arXiv subjects

Olivier Dulieu

Publications and source records attributed to Olivier Dulieu.

At least 55 records · Page 3Linked to original sources

arXiv2017

Long-range interactions between ultracold atoms and molecules

The term "long-range interactions" refers to electrostatic and magnetostatic potential energies between atoms and molecules with mutual distances ranging from a few tens to a few hundreds Bohr radii. The involved energies are much smaller than the usual chemical bond energies. However, they are comparable with the typical kinetic energies of particles in an ultracold gas ($T\ll 1K$), so that the long-range interactions play a central role in its dynamics. The progress of research devoted to ultracold gases shed a new light on the well-established topic of long-range interactions, because: (i) the interacting atoms and molecules can be prepared in a well-defined quantum (electronic, vibrational, rotational, fine or hyper-fine), ground or excited level; and (ii) long-range interactions can be tailored at will using external electromagnetic fields. In this chapter, we present the essential concepts and mathematical relations to calculate long-range potential energies. We start with deriving the multipolar expansion of the electrostatic interaction energy between classical charge distributions, both in Cartesian coordinates for pedagogical purpose, and in spherical coordinates for practical use. Then we combine multipolar expansion and quantum perturbation theory, to obtain the general first- and second-order energy corrections, including the well-known van der Waals energy. We consider two central examples in the current context of ultracold gases: (i) a pair of alkali-metal atoms and (ii) a pair of alkali-metal heteronuclear diatomic molecules submitted to an electric field. We highlight the key role of the total angular momenta of the interacting particles and of the complex, irrespective of their electronic or nuclear, orbital or spin nature.

quant-ph↗

arXiv2016

Polarizability of ultracold $\textrm{Rb}_2$ molecules in the rovibrational ground state of $\mathrm{a}^3Σ_u^+$

We study, both theoretically and experimentally, the dynamical polarizability $α(ω)$ of $\textrm{Rb}_2$ molecules in the rovibrational ground state of $\mathrm{a}^3Σ_u^+$. Taking all relevant excited molecular bound states into account, we compute the complex-valued polarizability $α(ω)$ for wave numbers up to $20000\:\textrm{cm}^{-1}$. Our calculations are compared to experimental results at $1064.5\:\textrm{nm}$ ($\sim9400\:\textrm{cm}^{-1}$) as well as at $830.4\:\textrm{nm}$ ($\sim12000\:\textrm{cm}^{-1}$). Here, we discuss the measurements at $1064.5\:\textrm{nm}$. The ultracold $\textrm{Rb}_2$ 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 $2\:\textrm{s}$ are observed. In addition, the dynamical polarizability for the $\mathrm{X}^1Σ_g^+$ state is calculated. We provide simple analytical expressions that reproduce the numerical results for $α(ω)$ for all vibrational levels of $\mathrm{a}^3Σ_u^+$ as well as $\mathrm{X}^1Σ_g^+$. 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 $\sim1064\:\textrm{nm}$ is of interest, since here, ultrastable high power lasers are available.

physics.atom-ph↗

arXiv2016

Photodissociation of trapped Rb$^+_2$ : Implications for simultaneous trapping of atoms and molecular ions

The direct photodissociation of trapped $^{85}$Rb$_2^+$ (rubidium) molecular ions by the cooling light for the $^{85}$Rb magneto-optical trap (MOT) is studied, both experimentally and theoretically. Vibrationally excited Rb$_{2}^{+}$ ions are created by photoionization of Rb$_{2}$ molecules formed photoassociatively in the Rb MOT and are trapped in a modified spherical Paul trap. The decay rate of the trapped Rb$_{2}^{+}$ ion signal in the presence of the MOT cooling light is measured and agreement with our calculated rates for molecular ion photodissociation is observed. The photodissociation mechanism due to the MOT light is expected to be active and therefore universal for all homonuclear diatomic alkali metal molecular ions.

physics.atom-ph↗

arXiv2016

Optical trapping of ultracold dysprosium atoms: transition probabilities, dynamic dipole polarizabilities and van der Waals $C_6$ coefficients

The efficiency of optical trapping of ultracold atoms depend on the atomic dynamic dipole polarizability governing the atom-field interaction. In this article, we have calculated the real and imaginary parts of the dynamic dipole polarizability of dysprosium in the ground and first excited level. Due to the high electronic angular momentum of those two states, the polarizabilities possess scalar, vector and tensor contributions that we have computed, on a wide range of trapping wavelengths, using the sum-over-state formula. Using the same formalism, we have also calculated the $C_6$ coefficients characterizing the van der Waals interaction between two dysprosium atoms in the two lowest levels. We have computed the energies of excited states and the transition probabilities appearing in the sums, using a combination of \textit{ab initio} and least-square-fitting techniques provided by the Cowan codes and extended in our group. Regarding the real part of the polarizability, for field frequencies far from atomic resonances, the vector and tensor contributions are two-order-of-magnitude smaller than the scalar contribution, whereas for the imaginary part, the vector and tensor contributions represent a noticeable fraction of the scalar contribution. This offers the possibility to control the decoherence and trap losses due to spontaneous emission.

physics.atom-ph↗

arXiv2016

Creation of an ultracold gas of ground-state $^{23}\rm{Na}^{87}\rm{Rb}$ molecules

We report the successful production of an ultracold sample of absolute ground-state $^{23}$Na$^{87}$Rb molecules. Starting from weakly-bound Feshbach molecules formed via magneto-association, the lowest rovibrational and hyperfine level of the electronic ground state is populated following a high efficiency and high resolution two-photon Raman process. The high purity absolute ground-state samples have up to 8000 molecules and densities of over $10^{11}$ cm$^{-3}$. By measuring the Stark shifts induced by external electric fields, we determined the permanent electric dipole moment of the absolute ground-state $^{23}$Na$^{87}$Rb and demonstrated the capability of inducing an effective dipole moment over one Debye. Bimolecular reaction between ground-state $^{23}$Na$^{87}$Rb molecules is endothermic, but we still observed a rather fast decay of the molecular sample. Our results pave the way toward investigation of ultracold molecular collisions in a fully controlled manner, and possibly to quantum gases of ultracold bosonic molecules with strong dipolar interactions.

cond-mat.quant-gas↗

arXiv2016

Long-range states of the NaRb molecule near the Na($3^2S_{1/2}$)+Rb($5^2P_{3/2}$) asymptote

We report a high-resolution spectroscopic investigation of the long-range states of the $^{23}$Na$^{87}$Rb molecule near its Na($3^2S_{1/2}$)+Rb($5^2P_{3/2}$) asymptote. This study was performed with weakly bound ultracold molecules produced via magneto-association with an inter-species Feshbach resonance. We observed several regular vibrational series, which are assigned to the 5 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($3^2S_{1/2}$)+Rb($5^2P_{1/2}$) asymptote. The long-range $C_6$ van der Waals coefficients extracted from our spectrum are in good agreement with theoretical values.

physics.atom-ph↗

arXiv2015

Four-body long-range interactions between ultracold weakly-bound diatomic molecules

Using the multipolar expansion of electrostatic and magnetostatic potential energies, we characterize the long-range interactions between two weakly-bound diatomic molecules, taking as an example the paramagnetic Er$_2$ Feshbach molecules which were produced recently. Since inside each molecule, individual atoms conserve their identity, the intermolecular potential energy can be expanded as the sum of pairwise atomic potential energies. In the case of Er$_2$ Feshbach molecules, we show that the interaction between atomic magnetic dipoles gives rise to the usual $R^{-3}$ term of the multipolar expansion, with $R$ the intermolecular distance, but also to additional terms scaling as $R^{-5}$, $R^{-7}$, and so on. Those terms are due to the interaction between effective molecular multipole moments, and are strongly anisotropic with respect to the orientation of the molecules. Similarly the atomic pairwise van der Waals interaction results in $R^{-6}$, $R^{-8}$, ... terms in the intermolecular potential energy. By calculating the reduced electric-quadrupole moment of erbium ground level $\langle J=6||\hat{Q}_2||J=6\rangle = -1.305$ a.u., we also demonstrate that the electric-quadrupole interaction energy is negligible with respect to the magnetic-dipole and van der Waals interaction energies. The general formalism presented in this article can be applied to calculate the long-range potential energy between arbitrary charge distributions composed of almost free subsystems.

physics.atom-ph↗

arXiv2015

Proposal for laser-cooling of rare-earth ions

The efficiency of laser-cooling relies on the existence of an almost closed optical-transition cycle in the energy spectrum of the considered species. In this respect rare-earth elements exhibit many transitions which are likely to induce noticeable leaks from the cooling cycle. In this work, to determine whether laser-cooling of singly-ionized erbium Er$^+$ is feasible, we have performed accurate electronic-structure calculations of energies and spontaneous-emission Einstein coefficients of Er$^+$, using a combination of \textit{ab initio} and least-square-fitting techniques. We identify five weak closed transitions suitable for laser-cooling, the broadest of which is in the kilohertz range. For the strongest transitions, by simulating the cascade dynamics of spontaneous emission, we show that repumping is necessary, and we discuss possible repumping schemes. We expect our detailed study on Er$^+$ to give a good insight into laser-cooling of neighboring ions like Dy$^+$.

physics.atom-ph↗

arXiv2015

Dynamics of ultracold dipolar particles in a confined geometry and tilted fields

We develop a collisional formalism adapted for the dynamics of ultracold dipolar particles in a confined geometry and in fields tilted relative to the confinement axis. Using tesseral harmonics instead of the usual spherical harmonics to expand the scattering wavefunction, we recover a good quantum number $ξ= \pm 1$ which is conserved during the collision. We derive the general expression of the dipole-dipole interaction in this convenient basis set as a function of the polar and azimuthal angles of the fields. We apply the formalism to the collision of fermionic and bosonic polar KRb molecules in a tilted electric field and in a one-dimensional optical lattice. The presence of a tilted field drastically changes the magnitude of the reactive and inelastic rates as well as the inelastic threshold properties at vanishing collision energies. Setting an appropriate strength of the confinement for the fermionic system, we show that the ultracold particles can even further reduce their kinetic energy by inelastic excitation to higher states of the confinement trap.

physics.atom-ph↗

arXiv2015

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 light-assisted ultracold chemical reaction. The calculation of the photoassociation rate of ultracold Cs atoms with ultracold Cs$_2$ molecules in their rovibrational ground state 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.

physics.atom-ph↗

arXiv2015

Formation of molecular ions by radiative association of cold trapped atoms and ions

Radiative emission during cold collisions between trapped laser-cooled Rb atoms and alkaline-earth ions (Ca$^+$, Sr$^+$, Ba$^+$) and Yb$^+$, and between Li and Yb$^+$, are studied theoretically, using accurate effective-core-potential based quantum chemistry calculations of potential energy curves and transition dipole moments of the related molecular ions. Radiative association of molecular ions is predicted to occur for all systems with a cross section two to ten times larger than the radiative charge transfer one. Partial and total rate constants are also calculated and compared to available experiments. Narrow shape resonances are expected, which could be detectable at low temperature with an experimental resolution at the limit of the present standards. Vibrational distributions are also calculated, showing that the final molecular ions are not created in their ground state level.

physics.atom-ph↗

arXiv2015

Theoretical study of radiative electron attachment to CN, C2H, and C4H radicals

A first-principle theoretical approach to study the process of radiative electron attachment is developed and applied to the negative molecular ions CN$^-$, C$_4$H$^-$, and C$_2$H$^-$. Among these anions, the first two have already been observed in the interstellar space. Cross sections and rate coefficients for formation of these ions by radiative electron attachment to the corresponding neutral radicals are calculated. For completeness of the theoretical approach, two pathways for the process have been considered: (i) A direct pathway, in which the electron in collision with the molecule spontaneously emits a photon and forms a negative ion in one of the lowest vibrational levels, and (ii) an indirect, or two-step pathway, in which the electron is initially captured through non-Born-Oppenheimer coupling into a vibrationally resonant excited state of the anion, which then stabilizes by radiative decay. We develop a general model to describe the second pathway and show that its contribution to the formation of cosmic anions is small in comparison to the direct mechanism. The obtained rate coefficients at 30~K are $7\times 10^{-16}$cm$^3$/s for CN$^-$, $7\times 10^{-17}$cm$^3$/s for C$_2$H$^-$, and $2\times 10^{-16}$cm$^3$/s for C$_4$H$^-$. These rates weakly depend on temperature between 10K and 100 K. The validity of our calculations is verified by comparing the present theoretical results with data from recent photodetachment experiments.

physics.chem-ph↗

arXiv2014

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

We produce ultracold dense trapped samples of 87Rb133Cs 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.

cond-mat.quant-gas↗

arXiv2014

Statistical product distributions for ultracold reactions in external fields

The main limitation of most ultracold chemistry studies to date is the lack of an analysis of reaction products. Here, we discuss the first generally tractable, rigorous theoretical framework for computing statistical product-state distributions for ultracold reactions in external fields. We show that fields have two main effects on the products of a statistical reaction, by: (1) modifying the product energy levels thus potentially reshaping the product distributions; and/or (2) adding or removing product states by changing the reaction exothermicity. By analyzing these effects and the strength of the formalism to distinguish between different reaction mechanisms in benchmark reactions involving $^{40}$K and $^{87}$Rb species, we argue that statistical predictions will help understanding product formation and control, and lead developments to realize the full potential of ultracold chemistry.

physics.chem-ph↗

arXiv2014

Ground and excited state properties of the polar and paramagnetic RbSr molecule: a comparative study

This paper deals with the electronic structure of RbSr, a molecule possessing both a permanent magnetic and electric dipole moment in its own frame allowing its manipulation with external fields. Two complementary ab-initio approaches are used for the ground and lowest excited states: first, an approach relying on optimized effective core potentials with core polarization potentials based on a full configuration interaction involving three valence electrons, and second, an approach using a small-size effective core potential with 19 correlated electrons in the framework of coupled-cluster theory. We have found excellent agreement between these two approaches for the ground state properties including the permanent dipole moment. We have focused on studies of excited states correlated to the two lowest asymptotes Rb(5p)+Sr(5s) and Rb(5s)+Sr(5s5p) relevant for ongoing experiments on quantum degenerate gases. We present also the Hund c) case potential curves obtained using atomic spin-orbit constants. These potential curves are an excellent starting point for experimental studies of molecular structure of RbSr using high-resolution spectroscopy.

physics.chem-ph↗

arXiv2013

Anisotropic optical trapping of ultracold erbium atoms

Ultracold atoms confined in a dipole trap are submitted to a potential whose depth is proportional to the real part of their dynamic dipole polarizability. The atoms also experience photon scattering whose rate is proportional to the imaginary part of their dynamic dipole polarizability. In this article we calculate the complex dynamic dipole polarizability of ground-state erbium, a rare-earth atom that was recently Bose-condensed. The polarizability is calculated with the sum-over-state formula inherent to second-order perturbation theory. The summation is performed on transition energies and transition dipole moments from ground-state erbium, which are computed using the Racah-Slater least-square fitting procedure provided by the Cowan codes. This allows us to predict 9 unobserved odd-parity energy levels of total angular momentum J=5, 6 and 7, in the range 25000-31000 cm-1 above the ground state. Regarding the trapping potential, we find that ground-state erbium essentially behaves like a spherically-symmetric atom, in spite of its large electronic angular momentum. We also find a mostly isotropic van der Waals interaction between two ground-state erbium atoms, characterized by a coefficient C_6^{iso}=1760 a.u.. On the contrary, the photon-scattering rate shows a pronounced anisotropy, since it strongly depends on the polarization of the trapping light.

physics.atom-ph↗

arXiv2013

Long-range interactions between polar alkali-metal diatoms in external electric fields

We computed the long-range interactions between two identical polar bialkali molecules in their rovibronic ground level, for all ten species involving Li, Na, K, Rb and Cs, using accurate quantum chemistry results combined with available spectroscopic data. Huge van der Waals interaction is found for eight species in free space. The competition of the van der Waals interaction with the dipole-dipole interaction induced by an external electric field parallel or perpendicular to the intermolecular axis is investigated by varying the electric field magnitude and the intermolecular distance. Our calculations predict a regime with the mutual orientation of the two molecules but with no preferential direction in the laboratory frame. A mechanism for the stimulated one-photon radiative association of a pair of ultracold polar molecules into ultracold tetramers is proposed, which would open the way towards the optical manipulation of ultracold polyatomic molecules.

physics.atom-ph↗

arXiv2013

Resonant states of H$_3^-$ molecule and its isotopologues D$_2$H$^-$ and H$_2$D$^-$

Using the ground potential energy surface[M. Ayouz \textit{et\, al}. J. Chem Phys \textbf{132} 194309 (2010)] of the H$_3^-$ molecule, we have determined the energies and widths of the complex resonant levels of H$_3^-$ located up to 4000 cm$^{-1}$ above the dissociation limit H$^-$+H$_2(v_d=0,j_d=0)$. Bound and resonant levels of the H$_2$D$^-$ and D$_2$H$^-$ isotopologues have been also characterized within the same energy range. The method combines the hyperspherical adiabatic approach, slow variable discretization method, and complex absorbing potential. These results represent the first step for modeling the dynamics of the associated diatom-negative ion collision at low energy involving rotational quenching of the diatom and reactive nucleus exchange via weak tunneling effect through the potential barrier of the potential energy surface.

physics.atom-ph↗