+) and (4)(1)Σ(+) → A(1)Σ(+) - b(3)Π laser-induced fluorescence (LIF) spectra were recorded for the natural mixture of the (85)Rb(133)Cs and (87)Rb(133)Cs isotopologues produced in a heat pipe oven. Overall 8730 rovibronic term values of A(1)Σ(+) and b(3)Π states were determined with an uncertainty of 0.01 cm(-1) in the energy range [9012, 14087] cm(-1), covering rotational quantum numbers J ∈ [6, 324]. An energy-based deperturbation analysis performed in the framework of the four A(1)Σ(+) - b(3)Π(Ω = 0, 1, 2) coupled-channels approach reproduces 97% of the experimental term values of both isotopologues with a standard deviation of 0.0036 cm(-1). The reliability of the deperturbed mass-invariant potentials and spin-orbit coupling functions of the interacting A(1)Σ(+) and b(3)Π states is additionally proved by a good reproduction of the A - b → X and (4)(1)Σ(+) → A - b relative intensity distributions. The achieved accuracy of the A - b complex description allowed us to use the latter to assign the observed (5)(1)Σ(+) → A - b and (3)(1)Π → A - b transitions. As is demonstrated, LIF to the A - b complex becomes as informative as to the ground X(1)Σ(+) state, which is confirmed by comparing the results of (4)(1)Σ(+) state analysis based on (4)(1)Σ(+) → A - b LIF with the data from V. Zuters et al. [Phys. Rev. A 87, 022504 (2013)] based on (4)(1)Σ(+) → X LIF.

Ultracold dense samples of dipolar RbCs molecules in the rovibrational and hyperfine ground state.

We produce ultracold dense trapped samples of ^{87}Rb^{133}Cs molecules in their rovibrational ground state, with full nuclear hyperfine state control, by stimulated Raman adiabatic passage (STIRAP) with efficiencies of 90%. We observe the onset of hyperfine-changing collisions when the magnetic field is ramped so that the molecules are no longer in the hyperfine ground state. A strong quadratic shift of the transition frequencies as a function of applied electric field shows the strongly dipolar character of the RbCs ground-state molecule. Our results open up the prospect of realizing stable bosonic dipolar quantum gases with ultracold molecules.

Wave packet and statistical quantum calculations for the He + NeH+ → HeH+ + Ne reaction on the ground electronic state

A real wave packet based time-dependent method and a statistical quantum method have been used to study the He + NeH(+) (v, j) reaction with the reactant in various ro-vibrational states, on a recently calculated ab initio ground state potential energy surface. Both the wave packet and statistical quantum calculations were carried out within the centrifugal sudden approximation as well as using the exact Hamiltonian. Quantum reaction probabilities exhibit dense oscillatory pattern for smaller total angular momentum values, which is a signature of resonances in a complex forming mechanism for the title reaction. Significant differences, found between exact and approximate quantum reaction cross sections, highlight the importance of inclusion of Coriolis coupling in the calculations. Statistical results are in fairly good agreement with the exact quantum results, for ground ro-vibrational states of the reactant. Vibrational excitation greatly enhances the reaction cross sections, whereas rotational excitation has relatively small effect on the reaction. The nature of the reaction cross section curves is dependent on the initial vibrational state of the reactant and is typical of a late barrier type potential energy profile.

State-to-state quantum versus classical dynamics study of the OH + CO → H + CO2 reaction in full dimensions (J = 0): checking the validity of the quasi-classical trajectory method

We report full-dimensional state-to-state quantum mechanical (QM) and quasi-classical trajectory (QCT) calculations on the title reaction for the ground rovibrational initial state with total angular momentum fixed at zero on the accurate potential energy (PES) constructed recently by using permutation-invariant polynomial–neural network method (Li et al. in J Chem Phys 140:044327, 2014), to check the validity of the QCT method for the reaction. It is found that the QM state-to-state results strongly depend on the resonance structures in reaction, but the collision energy-averaged results show a smooth change with the increase of collision energy. Overall, the agreement between collision energy-averaged QM and QCT state-to-state results is satisfactory, in particular at high collision energy region, indicating that the QCT method is rather accurate on describing dynamics of the reaction on the PES. On the other hand, because earlier studies revealed the QCT results on the PES do not agree very well with the experimental measurements available, more theoretical and experimental studies should be carried out to achieve a full understanding on the dynamics of this benchmark complex-forming reaction.

Prospects for transferring87Rb84Srdimers to the rovibrational ground state based on calculated molecular structures

Using fitted model potential curves of the ground and lowest three excited states yielded by the relativistic Kramers-restricted multireference configuration interaction method with 19 electrons correlated, we theoretically investigate the rovibrational properties including the number of vibrational state and diagonally distributed Franck-Condon factors for a ${}^{87}\text{Rb}{}^{84}\text{Sr}$ molecule. Benefiting from a turning point at about ${v}^{\ensuremath{'}}=20$ for the Franck-Condon factors between the ground state and spin-orbit $2(\ensuremath{\Omega}=1/2)$ excited state, we choose $|2(\ensuremath{\Omega}=1/2),{v}^{\ensuremath{'}}=21,{J}^{\ensuremath{'}}=1\ensuremath{\rangle}$ as the intermediate state in the three-level model to theoretically analyze the possibility of performing stimulated Raman adiabatic passage to transfer weakly bound RbSr molecules to the rovibrational ground state. With 1550 nm pump laser (2 W/${\text{cm}}^{2}$) and 1342 nm dump laser (10 mW/${\text{cm}}^{2}$) employed and appropriate settings of pulse time length (about 300 $\ensuremath{\mu}$s), we have formalistically achieved a round-trip transfer efficiency of 60%, namely 77% for one-way transfer. The results demonstrate the possibility of producing polar ${}^{87}\text{Rb}{}^{84}\text{Sr}$ molecules efficiently in a submicrokelvin regime, and further provide promising directions for future theoretical and experimental studies on alkali-alkaline(rare)-earth dimers.

Magnetic Feshbach resonances in collisions of nonmagnetic closed-shell1Σmolecules

Magnetic Feshbach resonances play a central role in experimental research of atomic gases at ultracold temperatures, as they allow one to control the microscopic interactions between ultracold atoms by tuning an applied magnetic field. These resonances arise due to strong hyperfine interactions between the unpaired electron and the nuclear magnetic moment of the alkali metal atoms. A major thrust of current research is to create an ultracold gas of diatomic alkali-metal molecules in the ground rovibrational state of the ground electronic $^1\Sigma$ state. Unlike alkali metal atoms, $^1\Sigma$ diatomic molecules have no unpaired electrons. However, the hyperfine interactions of molecules may give rise to magnetic Feshbach resonances. We use quantum scattering calculations to study the possible width of these resonances. Our results show that the widths of magnetic Feshbach resonances in ultracold molecule-molecule collisions for $^1\Sigma$ molecules may exceed 1 milliGauss, rendering such resonances experimentally detectable. We hope that this work will stimulate the experimental search of these resonances.

Prospects for narrow-line cooling of KRb molecules in the rovibrational ground state

We propose and experimentally investigate a scheme for narrow-line cooling of KRb molecules in the rovibrational ground state. We show that the spin-forbidden $\mathrm{X^1\Sigma^+} \rightarrow \mathrm{b^3\Pi_{0^+}}$ transition of KRb is ideal for realizing narrow-line laser cooling of molecules because it has highly diagonal Franck-Condon factors and narrow linewidth. In order to confirm the prediction, we performed the optical and microwave spectroscopy of ultracold $^{41}$K$^{87}$Rb molecules, and determined the linewidth ($2\pi\times$ 4.9(4) kHz) and Franck-Condon factors for the $\mathrm{X^1\Sigma^+} (v''=0) \rightarrow \mathrm{b^3\Pi_{0^+}} (v'=0)$ transition (0.9474(1)). This result opens the door towards all-optical production of polar molecules at sub-microkelvin temperatures.

Using coherent control to extract the phases of electronic transition-dipole matrices: the LiRb case

We show that “bichromatic coherent control” (BCC) enables the determination of the amplitudes (= magnitudes + phases) of individual transition-dipole matrix elements (TDMs) and the amplitude of time-evolving wave packets from time-resolved fluorescence data. In the present use of BCC, one induces quantum interferences using two external laser fields to coherently deplete the population of different pairs of excited energy eigenstates. The BCC-induced depletion is supplemented by the computation of the Fourier integral of the time-resolved fluorescence at the beat frequencies of the two states involved. The combination of BCC and Fourier transform enables the determination of both the expansion coefficients of the wave packet in a basis of vibrational energy eigenstates and the amplitudes of the [Formula: see text] electronic TDMs linking the excited and ground rovibrational states. We illustrate our method by determining the amplitudes of the TDMs linking the vibrational states of the [Formula: see text] spin orbit coupled potentials to both the singlet [Formula: see text] and the triplet [Formula: see text] electronic ground states in LiRb. The approach, which is found to be quite robust against errors in the BCC procedure and experimental data, can be readily generalized to the imaging of wave packets of polyatomic molecules.

Six-dimensional potential energy surface of the dissociative chemisorption of HCl on Au(111) using neural networks

We constructed a six-dimensional potential energy surface (PES) for the dissociative chemisorption of HCl on Au(111) using the neural networks method based on roughly 70000 energies obtained from extensive density functional theory (DFT) calculations. The resulting PES is accurate and smooth, based on the small fitting errors and good agreement between the fitted PES and the direct DFT calculations. Time-dependent wave packet calculations show that the potential energy surface is very well converged with respect to the number of DFT data points, as well as to the fitting process. The dissociation probabilities of HCl initially in the ground rovibrational state from six-dimensional quantum dynamical calculations are quite different from the four-dimensional fixed-site calculations, indicating it is essential to perform full-dimensional quantum dynamical studies for the title molecule-surface interaction system.

Elastic and inelastic collisions of2Σmolecules in a magnetic field

We calculate the cross sections for elastic scattering and Zeeman relaxation in binary collisions of molecules in the ro-vibrational ground state of a $^2\Sigma$ electronic state and the Zeeman state with the electron spin projection $M_S=1/2$ on the magnetic field axis. This is the lowest-energy state of $^2\Sigma$ molecules confined in a magnetic trap. The results are averaged over calculations with multiple molecule - molecule interaction potentials, which yields the expectation intervals for the cross sections and the elastic-to-inelastic cross section ratios. We find that the elastic-to-inelastic cross section ratios under conditions corresponding to trapped molecular ensembles at $T \sim 10^{-3}$ K exceed 100 for the majority of $^2\Sigma$ molecules. The range of $^2\Sigma$ molecules expected to be collisionally unstable in magnetic traps at $T < 10^{-3}$ K is limited to molecules with the spin-rotation interaction constant $\gamma_{\rm SR} > 0.5$ cm$^{-1}$ and the rotational constant $B_e < 4$ cm$^{-1}$.

Production of translationally cold barium monohalide ions

We have produced sympathetically cooled barium monohalide ions Ba${X}^{+}$ ($X=\text{F}$, Cl, Br) by reacting trapped, laser-cooled Ba${}^{+}$ ions with room-temperature gas-phase neutral halogen-containing molecules. Reaction rates for two of these (SF${}_{6}$ and CH${}_{3}$Cl) have been measured and were found to be in agreement with classical models. Ba${X}^{+}$ ions are promising candidates for cooling to the rovibrational ground state, and our method presents a straightforward way to produce these polar molecular ions.

Multichannel modeling and two-photon coherent transfer paths in NaK

We explore possible pathways for the creation of ultracold polar NaK molecules in their absolute electronic and rovibrational ground state starting from ultracold Feshbach molecules. In particular, we present a multi-channel analysis of the electronic ground and K(4p)+Na(3s) excited state manifold of NaK, analyze the spin character of both the Feshbach molecular state and the electronically excited intermediate states and discuss possible coherent two-photon transfer paths from Feshbach molecules to rovibronic ground state molecules. The theoretical study is complemented by the demonstration of STIRAP transfer from the X^1\Sigma^+ (v=0) state to the a^3\Sigma^+ manifold on a molecular beam experiment.