Quantum Control of Atom-Ion Charge Exchange via Light-Induced Conical Intersections.

Conical intersections are crossing points or lines between two or more adiabatic electronic potential energy surfaces in the multidimensional coordinate space of colliding atoms and molecules. Conical intersections and corresponding nonadiabatic coupling can greatly affect molecular dynamics and chemical properties. In this paper, we predict significant or measurable nonadiabatic effects in an ultracold atom-ion charge-exchange reaction in the presence of laser-induced conical intersections (LICIs). We investigate the fundamental physics of these LICIs on molecular reactivity under unique conditions: those of relatively low laser intensity of 108 W/cm2 and ultracold temperatures below 1 mK. We predict irregular interference effects in the charge-exchange rate coefficients between K and Ca+ as functions of the laser frequency. These irregularities occur in our system due to the presence of two LICIs. To further elucidate the role of the LICIs on the reaction dynamics, we compare these rate coefficients with those computed for a system where the CIs have been "removed". In the laser frequency window, where conical interactions are present, the difference in rate coefficients can be as large as 1 × 10-9 cm3/s.

Quantum Spin State Selectivity and Magnetic Tuning of Ultracold Chemical Reactions of Triplet Alkali-Metal Dimers with Alkali-Metal Atoms.

We demonstrate that it is possible to efficiently control ultracold chemical reactions of alkali-metal atoms colliding with open-shell alkali-metal dimers in their metastable triplet states by choosing the internal hyperfine and rovibrational states of the reactants as well as by inducing magnetic Feshbach resonances with an external magnetic field. We base these conclusions on coupled-channel statistical calculations that include the effects of hyperfine contact and magnetic-field-induced Zeeman interactions on ultracold chemical reactions of hyperfine-resolved ground-state Na and the triplet NaLi(a^{3}Σ^{+}) producing singlet Na_{2}(^{1}Σ_{g}^{+}) and a Li atom. We find that the reaction rates are sensitive to the initial hyperfine states of the reactants. The chemical reaction of fully spin-polarized, high-spin states of rotationless NaLi(a^{3}Σ^{+},v=0,N=0) molecules with fully spin-polarized Na is suppressed by a factor of 10-100 compared to that of unpolarized reactants. We interpret these findings within the adiabatic state model, which treats the reaction as a sequence of nonadiabatic transitions between the initial nonreactive high-spin state and the final low-spin states of the reaction complex. In addition, we show that magnetic Feshbach resonances can similarly change reaction rate coefficients by several orders of magnitude. Some of these resonances are due to resonant trimer bound states dissociating to the N=2 rotational state of NaLi(a^{3}Σ^{+},v=0) and would thus exist in systems without hyperfine interactions.

Realizing Hopf Insulators in Dipolar Spin Systems.

The Hopf insulator is a weak topological insulator characterized by an insulating bulk with conducting edge states protected by an integer-valued linking number invariant. The state exists in three-dimensional two-band models. We demonstrate that the Hopf insulator can be naturally realized in lattices of dipolar-interacting spins, where spin exchange plays the role of particle hopping. The long-ranged, anisotropic nature of the dipole-dipole interactions allows for the precise detail required in the momentum-space structure, while different spin orientations ensure the necessary structure of the complex phases of the hoppings. Our model features robust gapless edge states at both smooth edges, as well as sharp edges obeying a certain crystalline symmetry, despite the breakdown of the two-band picture at the latter. In an accompanying paper [T. Schuster et al., Phys. Rev. A 103, AW11986 (2021)PLRAAN2469-9926] we provide a specific experimental blueprint for implementing our proposal using ultracold polar molecules of ^{40}K^{87}Rb.

Non-adiabatic quantum interference in the ultracold Li + LiNa → Li2 + Na reaction.

Electronically non-adiabatic effects play an important role in many chemical reactions. However, how these effects manifest in cold and ultracold chemistry remains largely unexplored. Here for the first time we present from first principles the non-adiabatic quantum dynamics of the reactive scattering between ultracold alkali-metal LiNa molecules and Li atoms. We show that non-adiabatic dynamics induces quantum interference effects that dramatically alter the ultracold rotationally resolved reaction rate coefficients. The interference effect arises from the conical intersection between the ground and an excited electronic state that is energetically accessible even for ultracold collisions. These unique interference effects might be exploited for quantum control applications such as a quantum molecular switch. The non-adiabatic dynamics are based on full-dimensional ab initio potential energy surfaces for the two electronic states that includes the non-adiabatic couplings and an accurate treatment of the long-range interactions. A statistical analysis of rotational populations of the Li2 product reveals a Poisson distribution implying the underlying classical dynamics are chaotic. The Poisson distribution is robust and amenable to experimental verification and appears to be a universal property of ultracold reactions involving alkali metal dimers.

Tune-Out and Magic Wavelengths for Ground-State

We demonstrate a versatile, state-dependent trapping scheme for the ground and first excited rotational states of ^{23}Na^{40}K molecules. Close to the rotational manifold of a narrow electronic transition, we determine tune-out frequencies where the polarizability of one state vanishes while the other remains finite, and a magic frequency where both states experience equal polarizability. The proximity of these frequencies of only 10 GHz allows for dynamic switching between different trap configurations in a single experiment, while still maintaining sufficiently low scattering rates.

Photon-mediated charge exchange reactions between 39K atoms and 40Ca+ ions in a hybrid trap.

We present experimental evidence of charge exchange between laser-cooled potassium 39K atoms and calcium 40Ca+ ions in a hybrid atom-ion trap and give quantitative theoretical explanations for the observations. The 39K atoms and 40Ca+ ions are held in a magneto-optical (MOT) and a linear Paul trap, respectively. Fluorescence detection and high resolution time of flight mass spectra for both species are used to determine the remaining number of 40Ca+ ions, the increasing number of 39K+ ions, and 39K number density as functions of time. Simultaneous trap operation is guaranteed by alternating periods of MOT and 40Ca+ cooling lights, thus avoiding direct ionization of 39K by the 40Ca+ cooling light. We show that the K-Ca+ charge-exchange rate coefficient increases linearly from zero with 39K number density and the fraction of 40Ca+ ions in the 4p 2P1/2 electronically-excited state. Combined with our theoretical analysis, we conclude that these data can only be explained by a process that starts with a potassium atom in its electronic ground state and a calcium ion in its excited 4p 2P1/2 state producing ground-state 39K+ ions and metastable, neutral Ca (3d4p 3P1) atoms, releasing only 150 cm-1 equivalent relative kinetic energy. Charge-exchange between either ground- or excited-state 39K and ground-state 40Ca+ is negligibly small as no energetically-favorable product states are available. Our experimental and theoretical rate coefficients are in agreement given the uncertainty budgets.

Nondestructive dispersive imaging of rotationally excited ultracold molecules.

A barrier to realizing the potential of molecules for quantum information science applications is a lack of high-fidelity, single-molecule imaging techniques. Here, we present and theoretically analyze a general scheme for dispersive imaging of electronic ground-state molecules. Our technique relies on the intrinsic anisotropy of excited molecular rotational states to generate optical birefringence, which can be detected through polarization rotation of an off-resonant probe laser beam. Using 23Na87Rb and 87Rb133Cs as examples, we construct a formalism for choosing the molecular state to be imaged and the excited electronic states involved in off-resonant coupling. Our proposal establishes the relevant parameters for achieving degree-level polarization rotations for bulk molecular gases, thus enabling high-fidelity nondestructive imaging. We additionally outline requirements for the high-fidelity imaging of individually trapped molecules.

Quantum chaos in ultracold collisions of gas-phase erbium atoms.

Atomic and molecular samples reduced to temperatures below one microkelvin, yet still in the gas phase, afford unprecedented energy resolution in probing and manipulating the interactions between their constituent particles. As a result of this resolution, atoms can be made to scatter resonantly on demand, through the precise control of a magnetic field. For simple atoms, such as alkalis, scattering resonances are extremely well characterized. However, ultracold physics is now poised to enter a new regime, where much more complex species can be cooled and studied, including magnetic lanthanide atoms and even molecules. For molecules, it has been speculated that a dense set of resonances in ultracold collision cross-sections will probably exhibit essentially random fluctuations, much as the observed energy spectra of nuclear scattering do. According to the Bohigas-Giannoni-Schmit conjecture, such fluctuations would imply chaotic dynamics of the underlying classical motion driving the collision. This would necessitate new ways of looking at the fundamental interactions in ultracold atomic and molecular systems, as well as perhaps new chaos-driven states of ultracold matter. Here we describe the experimental demonstration that random spectra are indeed found at ultralow temperatures. In the experiment, an ultracold gas of erbium atoms is shown to exhibit many Fano-Feshbach resonances, of the order of three per gauss for bosons. Analysis of their statistics verifies that their distribution of nearest-neighbour spacings is what one would expect from random matrix theory. The density and statistics of these resonances are explained by fully quantum mechanical scattering calculations that locate their origin in the anisotropy of the atoms' potential energy surface. Our results therefore reveal chaotic behaviour in the native interaction between ultracold atoms.

Engineering Excited-State Interactions at Ultracold Temperatures.

Using a recently developed method for precisely controlling collision energy, we observe a dramatic suppression of inelastic collisions between an atom and ion (Ca+Yb^{+}) at low collision energy. This suppression, which is expected to be a universal phenomenon, arises when the spontaneous emission lifetime of the excited state is comparable to or shorter than the collision complex lifetime. We develop a technique to remove this suppression and engineer excited-state interactions. By dressing the system with a strong catalyst laser, a significant fraction of the collision complexes can be excited at a specified atom-ion separation. This technique allows excited-state collisions to be studied, even at ultracold temperature, and provides a general method for engineering ultracold excited-state interactions.

Evidence for sympathetic vibrational cooling of translationally cold molecules.

Compared with atoms, molecules have a rich internal structure that offers many opportunities for technological and scientific advancement. The study of this structure could yield critical insights into quantum chemistry, new methods for manipulating quantum information, and improved tests of discrete symmetry violation and fundamental constant variation. Harnessing this potential typically requires the preparation of cold molecules in their quantum rovibrational ground state. However, the molecular internal structure severely complicates efforts to produce such samples. Removal of energy stored in long-lived vibrational levels is particularly problematic because optical transitions between vibrational levels are not governed by strict selection rules, which makes laser cooling difficult. Additionally, traditional collisional, or sympathetic, cooling methods are inefficient at quenching molecular vibrational motion. Here we experimentally demonstrate that the vibrational motion of trapped BaCl(+) molecules is quenched by collisions with ultracold calcium atoms at a rate comparable to the classical scattering, or Langevin, rate. This is over four orders of magnitude more efficient than traditional sympathetic cooling schemes. The high cooling rate, a consequence of a strong interaction potential (due to the high polarizability of calcium), along with the low collision energies involved, leads to molecular samples with a vibrational ground-state occupancy of at least 90 per cent. Our demonstration uses a novel thermometry technique that relies on relative photodissociation yields. Although the decrease in vibrational temperature is modest, with straightforward improvements it should be possible to produce molecular samples with a vibrational ground-state occupancy greater than 99 per cent in less than 100 milliseconds. Because sympathetic cooling of molecular rotational motion is much more efficient than vibrational cooling in traditional systems, we expect that the method also allows efficient cooling of the rotational motion of the molecules. Moreover, the technique should work for many different combinations of ultracold atoms and molecules.

Extending Rotational Coherence of Interacting Polar Molecules in a Spin-Decoupled Magic Trap.

Superpositions of rotational states in polar molecules induce strong, long-range dipolar interactions. Here we extend the rotational coherence by nearly 1 order of magnitude to 8.7(6) ms in a dilute gas of polar ^{23}Na^{40}K molecules in an optical trap. We demonstrate spin-decoupled magic trapping, which cancels first-order and reduces second-order differential light shifts. The latter is achieved with a dc electric field that decouples nuclear spin, rotation, and trapping light field. We observe density-dependent coherence times, which can be explained by dipolar interactions in the bulk gas.

Laser controlled charge-transfer reaction at low temperatures.

We study the low-temperature charge transfer reaction between a neutral atom and an ion under the influence of near-resonant laser light. By setting up a multi-channel model with field-dressed states, we demonstrate that the reaction rate coefficient can be enhanced by several orders of magnitude with laser intensities of 106 W/cm2 or larger. In addition, depending on laser frequency, one can induce a significant enhancement or suppression of the charge-exchange rate coefficient. For our intensities, multi-photon processes are not important.

Photodissociation spectroscopy of the dysprosium monochloride molecular ion.

We have performed a combined experimental and theoretical study of the photodissociation cross section of the molecular ion DyCl(+). The photodissociation cross section for the photon energy range 35,500 cm(-1) to 47,500 cm(-1) is measured using an integrated ion trap and time-of-flight mass spectrometer; we observe a broad, asymmetric profile that is peaked near 43,000 cm(-1). The theoretical cross section is determined from electronic potentials and transition dipole moments calculated using the relativistic configuration-interaction valence-bond and coupled-cluster methods. The electronic structure of DyCl(+) is extremely complex due to the presence of multiple open electronic shells, including the 4f(10) configuration. The molecule has nine attractive potentials with ionically bonded electrons and 99 repulsive potentials dissociating to a ground state Dy(+) ion and Cl atom. We explain the lack of symmetry in the cross section as due to multiple contributions from one-electron-dominated transitions between the vibrational ground state and several resolved repulsive excited states.

Controlling interactions between highly magnetic atoms with Feshbach resonances.

This paper reviews current experimental and theoretical progress in the study of dipolar quantum gases of ground and meta-stable atoms with a large magnetic moment. We emphasize the anisotropic nature of Feshbach resonances due to coupling to fast-rotating resonant molecular states in ultracold s-wave collisions between magnetic atoms in external magnetic fields. The dramatic differences in the distribution of resonances of magnetic (7)S3 chromium and magnetic lanthanide atoms with a submerged 4f shell and non-zero electron angular momentum is analyzed. We focus on dysprosium and erbium as important experimental advances have been recently made to cool and create quantum-degenerate gases for these atoms. Finally, we describe progress in locating resonances in collisions of meta-stable magnetic atoms in electronic P-states with ground-state atoms, where an interplay between collisional anisotropies and spin-orbit coupling exists.

Ultracold heteronuclear mixture of ground and excited state atoms.

We report on the realization of an ultracold mixture of lithium atoms in the ground state and ytterbium atoms in an excited metastable (3P2) state. Such a mixture can support broad magnetic Feshbach resonances which may be utilized for the production of ultracold molecules with an electronic spin degree of freedom, as well as novel Efimov trimers. We investigate the interaction properties of the mixture in the presence of an external magnetic field and find an upper limit for the background interspecies two-body inelastic decay coefficient of K2'<3×10(-12) cm3/s for the 3P2 mJ=-1 substate. We calculate the dynamic polarizabilities of the Yb(3P2) magnetic substates for a range of wavelengths, and find good agreement with our measurements at 1064 nm. Our calculations also allow the identification of magic frequencies where Yb ground and metastable states are identically trapped and the determination of the interspecies van der Waals coefficients.

Action spectroscopy of SrCl⁺ using an integrated ion trap time-of-flight mass spectrometer.

The photodissociation cross-section of SrCl(+) is measured in the spectral range of 36,000-46,000 cm(-1) using a modular time-of-flight mass spectrometer (TOF-MS). By irradiating a sample of trapped SrCl(+) molecular ions with a pulsed dye laser, X(1)Σ(+) state molecular ions are electronically excited to the repulsive wall of the A(1)Π state, resulting in dissociation. Using the TOF-MS, the product fragments are detected and the photodissociation cross-section is determined for a broad range of photon energies. Detailed ab initio calculations of the SrCl(+) molecular potentials and spectroscopic constants are also performed and are found to be in good agreement with experiment. The spectroscopic constants for SrCl(+) are also compared to those of another alkaline earth halogen, BaCl(+), in order to highlight structural differences between the two molecular ions. This work represents the first spectroscopy and ab initio calculations of SrCl(+).

Quantum scattering of icosahedron fullerene C60 with noble-gas atoms.

There exist multiple ways to cool neutral molecules. A front runner is the technique of buffer gas cooling, where momentum-changing collisions with abundant cold noble-gas atoms cool the molecules. This approach can, in principle, produce the most diverse samples of cold molecules. We present quantum mechanical and semiclassical calculations of the elastic scattering differential cross sections and rate coefficients of the C60 fullerene with He and Ar noble-gas atoms in order to quantify the effectiveness of buffer gas cooling for this molecule. We also develop new three-dimensional potential energy surfaces for this purpose using dispersion-corrected density functional theory (DFT) with counterpoise correction. The icosahedral anisotropy of the molecular system is reproduced by expanding the potential in terms of symmetry-allowed spherical harmonics. Long-range dispersion coefficients have been computed from frequency dependent polarizabilities of C60 and the noble-gas atoms. We find that the potential of the fullerene with He is about five times shallower than that with Ar. Anisotropic corrections are very weak for both systems and omitted in the quantum scattering calculations giving us a nearly quantitative estimate of elastic scattering observables. Finally, we have computed differential cross sections at the collision energies used in experiments by Han et al. (Chem Phys Lett 235:211, 1995), corrected for the sensitivity of their apparatus, and we find satisfactory agreement for C60 scattering with Ar.

Signatures of Non-universal Quantum Dynamics of Ultracold Chemical Reactions of Polar Alkali Dimer Molecules with Alkali Metal Atoms: Li(2S) + NaLi(a3Σ+) → Na(2S) + Li2(a3Σu+).

Ultracold chemical reactions of weakly bound triplet-state alkali metal dimer molecules have recently attracted much experimental interest. We perform rigorous quantum scattering calculations with a new ab initio potential energy surface to explore the chemical reaction of spin-polarized NaLi(a3Σ+) and Li(2S) to form Li2(a3Σu+) and Na(2S). The reaction is exothermic and proceeds readily at ultralow temperatures. Significantly, we observe strong sensitivity of the total reaction rate to small variations of the three-body part of the Li2Na interaction at short range, which we attribute to a relatively small number of open Li2(a3Σu+) product channels populated in the reaction. This provides the first signature of highly non-universal dynamics seen in rigorous quantum reactive scattering calculations of an ultracold exothermic insertion reaction involving a polar alkali dimer molecule, opening up the possibility of probing microscopic interactions in atom+molecule collision complexes via ultracold reactive scattering experiments.

Anisotropy-induced Feshbach resonances in a quantum dipolar gas of highly magnetic atoms.

We explore the anisotropic nature of Feshbach resonances in the collision between ultracold highly magnetic submerged-shell dysprosium atoms in their energetically lowest magnetic sublevel, which can only occur due to couplings to rotating bound states. This is in contrast to well-studied alkali-metal atom collisions, where broadest (strongest) Feshbach resonances are hyperfine induced and due to rotationless bound states. Our first-principle coupled-channel calculation of the collisions between these spin-polarized bosonic dysprosium atoms reveals a strong interplay between the anisotropies in the dispersion and magnetic dipole-dipole interaction. The former anisotropy is absent in alkali-metal and chromium collisions. We show that both types of anisotropy significantly affect the Feshbach spectrum as a function of an external magnetic field. Effects of the electrostatic quadrupole-quadrupole interaction are small. Over a 20 mT magnetic field range, we predict about 10 Feshbach resonances and show that the resonance locations depend on the dysprosium isotope.

Role of electronic excitations in ground-state-forbidden inelastic collisions between ultracold atoms and ions.

The role of electronic excitation in inelastic collisions between ultracold Ca atoms and Ba(+) ions, confined in a hybrid trap, is studied for the first time. Unlike previous investigations, this system is energetically precluded from undergoing inelastic collisions in its ground state, allowing a relatively simple experimental determination and interpretation of the influence of electronic excitation. It is found that while the electronic state of the ion can critically influence the inelastic collision rate, the polarizability mismatch of the neutral atom electronic states suppresses short-range collisions, and thus inelastic processes, involving electronically excited neutral atoms. As a result of these features, it is experimentally demonstrated that it is possible to mitigate inelastic collision loss mechanisms in these systems, marking an important step toward long-lived hybrid atom-ion devices.