We explore the physical origin and the general validity of a propensity rule for the conservation of the hyperfine spin state in three-body recombination. This rule was recently discovered for the special case of ${}^{87}\mathrm{Rb}$ with its nearly equal singlet and triplet scattering lengths. Here, we test the propensity rule for ${}^{85}\mathrm{Rb}$ for which the scattering properties are very different from ${}^{87}\mathrm{Rb}$. The ${\mathrm{Rb}}_2$ molecular product distribution is mapped out in a state-to-state fashion using resonance-enhanced multiphoton ionization detection schemes which fully cover all possible molecular spin states. Interestingly, for the experimentally investigated range of binding energies from zero to $\sim 13\mathrm{GHz}\times h$ we observe that the spin-conservation propensity rule also holds for ${}^{85}\mathrm{Rb}$. From these observations and a theoretical analysis we derive an understanding for the conservation of the hyperfine spin state. We identify several criteria to judge whether the propensity rule will also hold for other elements and collision channels.

The influence of the magnetic component of the driving electromagnetic field is often neglected when investigating light-matter interaction. We show that the magnetic component of the light field plays an important role in nonsequential double ionization, which serves as a powerful tool to investigate electron correlation. We investigate the magnetic-field effects in double ionization of xenon atoms driven by near-infrared ultrashort femtosecond laser pulses and find that the mean forward shift of the electron momentum distribution in light-propagation direction agrees well with the classical prediction, where no under-barrier or recollisional nondipole enhancement is observed. By extending classical trajectory Monte Carlo simulations beyond the dipole approximation, we reveal that double ionization proceeds via recollision-induced doubly excited states, followed by subsequent sequential over-barrier field ionization of the two electrons. In agreement with this model, the binding energies do not lead to an additional nondipole forward shift of the electrons. Our findings provide a new method to study electron correlation by exploiting the effect of the magnetic component of the electromagnetic field.

We measure chemical reactions between a single trapped ${}^{174}{\mathrm{Yb}}^{+}$ ion and ultracold ${\mathrm{Li}}_2$ dimers. This produces ${\mathrm{LiYb}}^{+}$ molecular ions that we detect via mass spectrometry. We explain the reaction rates by modeling the dimer density as a function of the magnetic field and obtain excellent agreement when we assume the reaction to follow the Langevin rate. Our results present a novel approach towards the creation of cold molecular ions and point to the exploration of ultracold chemistry in ion molecule collisions. What is more, with a detection sensitivity below molecule densities of ${10}^{14}{\mathrm{m}}^{-3}$, we provide a new method to detect low-density molecular gases.

Optically trapped mixed-species single atom arrays with arbitrary geometry are an attractive and promising platform for various applications, because tunable quantum systems with multiple components provide extra degrees of freedom for experimental control. Here, we report the first demonstration of two-dimensional $6\times 4$ dual-species atom assembly of ${}^{85}\mathrm{Rb}$ (${}^{87}\mathrm{Rb}$) atoms with a filling fraction of 0.88 (0.89). This mixed-species atomic synthesis is achieved via rearranging initially randomly distributed atoms by a sorting algorithm (heuristic heteronuclear algorithm) which is designed for bottom-up atom assembly with both user-defined geometries and two-species atom number ratios. Our fully tunable hybrid-atom systems with scalable advantages are a good starting point for high-fidelity quantum logic, many-body quantum simulation, and single molecule array formation.

We realize a scanning probe microscope using single trapped ${}^{87}\mathrm{Rb}$ atoms to measure optical fields with subwavelength spatial resolution. Our microscope operates by detecting fluorescence from a single atom driven by near-resonant light and determining the ac Stark shift of an atomic transition from other local optical fields via the change in the fluorescence rate. We benchmark the microscope by measuring two standing-wave Gaussian modes of a Fabry-Pérot resonator with optical wavelengths of 1560 and 781 nm. We attain a spatial resolution of 300 nm, which is superresolving compared to the limit set by the 780 nm wavelength of the detected light. Sensitivity to short length scale features is enhanced by adapting the sensor to characterize an optical field via the force it exerts on the atom.

Analog computing based on wave interactions with metamaterials has been raising significant interest as a low-energy, ultrafast platform to process large amounts of data. Engineered materials can be tailored to impart mathematical operations of choice on the spatial distribution of the impinging signals, but they also require extended footprints and precise large-area fabrication, which may hinder their practical applicability. Here we show that the nonlocal response of a compact scatterer can be engineered to impart operations of choice on arbitrary impinging waves, and even to solve integro-differential equations, whose solution is observed in the scattered fields. The lack of strongly resonant phenomena makes the response robust, and the compact nature opens to scalability and cascading of these processes, paving the way to efficient, compact analog computers based on engineered microstructures.

We experimentally and theoretically investigate collective radiative effects in an ensemble of cold atoms coupled to a single-mode optical nanofiber. Our analysis unveils the microscopic dynamics of the system, showing that collective interactions between the atoms and a single guided photon gradually build up along the atomic array in the direction of propagation of light. These results are supported by time-resolved measurements of the light transmitted and reflected by the ensemble after excitation via nanofiber-guided laser pulses, whose rise and fall times are shorter than the atomic lifetime. Superradiant decays more than 1 order of magnitude faster than the single-atom free-space decay rate are observed for emission in the forward-propagating guided mode, while at the same time, no speed-up of the decay rate is measured in the backward direction. In addition, position-resolved measurements of the light that is transmitted past the atoms are performed by inserting the nanofiber-coupled atomic array in a 45-m-long fiber ring resonator, which allow us to experimentally reveal the progressive growth of the collective response of the atomic ensemble. Our results highlight the unique opportunities offered by nanophotonic cold atom systems for the experimental investigation of collective light-matter interaction.

We demonstrate coupling between the motions of two independently trapped ions with a separation distance of $620\mu \mathrm{m}$. The ion-ion interaction is enhanced via a room-temperature electrically floating metallic wire which connects two surface traps. Tuning the motion of both ions into resonance, we show flow of energy with a coupling rate of 11 Hz. Quantum-coherent coupling is hindered by strong surface electric-field noise in our device. Our ion-wire-ion system demonstrates that room-temperature conductors can be used to mediate and tune interactions between independently trapped charges over distances beyond those achievable with free-space dipole-dipole coupling. This technology may be used to sympathetically cool or entangle remotely trapped charges and enable coupling between disparate physical systems.

We show that a Tonks-Girardeau (TG) gas that is immersed in a Bose-Einstein condensate can undergo a transition to a crystal-like Mott state with regular spacing between the atoms without any externally imposed lattice potential. We characterize this phase transition as a function of the interspecies interaction and temperature of the TG gas, and show how it can be measured via accessible observables in cold atom experiments. We also develop an effective model that accurately describes the system in the pinned insulator state and which allows us to derive the critical temperature of the transition.

We experimentally and theoretically investigate the influence of the magnetic component of an electromagnetic field on high-order above-threshold ionization of xenon atoms driven by ultrashort femtosecond laser pulses. The nondipole shift of the electron momentum distribution along the light-propagation direction for high energy electrons beyond the $2U_p$ classical cutoff is found to be vastly different from that below this cutoff, where $U_p$ is the ponderomotive potential of the driving laser field. A local minimum structure in the momentum dependence of the nondipole shift above the cutoff is identified for the first time. With the help of classical and quantum-orbit analysis, we show that large-angle rescattering of the electrons strongly alters the partitioning of the photon momentum between electron and ion. The sensitivity of the observed nondipole shift to the electronic structure of the target atom is confirmed by three-dimensional time-dependent Schrödinger equation simulations for different model potentials. Our work paves the way toward understanding the physics of extreme light-matter interactions at long wavelengths and high electron kinetic energies.

A self-consistent field method is presented within density matrix functional theory. The computational cost for a correlated many-electron calculation is reduced to that of the self-consistent-field Hartree-Fock method, while the accuracy still reaches that of sophisticated configuration interaction based methods. In this method, the two-electron cumulant energy is measured with an information entropy associated with the Fermi-Dirac distribution of the occupation numbers. An eigenvalue equation for the orbitals is obtained, with the eigenvalues (orbital energies) connected to the occupation numbers through the Fermi-Dirac distribution. The occupation numbers for the strongly occupied orbitals are very close to the natural orbital occupation numbers from wave function methods. It covers in a single scheme the nondynamical correlation in weak or breaking bonds as well as the dynamical correlation at all distances. The method is well suited to large-scale potential energy surface calculation and molecular dynamics simulation.

Laser-induced tunneling ionization is one of the fundamental light-matter interaction processes. An accurate description of the tunnel-ionized electron wave packet is central to understanding and controlling subsequent electron dynamics. Because of the anisotropic molecular structure, tunneling ionization of molecules involves considerable challenges in accurately describing the tunneling electron wave packet. Up to now, some basic properties of the tunneling electron from molecules still remain unexplored. Here, we demonstrate that the tunneling electron from a molecule is not always emitted from the geometric center of the molecule along the tunnel direction. Rather, the photoemission position depends on the molecular orientation. Using a photoelectron holographic technique, we determine the photoemission position for a nitrogen molecule relative to the molecular geometric center to be $95\pm 21\mathrm{pm}$ when the molecular axis is oriented along the tunnel direction. Our Letter poses, and answers experimentally, a fundamental question as to where the molecular photoionization actually begins, which has significant implications for time-resolved probing of valence electron dynamics in molecules.

We report laser cooling and trapping of yttrium monoxide molecules in an optical lattice. We show that gray molasses cooling remains exceptionally efficient for yttrium monoxide molecules inside the lattice with a molecule temperature as low as $6.1(6)\mu \mathrm{K}$. This approach has produced a trapped sample of 1200 molecules, with a peak spatial density of $\sim 1.2\times {10}^{10}{\mathrm{cm}}^{-3}$, and a peak phase-space density of $\sim 3.1\times {10}^{-6}$. By ramping down the lattice depth, we cool the molecules further to $1.0(2)\mu \mathrm{K}$, 20 times colder than previously reported for laser-cooled molecules in a trap.

We present a robust, continuous molecular decelerator that employs high magnetic fields and few optical pumping steps. CaOH molecules are slowed, accumulating at low velocities in a range sufficient for loading both magnetic and magneto-optical traps. During the slowing, the molecules scatter only seven photons, removing around 8 K of energy. Because large energies can be removed with only a few spontaneous radiative decays, this method can in principle be applied to nearly any paramagnetic atomic or molecular species, opening a general path to trapping of complex molecules.

By simultaneously measuring the cyclotron frequencies of an ${\mathrm{H}}_2^{+}$ ion and a deuteron in a coupled magnetron orbit we have made an extended series of measurements of their cyclotron frequency ratio. From the observed changes in ${\mathrm{H}}_2^{+}$ mass energy we have followed the decay of three ${\mathrm{H}}_2^{+}$ ions to the vibrational ground state. We are able to assign some of our measured ratios to specific rovibrational levels, hence reducing uncertainty due to ${\mathrm{H}}_2^{+}$ rotational energy. Assuming the most probable assignment, we obtain a deuteron-to-proton mass ratio, $m_d/m_p=1.999007501272(9)$. Combined with the atomic mass of the deuteron [S. Rau et al., Nature (London) 585, 43 (2020).] we also obtain a new value for the atomic mass of the proton, $m_p=1.007276466574(10)\mathrm{u}$.

We describe and demonstrate how 3D magnetic field alignment can be inferred from single absorption images of an atomic cloud. While optically pumped magnetometers conventionally rely on temporal measurement of the Larmor precession of atomic dipoles, here a cold atomic vapor provides a spatial interface between vector light and external magnetic fields. Using a vector vortex beam, we inscribe structured atomic spin polarization in a cloud of cold rubidium atoms and record images of the resulting absorption patterns. The polar angle of an external magnetic field can then be deduced with spatial Fourier analysis. This effect presents an alternative concept for detecting magnetic vector fields and demonstrates, more generally, how introducing spatial phases between atomic energy levels can translate transient effects to the spatial domain.

We report the development of a vibrational-electronic convergent close-coupling method for electron-molecule scattering with an ab-initio account of the coupling between the electronic and vibrational motions. The technique has been applied to scattering on molecular hydrogen, including coupling between vibrational levels in the first 11 electronic states. Distinct resonances associated with the temporary formation of the ${\mathrm{H}}_2^{-}$ ion are present between 10 and 14 eV for numerous transitions, including vibrational excitation of the $X{{}^1\mathrm{\Sigma }}_g^{+}$ state, dissociation via the $b{{}^3\mathrm{\Sigma }}_u^{+}$ state, and excitation of the $B{{}^1\mathrm{\Sigma }}_u^{+}$ state. With both resonant and nonresonant scattering treated in a single calculation, this method is capable of providing self-consistent sets of cross sections for electron-molecule scattering in regions where the adiabatic-nuclei approximation breaks down.

We report on the electrostatic trapping of neutral SrF molecules. The molecules are captured from a cryogenic buffer-gas beam source into the moving traps of a 4.5-m-long traveling-wave Stark decelerator. The SrF molecules in $X^2{\mathrm{\Sigma }}^{+}(v=0,N=1)$ state are brought to rest as the velocity of the moving traps is gradually reduced from $190\mathrm{m}/\mathrm{s}$ to zero. The molecules are held for up to 50 ms in multiple electric traps of the decelerator. The trapped packets have a volume (FWHM) of $1{\mathrm{mm}}^3$ and a velocity spread of $5(1)\mathrm{m}/\mathrm{s}$, which corresponds to a temperature of 60(20) mK. Our result demonstrates a factor 3 increase in the molecular mass that has been Stark decelerated and trapped. Heavy molecules ($\mathrm{mass}>100\mathrm{amu}$) offer a highly increased sensitivity to probe physics beyond the standard model. This work significantly extends the species of neutral molecules of which slow beams can be created for collision studies, precision measurement, and trapping experiments.

A single quantum emitter can possess a very strong intrinsic nonlinearity, but its overall promise for nonlinear effects is hampered by the challenge of efficient coupling to incident photons. Common nonlinear optical materials, on the other hand, are easy to couple to but are bulky, imposing a severe limitation on the miniaturization of photonic systems. In this Letter, we show that a single organic molecule acts as an extremely efficient nonlinear optical element in the strong coupling regime of cavity quantum electrodynamics. We report on single-photon sensitivity in nonlinear signal generation and all-optical switching. Our work promotes the use of molecules for applications such as integrated photonic circuits operating at very low powers.

We report on a joint experimental and theoretical study of photoelectron circular dichroism (PECD) in methyloxirane. By detecting O 1s photoelectrons in coincidence with fragment ions, we deduce the molecule’s orientation and photoelectron emission direction in the laboratory frame. Thereby, we retrieve a fourfold differential PECD clearly beyond 50%. This strong chiral asymmetry is reproduced by ab initio electronic structure calculations. Providing such a pronounced contrast makes PECD of fixed-in-space chiral molecules an even more sensitive tool for chiral recognition in the gas phase.