We consider collisions of electric and magnetic polar molecules, taking the OH radical as an example, subject to combined electric and magnetic static fields. We show that the relative orientation of the fields has an important effect on the collision processes for different fields magnitude at different collision energies. This is due to the way the molecules polarize in the combined electric and magnetic fields and hence the way the electric dipole-dipole interaction rises. If OH molecules are confined in magnetic quadrupole traps and if an electric field is applied, molecular collisions will strongly depend on the position as well as the velocity of the molecules, and consequences on the molecular dynamics are discussed.
Heavy polar diatomic molecules are the leading candidates in searches for the permanent electric dipole moment of the electron (eEDM). Next-generation eEDM search experiments ideally require extremely large coherence times, in large ensembles of trapped molecules that have a high sensitivity to the eEDM. We consider a family of molecules, mercury-alkali diatomics, that can be feasibly produced from ultracold atoms. We present calculations of the effective electric fields experienced by the electron in these molecules. The combination of reasonably large effective electric fields, and a straigh…
We demonstrate one-dimensional sub-Doppler laser cooling of a beam of YbF molecules to 100 $μ$K. This is a key step towards a measurement of the electron's electric dipole moment using ultracold molecules. We compare the effectiveness of magnetically-assisted and polarization-gradient sub-Doppler cooling mechanisms. We model the experiment and find good agreement with our data.
Permanent electric dipole moments (EDMs) of fundamental particles such as the electron are signatures of parity and time-reversal violation due to physics beyond the standard model. EDM measurements probe new physics at energy scales well beyond the reach of present-day colliders. Recent advances in assembling molecules from ultracold atoms have opened up new opportunities for improving the reach of EDM experiments. But better measurement techniques, that are not limited by the magnetic field sensitivity of such molecules, are necessary before these opportunities can be fully exploited. We pre…
We consider ultracold collisions of polar molecules confined in a one dimensional optical lattice. Using a quantum scattering formalism and a frame transformation method, we calculate elastic and chemical quenching rate constants for fermionic molecules. Taking KRb molecules as a prototype, we find that the rate of quenching collisions is enhanced at zero electric field as the confinement is increased, but that this rate is suppressed when the electric field is turned on. For molecules with 500 nK of collision energy, for realistic molecular densities, and for achievable experimental electric …
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 wave function of the atom-pair at short separations where photoassociation transitions occur according to 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 scattering wave function at short s…
The prospects for shielding ultracold, paramagnetic, dipolar molecules from inelastic and chemical collisions are investigated. Molecules placed in their first rotationally excited states are found to exhibit effective long-range repulsion for applied electric fields above a certain critical value, as previously shown for non-paramagnetic molecules. This repulsion can safely allow the molecules to scatter while reducing the risk of inelastic or chemically reactive collisions. Several molecular species of $^2Σ$ molecules of experimental interest -- RbSr, SrF, BaF, and YO -- are considered, and …
We report the observation of dipole-forbidden, but quadrupole-allowed, one-photon transitions to high Rydberg states in Rb. Using pulsed UV excitation of ultracold atoms in a magneto-optical trap, we excite $5s \to nd$ transitions over a range of principal quantum numbers $n=27-59$. Compared to dipole-allowed (E1) transitions from $5s \to np$, these E2 transitions are weaker by a factor of approximately 2000. We also report measurements of the anomalous $np_{3/2} : np_{1/2}$ fine-structure transition strength ratio for $n=28-75$. Both results are in agreement with theoretical predictions.
It is demonstrated that elastic collisions of ultracold atoms forming a heteronuclear collision complex can be manipulated by laboratory practicable dc electric fields. The mechanism of electric field control is based on the interaction of the instantaneous dipole moment of the collision pair with external electric fields. It is shown that this interaction is dramatically enhanced in the presence of a p-wave shape or Feshbach scattering resonance near the collision threshold, which leads to novel electric-field-induced Feshbach resonances.
The scattering length is commonly used to characterize the strength of ultracold atomic interactions, since it is the leading parameter in the low-energy expansion of the scattering phase shift. Its value can be modified via a magnetic field, by using a Feshbach resonance. However, the effective range term, which is the second parameter in the phase shift expansion, determines the width of the resonance and gives rise to important properties of ultracold gases. Independent control over this parameter is not possible by using a magnetic field only. We demonstrate that a combination of magnetic …
We use the quantum threshold laws combined with a classical capture model to provide an analytical estimate of the chemical quenching cross sections and rate coefficients of two colliding particles at ultralow temperatures. We apply this quantum threshold model (QT model) to indistinguishable fermionic polar molecules in an electric field. At ultracold temperatures and in weak electric fields, the cross sections and rate coefficients depend only weakly on the electric dipole moment d induced by the electric field. In stronger electric fields, the quenching processes scale as d^{4(L+1/2)} where…
We consider ultracold collisions of ground-state, heteronuclear alkali dimers that are susceptible to four-center chemical reactions 2 AB -> A2 + B2 even at sub-microKelvin temperature. These reactions depend strongly on species, temperature, electric field, and confinement in an optical lattice. We calculate ab initio van der Walls coefficients for these interactions, and use a quantum formalism to study the scattering properties of such molecules under an external electric field and optical lattice. We also apply a quantum threshold model to explore the dependence of reaction rates on the va…
We report on hyperfine-resolved spectroscopic measurements of the electric-dipole forbidden 5$p_{3/2} \to 8p_{1/2}$ transition in a sample of ultracold $^{87}$Rb atoms. The hyperfine selection rules enable the weak magnetic-dipole (M1) contribution to the transition strength to be distinguished from the much stronger electric-quadrupole (E2) contribution. An upper limit on the M1 transition strength is determined that is about 50 times smaller than an earlier experimental determination. We also calculate the expected value of the M1 matrix element and find that it is less than the upper limit …
Electrons in an expanding ultracold plasma are expected to be in quasi-equilibrium, since the collision times are short compared to the plasma lifetime, yet we observe electrons evaporating out as the ion density decreases during expansion. We observe that a small electric field that shifts the electron cloud with respect to the ions increases the evaporation rate. We have calculated the spatial distribution of a zero-temperature electron cloud as a function of applied field and ion density, which is assumed to be Gaussian at all times. This calculation allows us to predict the flux of cold el…
The properties of the electronic ground state of the polar and paramagnetic chromium--closed-shell-atom molecules have been investigated. State-of-the-art \textit{ab initio} techniques have been applied to compute the potential energy curves for the chromium--alkaline-earth-metal-atom, CrX (X = Be, Mg, Ca, Sr, Ba), and chromium--ytterbium, CrYb, molecules in the Born-Oppenheimer approximation for the $X^7Σ^+$ high-spin electronic ground state. The spin restricted open-shell coupled cluster method restricted to single, double, and noniterative triple excitations, RCCSD(T), was employed and the …
We report on a combined experimental and theoretical study of polarization self-rotation in an ultracold atomic sample. In the experiments, a probe laser is tuned in the spectral vicinity of the D1 line to observe polarization self-rotation in a sample of ultracold Rb prepared in a magneto-optical trap. Systematic measurements of the rotation angle of the light-polarization ellipse as a function of laser intensity, initial ellipticity and detuning are made. The observations, in good agreement with theoretical simulations, are indicative of the presence of a residual static magnetic field, resu…
In this paper, we present an electrode geometry for the manipulation of ultracold rovibrational ground state NaK molecules. The electrode system allows to induce a dipole moment in trapped diatomic NaK molecules with a magnitude up to $68 \%$ of their internal dipole moment along any direction in a given two-dimensional plane. The strength, the sign and the direction of the induced dipole moment is therefore fully tunable. Furthermore, the possibility to create strong electric field gradients provides the opportunity to address molecules in single layers of an optical lattice. The maximal rela…
The cross section of dipole-magnetic photodisintegration of the negative hydrogen ion has been calculated within the framework of an effective-range theory. The dipole-magnetic cross section of photodetachment within the very narrow range of energy near the process threshold dominates over the dipole-electric one. It has been shown that in ultracold hydrogen plasma at temperatures below kT=3.29.10-4 K the dipole-magnetic photo-recombination becomes a main mechanism of electron capture by hydrogen atoms.
Trapped ultracold neutrons (UCN) have for many years been the mainstay of experiments to search for the electric dipole moment (EDM) of the neutron, a critical parameter in constraining scenarios of new physics beyond the Standard Model. Because their energies are so low, UCN preferentially populate the lower region of their physical enclosure, and do not sample uniformly the ambient magnetic field throughout the storage volume. This leads to a substantial increase in the rate of depolarization, as well as to shifts in the measured frequency of the stored neutrons. Consequences for EDM measure…
We theoretically study collisions between ultracold polar molecules that are polarized by microwave or static electric fields. We systematically study the dependence on field strength, microwave polarization, and detuning from rotational transitions. We calculate the loss in two-body collisions that is observable experimentally and compare to the results expected for purely first-order dipolar interactions. For ground state molecules polarized by a static electric field, the dynamics are accurately described by first-order dipolar interactions. For microwave dressing, instead, resonant dipolar…
We propose a new method to produce an electric and magnetic dipolar gas of ultracold dysprosium atoms. The pair of nearly degenerate energy levels of opposite parity, at 17513.33 cm$^{-1}$ with electronic angular momentum $J=10$, and at 17514.50 cm$^{-1}$ with $J=9$, can be mixed with an external electric field, thus inducing an electric dipole moment in the laboratory frame. For field amplitudes relevant to current-day experiments, we predict a magnetic dipole moment up to 13 Bohr magnetons, and an electric dipole moment up to 0.22 Debye, which is similar to the values obtained for alkali-met…
We briefly introduce the formalism for describing dipolar molecules in an ultracold gaseous environment. This treatment includes the quantum mechanical states of the dipoles, the electric fields they produce, and their interactions with one another.
We present a time-independent quantum formalism to describe the dynamics of molecules with permanent electric dipole moments in a two-dimensional confined geometry such as a one-dimensional optical lattice, in the presence of an electric field. Bose/Fermi statistics and selection rules play a crucial role in the dynamics. As examples, we compare the dynamics of confined fermionic and bosonic polar KRb molecules under different confinements and electric fields. We show how chemical reactions can be suppressed, either by a "statistical suppression" which applies for fermions at small electric fi…
We report on a measurement of the characteristic temperature of an ultracold rubidium ion source, in which a cloud of laser-cooled atoms is converted to ions by photo-ionization. Extracted ion pulses are focused on a detector with a pulsed-field technique. The resulting experimental spot sizes are compared to particle-tracking simulations, from which a source temperature $T = (1 \pm 2)$ mK and the corresponding transversal reduced emittance $ε_r = 7.9 X 10^{-9}$ m rad $\sqrt{\rm{eV}}$ are determined. We find that this result is likely limited by space charge forces even though the average numb…
We investigate the electric field shielding of ultracold collisions of dipolar rotors, initially in their first rotational excited state, using an adimensional approach. We establish a map of good and bad candidates for efficient evaporative cooling based on this shielding mechanism, by presenting the ratio of elastic over quenching processes as a function of a rescaled rotational constant $\tilde{B} = B/s_{E_3}$ and a rescaled electric field $\tilde{F} = dF/B$. $B, d, F, s_{E_3}$ are respectively the rotational constant, the full electric dipole moment of the molecules, the applied electric f…
Selection of "magic" trapping conditions with ultracold atoms or molecules, where pairs of internal states experience identical trapping potentials, brings substantial benefits to precision measurements and quantum computing schemes. Working at such conditions could ensure that detrimental effects of inevitable inhomogeneities across an ultracold sample are significantly reduced. However, this aspect of confinement remains unexplored for ultracold polar molecules. Here, we present means to control the AC Stark shift of rotational states of ultracold polar molecules, when subjected to both trap…
We describe the realization of a dc electric-field trap for ultracold polar molecules, the thin-wire electrostatic trap (TWIST). The thin wires that form the electrodes of the TWIST allow us to superimpose the trap onto a magneto-optical trap (MOT). In our experiment, ultracold polar NaCs molecules in their electronic ground state are created in the MOT via photoassociation, achieving a continuous accumulation in the TWIST of molecules in low-field seeking states. Initial measurements show that the TWIST trap lifetime is limited only by the background pressure in the chamber.
We calculate pair potential curves for interacting Rydberg atoms in a constant electric field and use them to determine the effective $C_3$ dipole-dipole and $C_6$ van der Waals coefficients. We compare the $C_3$ and $C_6$ with experiments where the angle of a polarizing electric field is varied with respect to the axis of a quasi-1-dimensional trap at ultracold temperatures. The dipoles produced via polarization of the atoms have an angular dependent dipole-dipole interaction. We focus on the interaction potential of two rubidium Rydberg atoms in $50S_{1/2}$ states in the blockade regime. For…
We create fermionic dipolar $^{23}$Na$^6$Li molecules in their triplet ground state from an ultracold mixture of $^{23}$Na and $^6$Li. Using magneto-association across a narrow Feshbach resonance followed by a two-photon STIRAP transfer to the triplet ground state, we produce $3\,{\times}\,10^4$ ground state molecules in a spin-polarized state. We observe a lifetime of $4.6\,\text{s}$ in an isolated molecular sample, approaching the $p$-wave universal rate limit. Electron spin resonance spectroscopy of the triplet state was used to determine the hyperfine structure of this previously unobserve…
Ultracold collisions of LiO molecules in the $^{2}Π_{3/2}$ ground state are considered, under the influence of either an external magnetic or electric field. Inelastic collisions are shown to be suppressed in the presence of modest laboratory strength magnetic and electric fields. The rate of elastic collisions that rethermalize the thermal distribution, and the corresponding low rate of heating state-changing collisions, suggest that quantum degeneracy or even molecular Bose-Einstein condensation of LiO gas may be attainable, provided that the initial temperatures in the milliKelvin range are…
We investigate the ultracold collisions of rotationally excited dipolar molecules in free-space, taking the hetero-nuclear bi-alkali molecule of KRb as an example. We show that we can sharply tune the elastic, inelastic and reactive rate coefficients of lossy molecular collisions when a second rotationally excited colliding channel crosses the threshold of the initial colliding channel, with the help of an applied electric field, as found by Avdeenkov et al. for non-lossy molecules [Phys. Rev. A 73, 022707 (2006)]. We can increase or decrease the loss processes whether the second channel is ab…
The dipolar collision between ultracold polar molecules is an important topic both by its own right from the fundamental point of view and for the successful exploration of many-body physics with strong and long-range dipolar interactions. Here, we report the investigation of collisions between ultracold ground-state sodium-rubidium molecules in electric fields with induced electric dipole moments as large as 0.7$\;$D. We observe a step-wise enhancement of losses due to the coupling between different partial waves induced by the increasingly stronger anisotropic dipolar interactions. Varying t…
Recent improvements in experimental techniques for preparing ultracold molecules that contain alkali atoms (e.g., Li, Na, and K) have been reported. Based on these advances in ultracold molecules, new searches for the electric dipole moment of the electron and the scalar-pseudoscalar interaction can be proposed on such systems. We calculate the effective electric fields (Eeff) and the S-PS coefficients (Ws) of SrA and HgA (A = Li, Na, and K) molecules at the Dirac-Fock (DF) and the relativistic coupled cluster (RCC) levels. We elaborate on the following points: i) Basis set dependence of the m…
We have realized a high-resolution time-of-flight mass spectrometer combined with a magneto-optical trap. The spectrometer enables excellent optical access to the trapped atomic cloud using specifically devised acceleration and deflection electrodes. The ions are extracted along a laser beam axis and deflected onto an off axis detector. The setup is applied to detect atoms and molecules photoassociated from ultracold atoms. The detection is based on resonance-enhanced multi-photon ionization. Mass resolution up to m/Delta m_rms = 1000 at the mass of 133Cs is achieved. The performance of this s…
We determine trapping conditions for ultracold polar molecules, where pairs of internal states experience identical trapping potentials. Such conditions could ensure that detrimental effects of inevitable inhomogeneities across an ultracold sample are significantly reduced. In particular, we investigate the internal rovibronic and hyperfine quantum states of ultracold fermionic ground-state $^{40}$K$^{87}$Rb polar molecules, when static magnetic, static electric, and trapping laser fields are simultaneously applied. Understanding the effect of changing the relative orientation or polarization …
We recently reported the formation of ultracold LiCs molecules in the rovibrational ground state X1Sigma+,v''=0,J''=0 [J. Deiglmayr et al., PRL 101, 133004 (2008)]. Here we discuss details of the experimental setup and present a thorough analysis of the photoassociation step including the photoassociation line shape. We predict the distribution of produced ground state molecules using accurate potential nergy curves combined with an ab-initio dipole transition moment and compare this prediction with experimental ionization spectra. Additionally we improve the value of the dissociation energy f…
We use two-dimensional transverse laser cooling to produce an ultracold beam of YbF molecules. Through experiments and numerical simulations, we study how the cooling is influenced by the polarization configuration, laser intensity, laser detuning and applied magnetic field. The ultracold part of the beam contains more than $2 \times 10^5$ molecules per shot and has a temperature below 200 $μ$K, and the cooling yields a 300-fold increase in the brightness of the beam. The method can improve the precision of experiments that use molecules to test fundamental physics. In particular, the beam is …
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 c…
Ultracold polar molecules offer the possibility of exploring quantum gases with interparticle interactions that are strong, long-range, and spatially anisotropic. This is in stark contrast to the dilute gases of ultracold atoms, which have isotropic and extremely short-range, or "contact", interactions. The large electric dipole moment of polar molecules can be tuned with an external electric field; this provides unique opportunities such as control of ultracold chemical reactions, quantum information processing, and the realization of novel quantum many-body systems. In spite of intense exper…
We report on the compensation of excess micromotion due to parasitic rf-electric fields in a Paul trap. The parasitic rf-electric fields stem from the Paul trap drive but cause excess micromotion, e.g. due to imperfections in the setup of the Paul trap. We compensate these fields by applying rf-voltages of the same frequency but adequate phases and amplitudes to Paul trap electrodes. The magnitude of micromotion is probed by studying elastic collision rates of the trapped ion with a gas of ultracold neutral atoms. Furthermore, we demonstrate that also reactive collisions can be used to quantif…
We investigate pump-dump photoassociation of ultracold molecules with amplitude- and phase-modulated femtosecond laser pulses. For this purpose a perturbative model for the light-matter interaction is developed and combined with a genetic algorithm for adaptive feedback control of the laser pulse shapes. The model is applied to the formation of 85Rb2 molecules in a magneto-optical trap. We find for optimized pulse shapes an improvement for the formation of ground state molecules by more than a factor of 10 compared to unshaped pulses at the same pump-dump delay time, and by 40% compared to uns…
Measurements of interactions between cold molecules and ultracold atoms can allow for a detailed understanding of fundamental collision processes. These measurements can be done using various experimental geometries including where both species are in a beam, where one species is trapped, or when both species are trapped. Simultaneous trapping offers significantly longer interaction times and an associated increased sensitivity to rare collision events. However, there are significant practical challenges associated with combining atom and molecule systems, which often have competing experiment…
This paper reviews recent advances in the study of strongly interacting systems of dipolar molecules. Heteronuclear molecules feature large and tunable electric dipole moments, which give rise to long-range and anisotropic dipole-dipole interactions. Ultracold samples of dipolar molecules with long-range interactions offer a unique platform for quantum simulations and the study of correlated many-body physics. We provide an introduction to the physics of dipolar quantum gases, both electric and magnetic, and summarize the multipronged efforts to bring dipolar molecules into the quantum regime.…
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 absol…
We propose a scheme to realize a heavy Rydberg system (HRS), a bound pair of oppositely charged ions, from a gas of ultracold atoms. The intermediate step to achieve large internuclear separations is the creation of a unique class of ultra-long-range Rydberg molecules bound in a stairwell potential energy curve. Here, a ground-state atom is bound to a Rydberg atom in an oscillatory potential emerging due to attractive singlet $p$-wave electron scattering. The utility of our approach originates in the large electronic dipole transition element between the Rydberg- and the ionic molecule, while …
We explore the feasibility of producing ultracold diatomic molecules with nonzero electric and magnetic dipole moments by magnetically associating two atoms, one with zero electron spin and one with nonzero spin. Feshbach resonances arise through the dependence of the hyperfine coupling on internuclear distance. We survey the Feshbach resonances in diatomic systems combining the nine stable alkali-metal isotopes with those of Yb, focussing on the illustrative examples of RbYb and CsYb. We show that the resonance widths may expressed as a product of physically comprehensible terms in the framew…
We predict that pairs of polar molecules can be weakly bound together in an ultracold environment, provided that a dc electric field is present. The field that links the molecules together also strongly influences the basic properties of the resulting dimer, such as its binding energy and predissociation lifetime. Because of their long-range character these dimers will be useful in disentangling cold collision dynamics of polar molecules. As an example, we estimate the microwave photoassociation yield for OH-OH cold collisions.
We have investigated Feshbach resonances in collisions of high-spin atoms such as Er and Dy with closed-shell atoms such as Sr and Yb, using coupled-channel scattering and bound-state calculations. We consider both low-anisotropy and high-anisotropy limits. In both regimes we find many resonances with a wide variety of widths. The wider resonances are suitable for tuning interatomic interactions, while some of the narrower resonances are highly suitable for magnetoassociation to form high-spin molecules. These molecules might be transferred to short-range states, where they would have large ma…
The collisional stability of ultracold polar molecules in electrostatic traps is considered. Rate constants for collisions that drive molecules from weak-field-seeking to strong-field-seeking states are estimated using a simple model. The rates are found to be quite large, of order 10^{-12} - 10^{-10} cm^3/sec, and moreover to grow rapidly in an externally applied electric field. It is argued that these results are generic for polar molecules, and that therefore polar molecules should be trapped by other than electrostatic means.
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 molecule…
We study polar alkali dimer scattering in a quasi-1D geometry for both reactive and non-reactive species. Elastic and reactive rates are computed as a function of the amplitude of a static electric field within a purely long-range model with suitable boundary conditions at shorter range. We describe the diatomic molecules as rigid rotors and results are compared to the fixed-dipole approximation. We show in particular that for molecules with a sufficiently strong induced dipole moment oriented perpendicular to the trap axis, the long-range repulsive interaction leads to the suppression of shor…
