Focus on New Frontiers of Cold Molecules Research

We analyze a system of polar molecules in a one-dimensional optical lattice. By controlling the internal structure of the polar molecules with static electric and microwave fields, we demonstrate the appearance of a quantum phase transition into a ferroelectric phase via spontaneous breaking of a U(1) symmetry. The phase diagram is first analyzed within mean-field theory, while in a second step the results are verified by a mapping onto the Bose–Hubbard model for hard-core bosons. The latter is studied within the well-established bosonization procedure. We find that the ferroelectric phase is characterized by (quasi) long-range order for the electric dipole moments.

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 ${{\rm{B}}}^{1}\Pi | v=4\rangle \sim {{\rm{c}}}^{3}{\Sigma }^{+}| v=25\rangle$, or of resonantly mixed character in ${{\rm{B}}}^{1}\Pi | v=12\rangle \sim {{\rm{c}}}^{3}{\Sigma }^{+}| v=35\rangle$. The dominantly singlet level is used to locate the absolute rovibrational singlet ground state ${{\rm{X}}}^{1}{\Sigma }^{+}| v=0,J=0\rangle$ 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.

We have studied the three-body complex formation rate of the hydroxyl anion with molecular hydrogen at low temperatures. The formed cluster is found to quickly undergo internal proton transfer to a hydrogen anion–water complex. This is probed by photodetachment spectroscopy, which clearly distinguishes the two isomeric structures. The product cluster is the only isomer found to be stably formed at the temperature and densities employed in the experiment. The cluster then binds an additional hydrogen molecule by a second three-body collision, which appears at a rate comparable to the first formation process. This is followed by a rapid growth to larger clusters.

We study, both theoretically and experimentally, the dynamical polarizability $\alpha (\omega )$ of ${\mathrm{Rb}}_{2}$ molecules in the rovibrational ground state of ${a}^{3}{\Sigma }_{u}^{+}$. Taking all relevant excited molecular bound states into account, we compute the complex-valued polarizability $\alpha (\omega )$ for wave numbers up to 20 000 ${{\rm{cm}}}^{-1}$. Our calculations are compared to experimental results at $1064.5\;\mathrm{nm}$ ($\sim 9400\;{{\rm{cm}}}^{-1}$) as well as at $830.4\;\mathrm{nm}$ ($\sim 12\;000\;{{\rm{cm}}}^{-1}$). Here, we discuss the measurements at $1064.5\;\mathrm{nm}$. 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 $2\;{\rm{s}}$ are observed. In addition, the dynamical polarizability for the ${X}^{1}{\Sigma }_{g}^{+}$ state is calculated. We provide simple analytical expressions that reproduce the numerical results for $\alpha (\omega )$ for all vibrational levels of ${a}^{3}{\Sigma }_{u}^{+}$ as well as ${X}^{1}{\Sigma }_{g}^{+}$. 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 $\sim 1064\;\mathrm{nm}$ is of interest, since here, ultrastable high power lasers are available.

A unique property of Zeeman effect based manipulation of paramagnetic particle's motion is the ability to control velocities of both atoms and molecules. In particular the moving magnetic trap decelerator is capable of slowing and eventually trapping mixtures of both cold atoms and cold molecules generated in a supersonic expansion. Here we report the deceleration of molecular oxygen together with metastable argon atoms. The cold mixture with temperature below 1 K is slowed from an initial velocity of 430 m s⁻¹ down to 100 m s⁻¹. Our decelerator spans 2.4 m and consists of 480 quadrupole traps. Our results pave the way for the study of sympathetic cooling of molecules by laser cooled atoms.

We consider the dynamics of rotational excitations placed on a single molecule in spatially disordered one-dimensional (1D), two-dimensional (2D) and three-dimensional (3D) ensembles of ultracold molecules trapped in optical lattices. The disorder arises from incomplete populations of optical lattices with molecules. This leads to a model corresponding to a quantum particle with long-range tunnelling amplitudes moving on a lattice with the same on-site energy but with forbidden access to random sites (vacancies). We examine the time and length scales of Anderson localization for this type of disorder with realistic experimental parameters in the Hamiltonian. We show that for an experimentally realized system of KRb molecules on an optical lattice this type of disorder leads to disorder-induced localization in 1D and 2D systems on a time scale $t\sim 1$ s. For 3D lattices with 55 sites in each dimension and vacancy concentration 90%, the rotational excitations diffuse to the edges of the lattice and show no signature of Anderson localization. We examine the role of the long-range tunnelling amplitudes allowing for transfer of rotational excitations between distant lattice sites. Our results show that the long-range tunnelling has little impact on the dynamics in the diffusive regime but affects significantly the localization dynamics in lattices with large concentrations of vacancies, enhancing the width of the localized distributions in 2D lattices by more than a factor of 2.

Interacting quantum spin models are remarkably useful for describing different types of physical, chemical, and biological systems. Significant understanding of their equilibrium properties has been achieved to date, especially for the case of spin models with short-range couplings. However, progress toward the development of a comparable understanding in long-range interacting models, in particular out-of-equilibrium, remains limited. In a recent work, we proposed a semiclassical numerical method to study spin models, the discrete truncated Wigner approximation (DTWA), and demonstrated its capability to correctly capture the dynamics of one- and two-point correlations in one-dimensional (1D) systems. Here we go one step forward and use the DTWA method to study the dynamics of correlations in two-dimensional (2D) systems with many spins and different types of long-range couplings, in regimes where other numerical methods are generally unreliable. We compute spatial and time-dependent correlations for spin-couplings that decay with distance as a power-law and determine the velocity at which correlations propagate through the system. Sharp changes in the behavior of those velocities are found as a function of the power-law decay exponent. Our predictions are relevant for a broad range of systems including solid state materials, atom–photon systems and ultracold gases of polar molecules, trapped ions, Rydberg, and magnetic atoms. We validate the DTWA predictions for small 2D systems and 1D systems, but ultimately, in the spirt of quantum simulation, experiments will be needed to confirm our predictions for large 2D systems.

We report results for reaction and vibrational quenching of the collision D with para-H₂($v,j=0$) and ortho-H₂($v,j=1$) at cold and ultracold temperatures. We investigate the effect of nuclear spin symmetry for barrier dominated processes ($0\leqslant v\leqslant 4$) and for one barrierless case (v = 5). We find resonant structures for energies in the range corresponding to 0.01–10 K, which depend on the nuclear spin of H₂, arising from contributions of specific partial waves. We discuss the implications on the results in this benchmark system for ultracold chemistry.

A previously developed approach for the numerical treatment of two particles that are confined in a finite optical-lattice potential and interact via an arbitrary isotropic interaction potential has been extended to incorporate an additional anisotropic dipole–dipole interaction (DDI). The interplay of a model but realistic short-range Born–Oppenheimer potential and the DDI for two confined particles is investigated. A variation of the strength of the DDI leads to diverse resonance phenomena. In a harmonic confinement potential some resonances show similarities to s-wave scattering resonances while in an anharmonic trapping potential like the one of an optical lattice additional inelastic confinement-induced dipolar resonances occur. The latter are due to a coupling of the relative and center-of-mass motion caused by the anharmonicity of the external confinement.

We report a quantum dynamics study of the Li + HF → LiF + H reaction at low temperatures of interest to cooling and trapping experiments. Contributions from non-zero partial waves are analyzed and results show narrow resonances in the energy dependence of the cross section that survive partial wave summation. The computations are performed using the ABC code and a simple modification of the ABC code that enables separate energy cutoffs for the reactant and product rovibrational energy levels is found to dramatically reduce the basis set size and computational expense. Results obtained using two ab initio electronic potential energy surfaces for the LiHF system show strong sensitivity to the choice of the potential. In particular, small differences in the barrier heights of the two potential surfaces are found to dramatically influence the reaction cross sections at low energies. Comparison with recent measurements of the reaction cross section (Bobbenkamp et al 2011 J. Chem. Phys. 135 204306) shows similar energy dependence in the threshold regime and an overall good agreement with experimental data compared to previous theoretical results. Also, usefulness of a recently introduced method for ultracold reactions that employ the quantum close-coupling method at short-range and the multichannel quantum defect theory at long-range, is demonstrated in accurately evaluating product state-resolved cross sections for D + H₂ and H + D₂ reactions.

Detecting the internal state of polar molecules is a substantial challenge when standard techniques such as resonance-enhanced multiphoton ionization or laser-induced fluorescense do not work. As this is the case for most polyatomic molecule species, in this paper we investigate an alternative based on state-selective removal of molecules from an electrically trapped ensemble. Specifically, we deplete molecules by driving rotational and/or vibrational transitions to untrapped states. Fully resolving the rotational state with this method can be a considerable challenge, as the frequency differences between various transitions are easily substantially less than the Stark broadening in an electric trap. However, by using a unique trap design that provides homogeneous fields in a large fraction of the trap volume, we successfully discriminate all rotational quantum numbers, including the rotational M-substate.

A Stark decelerator is used in combination with velocity map imaging to study collisions of NO radicals with rare gas atoms in a counterpropagating crossed beam geometry. This powerful combination of techniques results in scattering images with extremely high resolution, in which rotational and L-type rainbows with superimposed quantum mechanical diffraction oscillations are visible. The experimental data are in excellent agreement with quantum mechanical scattering calculations. Furthermore, hard-shell models and a partial wave analysis are used to clarify the origin of the various structures that are visible. A specific feature is found for NO molecules colliding with Ar atoms that is extremely sensitive to the precise shape of the potential energy surface. Its origin is explained in terms of interfering partial waves with very high angular momentum, corresponding to trajectories with large impact parameters.

We present a design for an atomic synchrotron consisting of 40 hybrid magnetic hexapole lenses arranged in a circle. We show that for realistic parameters, hydrogen atoms with a velocity up to 600 m s⁻¹ can be stored in a 1 m diameter ring, which implies that the atoms can be injected in the ring directly from a pulsed supersonic beam source. This ring can be used to study collisions between stored hydrogen atoms and supersonic beams of many different atoms and molecules. The advantage of using a synchrotron is two-fold: (i) the collision partners move in the same direction as the stored atoms, resulting in a small relative velocity and thus a low collision energy, and (ii) by storing atoms for many round-trips, the sensitivity to collisions is enhanced by a factor of 100–1000. In the proposed ring, the cross-sections for collisions between hydrogen, the most abundant atom in the universe, with any atom or molecule that can be put in a beam, including He, H₂, CO, ammonia and OH can be measured at energies below 100 K. We discuss the possibility of using optical transitions to load hydrogen atoms into the ring without influencing the atoms that are already stored. In this way it will be possible to reach high densities of stored hydrogen atoms.

We perform a comparative analysis of different computational approaches employed to explore the electronic structure of ultralong-range Rydberg molecules. Employing the Fermi pseudopotential approach, where the interaction is approximated by an s-wave bare delta function potential, one encounters a non-convergent behavior in basis set diagonalization. Nevertheless, the energy shifts within the first order perturbation theory coincide with those obtained by an alternative approach relying on Green's function calculation with the quantum defect theory. A pseudopotential that yields exactly the results obtained with the quantum defect theory, i.e. beyond first order perturbation theory, is the regularized delta function potential. The origin of the discrepancies between the different approaches is analytically explained.

We study the interspecies scattering properties of ultracold Li–Cs mixtures in their two energetically lowest spin channels in the magnetic field range between 800 and 1000 G. Close to two broad Feshbach resonances (FR) we create weakly bound LiCs dimers by radio-frequency association and measure the dependence of their binding energy on the external magnetic field strength. Based on the binding energies and complementary atom loss spectroscopy of three other Li–Cs s-wave FRs we construct precise molecular singlet and triplet electronic ground state potentials using a coupled-channels calculation. We extract the Li–Cs interspecies scattering length as a function of the external field and obtain almost a ten-fold improvement in the precision of the values for the pole positions and widths of the s-wave FRs as compared to our previous work (Pires et al 2014 Phys. Rev. Lett. 112 250404). We discuss implications on the Efimov scenario and the universal geometric scaling for LiCsCs trimers.

In addition to being suitable for laser cooling and trapping in a magneto-optical trap (MOT) using a relatively broad $(\sim 5\;{\rm MHz})$ transition, the molecule YO possesses a narrow-line transition. This forbidden transition between the ${{X}^{2}}\Sigma$ and $A{{^{\prime} }^{2}}{{\Delta }_{3/2}}$ states has linewidth $\sim 2\pi \times 160$ kHz. After cooling in a MOT on the 614 nm ${{X}^{2}}\Sigma$ to ${{A}^{2}}{{\Pi }_{1/2}}$ (orange) transition, the narrow 690 nm (red) transition can be used to further cool the sample, requiring only minimal additions to the first stage system. We estimate that the narrow line cooling stage will bring the temperature from ∼1 mK to ∼10 μK, significantly advancing the frontier on direct cooling achievable for molecules.

Magnetic Feshbach resonances have allowed great success in the production of ultracold diatomic molecules from bi-alkali mixtures, but have so far eluded observation in mixtures of alkali and alkaline-earth-like atoms. Inelastic collisional properties of ultracold atomic systems exhibit resonant behavior in the vicinity of such resonances, providing a detection signature. We study magnetic field dependent inelastic effects via atom loss spectroscopy in an ultracold heteronuclear mixture of alkali ⁶Li in the ground state and alkaline-earth-like ¹⁷⁴Yb in an excited electronic metastable state (³P₂, ${{m}_{J}}=-1$). We observe a variation of the interspecies inelastic two-body rate coefficient by nearly one order of magnitude over a 100–520 G magnetic field range. By comparing to ab initio calculations we link our observations to interspecies Feshbach resonances arising from anisotropic interactions in this novel collisional system.

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.

We study the reaction kinetics of chemical processes occurring in the ultracold regime and systematically investigate their dynamics. Quantum entanglement is found to play a key role in driving an ultracold reaction towards a dynamical equilibrium. In case of multiple concurrent reactions Hamiltonian chaos dominates the phase space dynamics in the mean field approximation.

The study of ultracold molecules tightly trapped in an optical lattice can expand the frontier of precision measurement and spectroscopy, and provide a deeper insight into molecular and fundamental physics. Here we create, probe, and image microkelvin ⁸⁸Sr₂ molecules in a lattice, and demonstrate precise measurements of molecular parameters as well as coherent control of molecular quantum states using optical fields. We discuss the sensitivity of the system to dimensional effects, a new bound-to-continuum spectroscopy technique for highly accurate binding energy measurements, and prospects for new physics with this rich experimental system.

We propose a method of stimulated laser decelerating of diatomic molecules by counter-propagating π-trains of ultrashort laser pulses. The decelerating cycles occur on the rovibrational transitions inside the same ground electronic manifold, thus avoiding the common problem of radiative branching in Doppler cooling of molecules. By matching the frequency comb spectrum of the pulse trains to the spectrum of the R-branch rovibrational transitions we show that stimulated deceleration can be carried out on several rovibrational transitions simultaneously. This enables an increase in the number of cooled molecules with only a single laser source. The exerted optical force does not rely on the decay rates in a system and can be orders of magnitude larger than the typical values of scattering force obtained in conventional Doppler laser cooling schemes.

We analyze the temporal evolution of the population of ultracold polar molecules in a microwave (mw) field with a circular polarization. The molecules are in their ground $^{1}\Sigma$ state and treated as rigid rotors with a permanent dipole moment which interact with each other via the dipole–dipole (DD) interaction V_dd. The mw field mixes states with different quantum and photon numbers and the collisional dynamics in the mw field is mostly controlled by the ratios of the mw field frequency versus the rotational constant, and mw field Rabi frequency versus the rotational constant. There exists a special scattering process which is elastic by nature and due to a rotational energy exchange between the ground and the first excited rotational states. To analyze dynamics of polar molecules system in the mw field the equation of motion for the bare and dressed states is solved under different mw field parameters and molecular gas characteristics. Depending on the ratio of the Rabi frequency of a mw field and the magnitude of the DD interaction, beatings and oscillations occur in the bare and dressed states time-development. At a certain relation between the magnitudes of the mw detuning δ and the DD interaction $\delta =\pm {{V}_{{\rm dd}}}$, peak structures appear in the population of the excited bare state. Each peak is associated with an avoided crossing between the dressed states adiabatic curves at the same position of mw detuning.

Non-resonant light interacting with diatomics via the polarizability anisotropy couples different rotational states and may lead to strong hybridization of the motion. The modification of shape resonances and low-energy scattering states due to this interaction can be fully captured by an asymptotic model, based on the long-range properties of the scattering (Crubellier et al 2015 New J. Phys. 17 045020). Remarkably, the properties of the field-dressed shape resonances in this asymptotic multi-channel description are found to be approximately linear in the field intensity up to fairly large intensity. This suggests a perturbative single-channel approach to be sufficient to study the control of such resonances by the non-resonant field. The multi-channel results furthermore indicate the dependence on field intensity to present, at least approximately, universal characteristics. Here we combine the nodal line technique to solve the asymptotic Schrödinger equation with perturbation theory. Comparing our single channel results to those obtained with the full interaction potential, we find nodal lines depending only on the field-free scattering length of the diatom to yield an approximate but universal description of the field-dressed molecule, confirming universal behavior.

The multichannel quantum defect theory (MQDT) in combination with the frame transformation (FT) approach is applied to model the Fano–Feshbach resonances measured for ⁷Li⁸⁷Rb and ⁶Li⁸⁷Rb Marzok et al (2009 Phys. Rev. A 79 012717). The MQDT results show a level of accuracy comparable to that of previous models based on direct, fully numerical solutions of the the coupled channel Schrödinger equations. Here, energy levels deduced from 2-photon photoassociation (PA) spectra for ⁷Li⁸⁵Rb are assigned by applying the MQDT approach, obtaining the bound state energies for the coupled channel problem. Our results confirm that MQDT yields a compact description of PA observables as well as the Fano–Feshbach resonance positions and widths.

We derive a universal model for atom pairs interacting with non-resonant light via the polarizability anisotropy, based on the long range properties of the scattering. The corresponding dynamics can be obtained using a nodal line technique to solve the asymptotic Schrödinger equation. It consists of imposing physical boundary conditions at long range and vanishing the wavefunction at a position separating the inner zone and the asymptotic region. We show that nodal lines which depend on the intensity of the non-resonant light can satisfactorily account for the effect of the polarizability at short range. The approach allows to determine the resonance structure, energy, width, channel mixing and hybridization even for narrow resonances.

We investigate the behaviour of single-channel theoretical models of cold and ultracold collisions that take account of inelastic and reactive processes using a single parameter to represent short-range loss. We present plots of the resulting energy-dependence of elastic and inelastic or reactive cross-sections over the full parameter space of loss parameters and short-range phase shifts. We then test the single-channel model by comparing it with the results of coupled-channel calculations of rotationally inelastic collisions between LiH molecules and Li atoms. We find that the range of cross-sections predicted by the single-channel model becomes increasingly accurate as the initial LiH rotational quantum number increases, with a corresponding increase in the number of open loss channels. The results suggest that coupled-channel calculations at very low energy (in the s-wave regime) could in some cases be used to estimate a loss parameter and then to predict the range of possible loss rates at higher energy, without the need for explicit coupled-channel calculations for higher partial waves.

We propose a method to produce, in a pulsed or continuous way, cold samples of highly polar molecules. Using a pulsed or continuous standard (supersonic) beam of these molecules, our idea consists of transforming the molecules into their anionic counterparts, which are decelerated to a standstill by a well-controlled external electric field and ultimately neutralized. The neutral-to-anion transformation occurs through collisions with Rydberg atoms coming from an additional atomic beam. This Rydberg electron transfer process is possible provided that the molecular species has a sufficiently strong electric dipole ($\gt 2.5$ D, i.e., $\gt 8.3\times {{10}^{-30}}$ cm). Whatever the mass of the species, the deceleration stage is realized by a temporally and spatially controlled electric field within a range of less than one centimeter, which is much shorter than in current deceleration experiments of neutral molecules. Once stopped, the molecular anions are neutralized by laser photodetachment or a pulsed electric field process. The resulting molecules might be held and accumulated, for instance, in a magnetic trap.

We show that congruent electric, magnetic and non-resonant optical fields acting concurrently on a polar paramagnetic (and polarizable) molecule offer possibilities to both amplify and control the directionality of the ensuing molecular states that surpass those available in double-field combinations or in single fields alone. At the core of these triple-field effects is the lifting of the degeneracy of the projection quantum number M by the magnetic field superimposed on the optical field and a subsequent coupling of the members of the 'doubled' (for states with $M\ne 0$) tunneling doublets due to the optical field by even a weak electrostatic field.

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.

We investigate single-particle energy spectra of the hydroxyl free radical (OH) in the lowest electronic and rovibrational level under combined static electric and magnetic fields, as an example of heteronuclear polar diatomic molecules. In addition to the fine-structure interactions, the hyperfine interactions and centrifugal distortion effects are taken into account to yield the zero-field spectrum of the lowest $^{2}{{\Pi }_{3/2}}$ manifold to an accuracy of less than 2 kHz. We also examine level crossings and repulsions in the hyperfine structure induced by applied electric and magnetic fields. Compared to previous work, we found more than 10% reduction of the magnetic fields at level repulsions in the Zeeman spectrum subjected to a perpendicular electric field. In addition, we find new level repulsions, which we call Stark-induced hyperfine level repulsions, that require both an electric field and hyperfine structure. It is important to take into account hyperfine structure when we investigate physics of OH molecules at micro-Kelvin temperatures and below.

We theoretically evaluate the feasibility to form magnetically-tunable Feshbach molecules in collisions between fermionic ⁶Li atoms and bosonic metastable ¹⁷⁴Yb(³P₂) atoms. In contrast to the well-studied alkali-metal atom collisions, collisions with meta-stable atoms are highly anisotropic. Our first-principle coupled-channel calculation of these collisions reveals the existence of broad Feshbach resonances due to the combined effect of anisotropic-molecular and atomic–hyperfine interactions. In order to fit our predictions to the specific positions of experimentally-observed broad resonance structures (Dowd et al 2014) we optimized the shape of the short-range potentials by direct least-square fitting. This allowed us to identify the dominant resonance by its leading angular momentum quantum numbers and describe the role of collisional anisotropy in the creation and broadening of this and other resonances.

Cold molecular ions are of great interest for applications in cold collision studies, chemistry, precision spectroscopy and quantum technologies. In this context, sympathetic cooling of molecular ions by the interaction with laser-cooled atomic ions is a powerful method to cool their translational motion and achieve translational temperatures in the millikelvin range. Recently, we implemented this method in a surface-electrode ion trap. The flexibility in shaping the trapping potentials offered by the surface-electrode structure enabled us to generate planar bicomponent Coulomb crystals and spatially separate the molecular from the atomic ions. Here, we present a detailed description of the fabrication and simulation of the trap as well as a theoretical and experimental investigation of the structural and energetic properties of the Coulomb crystals obtained in the device. We discuss in more detail the separation of different ion species using static electric fields and explore the effects of trap anharmoncities on the shape of bicomponent crystals.

We report Bose–Einstein condensation of two isotopes of the highly magnetic element dysprosium: ¹⁶²Dy and $^{160}$ Dy. For ¹⁶²Dy, condensates with 10⁵ atoms form below T = 50 nK. We find the evaporation efficiency for the isotope ¹⁶⁰Dy to be poor; however, by utilizing a low-field Fano–Feshbach resonance to carefully change the scattering properties, it is possible to produce a Bose–Einstein condensate of ¹⁶⁰Dy with 10³ atoms. The ¹⁶²Dy BEC reported is an order of magnitude larger in atom number than that of the previously reported ¹⁶⁴Dy BEC, and it may be produced within 18 s.

We investigate the occurrence of rotons in a quadrupolar Bose–Einstein condensate confined to two dimensions. Depending on the particle density, the ratio of the contact and quadrupole–quadrupole interactions, and the alignment of the quadrupole moments with respect to the confinement plane, the dispersion relation features two or four point-like roton minima or one ring-shaped minimum. We map out the entire parameter space of the roton behavior and identify the instability regions. We propose to observe the exotic rotons by monitoring the characteristic density wave dynamics resulting from a short local perturbation, and discuss the possibilities to detect the predicted effects in state-of-the-art experiments with ultracold homonuclear molecules.

Vibrational relaxation of strontium monohydroxide (SrOH) molecules in collisions with helium (He) at 2 K is studied. We find the diffusion cross section of SrOH at 2.2 K to be ${{\sigma }_{{\rm d}}}=(5\pm 2)\times {{10}^{-14}}\;{\rm c}{{{\rm m}}^{2}}$ and the vibrational quenching cross section for the (100) Sr–O stretching mode to be ${{\sigma }_{{\rm q}}}$ $\;=\;(7\pm 2)\times {{10}^{-17}}{\rm c}{{{\rm m}}^{2}}$. The resulting ratio ${{\gamma }_{100}}$ $\;=\;{{\sigma }_{{\rm d}}}/{{\sigma }_{{\rm q}}}\sim 700$ is more than an order of magnitude smaller than for previously studied few-atom radicals (Au et al 2014 Phys. Rev. A 90 032703 ). We also determine the Franck–Condon factor for SrOH (${{\tilde{A}}^{2}}{{\Pi }_{1/2}}(100)\leftarrow {{\tilde{X}}^{2}}{{\Sigma }^{+}}(000)$) to be $(4.8\pm 0.8)\times {{10}^{-2}}$.

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). We can increase or decrease the inelastic and reactive processes whether the second channel is above or below the initial channel. This is seen for both bosonic and fermionic molecules. Additionally, we include the electric quadrupole and octopole moment to the dipole moment in the expression of the long-range multipole–multipole interaction. We found that for processes mediated by the incident channel, such as elastic and reactive collisions, the inclusion of quadrupole and octopole moments is not important at ultralow energies. The moments are important for processes mediated by state-to-state transitions like inelastic collisions.

We present experimental results from a new scheme for magneto–optically trapping strontium monofluoride (SrF) molecules, which provides increased confinement compared to our original work. The improved trap employs a new approach to magneto–optical trapping presented by Tarbutt (2015 New J. Phys. 17 015007), which provided insight for the first time into the source of the restoring force in magneto–optical traps (MOTs) where the cycling transition includes dark Zeeman sublevels (known as type-II MOTs). We measure a radial spring constant $20\times$ greater than in our original work with SrF, comparable to the spring constants reported in atomic type-II MOTs. We achieve a trap lifetime ${{\tau }_{{\rm MOT}}}=136(2)$ ms, over $2\times$ longer than originally reported for SrF. Finally, we demonstrate further cooling of the trapped molecules by briefly increasing the trapping lasers' detunings. Our trapping scheme remains a straightforward extension of atomic techniques and marks a step towards the direct production of large, dense, ultracold molecular gases via laser cooling.

A new spectroscopic method that utilizes microwave transition of ultracold molecules is demonstrated. The narrow spectral linewidth (approximately 100 Hz) was guaranteed by preparing molecules at low temperature, and a high signal-to-noise ratio was achieved by preparing a significant fraction of molecules in the target internal state. The repetition rate of the experiment was approximately 10 Hz, which was only limited by the time needed to load ultracold atoms into the magneto-optical trap. To demonstrate the performance, we investigated the hyperfine structures of the vibrational ground states of the ${{X}^{1}}{{\Sigma }^{+}}$ and ${{b}^{3}}{{\Pi }_{{{0}^{+}}}}$ states of KRb molecules. This technique not only allows us to pursue the narrow-line laser cooling of KRb molecules, but also provided us with essential information for realizing precision spectroscopies e.g., the search for the temporal variation of the electron-to-proton mass ratio.

We use quantum and classical adiabatic capture theories to study the chemical reaction Li + CaH $\to$ LiH + Ca. Using a recently developed ab initio potential energy surface, which provides an accurate representation of long-range interactions in the entrance reaction channel, we calculate the adiabatic channel potentials by diagonalizing the Li-CaH Hamiltonian as a function of the atom-molecule separation. The resulting adiabatic channel potentials are used to calculate both the classical and quantum capture probabilities as a function of collision energy, as well as the temperature dependencies of the partial and total reaction rates. The calculated reaction rate agrees well with the measured value at 1 K (V Singh et al 2012 Phys. Rev. Lett. 108 203201), suggesting that the title reaction proceeds without an activation barrier. The calculated classical adiabatic capture rate agrees well with the quantum result in the multiple-partial-wave regime of relevance to the experiment. Significant differences are found only in the ultracold limit ($T\lt 1$ mK), demonstrating that adiabatic capture theories can predict the reaction rates with nearly quantitative accuracy in the multiple-partial-wave regime.

We demonstrate sympathetic sideband cooling of a ⁴⁰CaH⁺ molecular ion co-trapped with a ⁴⁰Ca⁺ atomic ion in a linear Paul trap. Both axial modes of the two-ion chain are simultaneously cooled to near the ground state of motion. The center of mass mode is cooled to an average quanta of harmonic motion ${{\bar{n}}_{{\rm COM}}}=0.13\pm 0.03$, corresponding to a temperature of $12.47\pm 0.03\;\mu {\rm K}$. The breathing mode is cooled to ${{\bar{n}}_{{\rm BM}}}=0.05\pm 0.02$, corresponding to a temperature of $15.36\pm 0.01\;\mu {\rm K}$.

We consider low energy threshold reactive collisions of particles interacting via a van der Waals potential at long range in the presence of external confinement and give analytic formulas for the confinement modified scattering in such circumstances. The reaction process is described in terms of the short range reaction probability. Quantum defect theory is used to express elastic and inelastic or reaction collision rates analytically in terms of two dimensionless parameters representing phase and reactivity. We discuss the modifications to Wigner threshold laws for quasi-one-dimensional and quasi-two-dimensional geometries. Confinement-induced resonances are suppressed due to reactions and are completely absent in the universal limit where the short-range loss probability approaches unity.

We present experimental results that demonstrate—for the first time—the Zeeman deceleration of helium atoms in the metastable 2³S₁ state. A more than 40% decrease of the kinetic energy of the beam is achieved for deceleration from 490 m s⁻¹ to a final velocity of 370 m s⁻¹. Metastable atom generation is achieved with an electron-impact-excitation source whose performance is enhanced through an additional discharge-type process which we characterize in detail. Metastable helium is efficiently generated even in a mixture of other noble gases that have much lower excitation energies. Comparison of deceleration data at different electron beam pulse durations confirms that a matching between the initial particle distribution and the phase-space acceptance of the decelerator is crucial for the production of a decelerated packet with a well-defined velocity distribution. The experimental findings are in good agreement with three-dimensional numerical particle trajectory simulations.

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.

We describe quantum simulations of ultracold ⁸⁷Rb₂ molecule formation using photoassociation (PA) with nanosecond-time-scale pulses of frequency chirped light. In particular, we compare the case of a linear chirp to one where the frequency evolution is optimized by local control (LC) of the phase, and find that LC can provide a significant enhancement. The resulting optimal frequency evolution corresponds to a rapid jump from the PA absorption resonance to a downward transition to a bound level of the lowest triplet state. We also consider the case of two frequencies and investigate interference effects. The assumed chirp parameters should be achievable with nanosecond pulse shaping techniques and are predicted to provide a significant enhancement over recent experiments with linear chirps.

A Ramsey-type interferometer is suggested, employing a cold trapped ion and two time-delayed off-resonant femtosecond laser pulses. The laser light couples to the molecular polarization anisotropy, inducing rotational wavepacket dynamics. An interferogram is obtained from the delay dependent populations of the final field-free rotational states. Current experimental capabilities for cooling and preparation of the initial state are found to yield an interferogram visibility of more than 80%. The interferograms can be used to determine the polarizability anisotropy with an accuracy of about ±2%, respectively ±5%, provided the uncertainty in the initial populations and measurement errors are confined to within the same limits.

We demonstrate that ultracold symmetric top molecules loaded into an optical lattice can realize highly tunable and unconventional models of quantum magnetism, such as an XYZ Heisenberg spin model. We show that anisotropic dipole–dipole interactions between molecules can lead to effective spin–spin interactions which exchange spin and orbital angular momentum. This exchange produces effective spin models which do not conserve magnetization and feature tunable degrees of spatial and spin–coupling anisotropy. In addition to deriving pure spin models when molecules are pinned in a deep optical lattice, we show that models of itinerant magnetism are possible when molecules can tunnel through the lattice. Additionally, we demonstrate rich tunability of effective model parameters using only a single microwave frequency, in contrast to proposals with $^{1}\Sigma$ diatomic molecules, which often require many microwave frequencies. Our results are germane not only for experiments with polyatomic symmetric top molecules, such as methyl fluoride (CH₃F), but also diatomic molecules with an effective symmetric top structure, such as the hydroxyl radical OH.

Laser cooling and magneto-optical trapping of molecules typically involves multiple transitions driven by several laser frequencies. We analyze how magneto-optical trapping forces depend on the angular momenta, F_l and F_u, and the g-factors, g_l and g_u, of the lower and upper states. When ${{F}_{{\rm l}}}\gt {{F}_{{\rm u}}}$ the polarizations must be reversed relative to cases where ${{F}_{{\rm u}}}\geqslant {{F}_{{\rm l}}}.$ The correct choice of circular polarization depends on the sign of g_u but not on the sign of g_l. If g_u is zero there is no trapping force, and the trapping force is very weak whenever g_u is small compared to g_l, which it usually is when the cooling transition is the $^{2}\Sigma$ to $^{2}{{\Pi }_{1/2}}$ transition of a molecule. For some molecules, mixing of the excited $^{2}{{\Pi }_{1/2}}$ state with a nearby $^{2}\Sigma$ excited state can greatly increase g_u, leading to stronger trapping forces. A strong trapping force can also be produced by rapidly and synchronously reversing both the magnetic field and the laser polarizations. We simulate a recent experiment on magneto-optical trapping of SrF molecules, and suggest that an alternative choice of laser beam polarizations will strengthen the trapping force.

We investigate magnetoassociation of ultracold Feshbach molecules from a Bose-Einstein condensate of Cs atoms and explore the spectrum of weakly bound molecular states close to the atomic threshold. By exploiting the variation of magnetic field experienced by a molecular cloud falling in the presence of a magnetic field gradient, we demonstrate the repeated output coupling of molecules from a single atomic cloud using a Feshbach resonance at 19.89 G. Using this method we are able to produce up to 24 separate pulses of molecules from a single atomic condensate, with a molecular pulse created every 7.2 ms. Furthermore, by careful control of the magnetic bias field and gradient we are able to utilise an avoided crossing in the bound state spectrum at 13.3 G to demonstrate exquisite control over the dynamics of the molecular clouds.