We have trained a deep (convolutional) neural network to predict the ground-state energy of an electron in four classes of confining two-dimensional electrostatic potentials. On randomly generated potentials, for which there is no analytic form for either the potential or the ground-state energy, the model was able to predict the ground-state energy to within chemical accuracy, with a median absolute error of 1.49 mHa. We also investigated the performance of the model in predicting other quantities such as the kinetic energy and the first excited-state energy.

We theoretically explore the crossover from three dimensions (3D) to two (2D) in a strongly interacting atomic Fermi superfluid through confining the transverse spatial dimension. Using the Gaussian pair fluctuation theory, we determine the zero-temperature equation of state and Landau critical velocity as functions of the spatial extent of the transverse dimension and interaction strength. In the presence of strong interactions, we map out a dimensional crossover diagram from the location of maximum critical velocity, which exhibits distinct dependence on the transverse dimension from 2D to quasi-2D, and to 3D. We calculate the dynamic structure factor to characterize the low-energy excitations of the system and propose that the intermediate quasi-2D regime can be experimentally probed using Bragg spectroscopy.

We propose a two-qubit gate for neutral atoms in which one of the logical state components adiabatically follows a two-atom dark state formed by the laser coupling to a Rydberg state and a strong resonant dipole-dipole exchange interaction between two Rydberg excited atoms. Our gate exhibits optimal scaling of the intrinsic error probability $E\propto {\left(B\tau \right)}^{-1}$ with the interatomic interaction strength $B$ and the Rydberg state lifetime $\tau$. Moreover, the gate is resilient to variations in the interaction strength, and even for finite probability of double Rydberg excitation the gate does not excite atomic motion and experiences no decoherence due to internal-translational entanglement.

We report on the observation of the motional Stark effect of highly excited ${}^{87}\mathrm{Rb}$ Rydberg atoms moving in the presence of a weak homogeneous magnetic field in a vapor cell. Employing electromagnetically induced transparency for spectroscopy of an atomic vapor, we observe the velocity-, quantum state-, and magnetic-field-dependent transition frequencies between the ground and Rydberg excited states. For atoms moving at velocities around 400 m/s, the principal quantum number $n=100$ of the valence electron, and a magnetic field of $B=100$ G, we measure a motional Stark shift of $\sim 10$ MHz. Our experimental results are supported by numerical calculations based on a diagonalization of the effective Hamiltonian governing the valence electron of ${}^{87}\mathrm{Rb}$ in the presence of crossed electric and magnetic fields.

The softness of elastic atomic collisions, defined as the average number of collisions each atom undergoes until its energy decorrelates significantly, can have a considerable effect on the decay dynamics of atomic coherence. In this paper we combine two spectroscopic methods to measure these dynamics and obtain the collisional softness of ultracold atoms in an optical trap: Ramsey spectroscopy to measure the energy decorrelation rate and echo spectroscopy to measure the collision rate. We obtain a value of 2.5(3) for the collisional softness, in good agreement with previously reported numerical molecular-dynamics simulations. This fundamental quantity is used to determine the $s$-wave scattering lengths of different atoms but has not been directly measured. We further show that the decay dynamics of the revival amplitudes in the echo experiment has a transition in its functional decay. The transition time is related to the softness of the collisions and provides yet another way to approximate it. These conclusions are supported by Monte Carlo simulations of the full echo dynamics. The methods presented here can allow measurement of a generalized softness parameter for other two-level quantum systems with discrete spectral fluctuations.

A polarizable body moving in an external electromagnetic field will slow down. This effect is referred to as radiation damping and is analogous to Doppler cooling in atomic physics. Using the principles of special relativity we derive an expression for the radiation damping force and find that it solely depends on the scattered power. The cooling of the particle's center-of-mass motion is balanced by heating due to radiation pressure shot noise, giving rise to an equilibrium that depends on the ratio of the field's frequency and the particle's mass. While damping is of relativistic nature, heating has its roots in quantum mechanics.

The nature of quantum correlations in networks featuring independent sources of entanglement remains poorly understood. Here, focusing on the simplest network of entanglement swapping, we start a systematic characterization of the set of quantum states leading to violation of the so-called “bilocality” inequality. First, we show that all possible pairs of entangled pure states can violate the inequality. Next, we derive a general criterion for violation for arbitrary pairs of mixed two-qubit states. Notably, this reveals a strong connection between the Clauser-Horne-Shimony-Holt (CHSH) Bell inequality and the bilocality inequality, namely, that any entangled state violating CHSH also violates the bilocality inequality. We conclude with a list of open questions.

We propose a realistic scheme to implement discrete-time quantum walks in the Brillouin zone (i.e., in quasimomentum space) with a spinor Bose-Einstein condensate. Relying on a static optical lattice to suppress tunneling in real space, the condensate is displaced in quasimomentum space in discrete steps conditioned upon the internal state of the atoms, while short pulses periodically couple the internal states. We show that tunable twisted boundary conditions can be implemented in a fully natural way by exploiting the periodicity of the Brillouin zone. The proposed setup does not suffer from off-resonant scattering of photons and could allow for a robust implementation of quantum walks with several tens of steps at least. In addition, on-site atom-atom interactions can be used to simulate interactions with infinitely long range in the Brillouin zone.

High-precision QED calculations of ground-state ionization energies are performed for all boronlike ions with nuclear charge numbers in the range $16\le Z\le 96$. Rigorous QED calculations are performed within the extended Furry picture and include all many-electron QED effects up to the second order of the perturbation theory. The contributions of third- and higher-order electron-correlation effects are accounted for within the Breit approximation. Nuclear recoil and nuclear polarization effects are taken into account as well. In comparison with previous evaluations of the ground-state ionization energies of boronlike ions the accuracy of the theoretical predictions is improved significantly.

We investigate the effect of far-off-resonant trapping light on ultracold bosonic ${}^{87}\mathrm{Rb}{}^{133}\mathrm{Cs}$ molecules. We use kHz-precision microwave spectroscopy to measure the differential ac Stark shifts between the ground and first excited rotational levels of the molecule with hyperfine-state resolution. We demonstrate through both experiment and theory that coupling between neighboring hyperfine states manifests in rich structure with many avoided crossings. This coupling may be tuned by rotating the polarization of the linearly polarized trapping light. A combination of spectroscopic and parametric heating measurements allows complete characterization of the molecular polarizability at a wavelength of 1550 nm in both the ground and first excited rotational states.

We present an all-optical technique to prepare a sample of ${}^{39}\mathrm{K}$ in a magnetically insensitive state with 95% purity while maintaining a temperature of 6 $\mu \mathrm{K}$. This versatile preparation scheme is particularly well suited to performing matter-wave interferometry with species exhibiting closely separated hyperfine levels, such as the isotopes of lithium and potassium, and opens new possibilities for metrology with these atoms. We demonstrate the feasibility of such measurements by realizing an atomic gravimeter and a Ramsey-type spectrometer, both of which exhibit a state-of-the-art sensitivity for cold potassium.

We time-resolve coupled electronic and nuclear dynamics during strong-field molecular ionization by measuring the momentum-resolved photoelectron yield as a function of pump-probe delay for a pair of strong-field laser pulses. The sub-10-fs pulses are generated using a specially designed ultrafast optical pulse shaper and the electrons are measured using velocity map imaging. Our measurements, in conjunction with calculations that solve the time-dependent Schrödinger equation, allow us to time-resolve resonance-enhanced strong-field ionization and break it down into three basic steps: (1) Stark-shifted resonant excitation of a high-lying neutral state of the molecule, (2) nonadiabatic dynamics (internal conversion) in which multiple electronic states are coupled, and (3) coupling to the continuum (ionization).

By preparing a cold-atom ensemble of mixtures of the ground ${}^{1}S_0$ and metastable ${}^{3}P_2$ states of ytterbium atoms ${}^{171}\mathrm{Yb}$, we successfully associate a Feshbach molecule ${}^{171}\mathrm{Yb}_2$ with one ${}^{171}\mathrm{Yb}$ atom in its electronically excited state and another one in the ground state, by sweeping a magnetic field across a Feshbach resonance. The atom-molecule conversion efficiency reaches about 50%, confirmed by a separate image of atoms and molecules with a Stern-Gerlach effect and an atom loss measurement. In addition, we successfully implement a spin-orbit coupling with a one-photon process between the ${}^{3}P_2$ (pseudo-spin-up) and ground ${}^{1}S_0$ (pseudo-spin-down) states of a Yb atom. As a benchmark, we observe a spin-momentum locking behavior at a large Rabi frequency. The achieved successful production of Feshbach molecules, along with the implementation of spin-orbital coupling between the ${}^{1}S_0$ and ${}^{3}P_2$ states, provides an important step towards the study of a topological superfluid.

Optomechanical systems cooled to the quantum level provide a promising mechanism for a high-fidelity quantum memory that is faithful to a given temporal mode structure, and can be recovered synchronously. We carry out full, probabilistic quantum simulation of a quantum optomechanical memory, including nonlinear effects that are usually ignored. This is achieved using both the approximate truncated Wigner and the exact positive $P$ phase-space representations. By considering the nonlinear quantum optomechanical Hamiltonian, our simulations allow us to probe the regime where the linearization approximation fails to hold. We show evidence for large spectral overlap between the quantum signal and the transfer field in typical optomechanical quantum memory experiments. Methods for eliminating this overlap to accurately recover the quantum signal are discussed. This allows us to give a complete model for the quantum storage of a coherent state. We treat the mode matching that is necessary to accurately retrieve the stored quantum state, by including the internal dynamics of the mechanical system as well as the optical system. We also include the finite switching time of the control transfer field. The fidelity for the storage of a coherent state is computed numerically using currently realistic experimental parameters in the electromechanical case. We find the expected fidelity is lower than required to demonstrate true quantum state transfers. Significant improvements in the quality factor of the cavity and mechanical systems will, however, increase the fidelity beyond the quantum threshold.

A differential measurement scheme is proposed which allows for clear observation of the giant thermal effect for the Casimir force, which was recently predicted to occur in graphene systems at short separation distances. The difference among the Casimir forces acting between a metal-coated sphere and the two halves of a dielectric plate, one uncoated and the other coated with graphene, is calculated in the framework of the Dirac model using the rigorous formalism of the polarization tensor. It is shown that in the proposed configuration both the difference among the Casimir forces and its thermal contribution can be easily measured using existing experimental setups. An observation of the giant thermal effect should open opportunities for modulation and control of dispersion forces in micromechanical systems based on graphene and other novel two-dimensional (2D) materials.

We study laser-assisted photodetachment time delays by attosecond pulse trains from the closed-shell negative ions ${\mathrm{F}}^{-}$ and ${\mathrm{Cl}}^{-}$. We investigate the separability of the delay into two contributions: (i) the Wigner-like delay associated with one-photon ionization by the attosecond pulse train and (ii) the delay associated with the exchange of an additional laser photon in the presence of the potential of the remaining target. Based on the asymptotic form of the wave packet, the latter term is expected to be negligible because the ion is neutralized, leading to a vanishing laser-ion interaction with increasing electron-atom separation. While this asymptotic behavior is verified at high photoelectron energies, we also quantify sharp deviations at low photoelectron energies. Further, these low-energy delays are clearly different for the two studied anions, indicating a breakdown of the universality of laser-ion-induced delays. The fact that the short-range potential can induce a delay of as much as 50 as can have implications for the interpretation of delay measurements also in other systems that lack long-range potential.

We associate Sr atom pairs on sites of a Mott insulator optically and coherently into weakly bound ground-state molecules, achieving an efficiency above 80%. This efficiency is 2.5 times higher than in our previous work [S. Stellmer, B. Pasquiou, R. Grimm, and F. Schreck, Phys. Rev. Lett. 109, 115302 (2012)] and obtained through two improvements. First, the lifetime of the molecules is increased beyond one minute by using an optical lattice wavelength that is further detuned from molecular transitions. Second, we compensate undesired dynamic light shifts that occur during the stimulated Raman adiabatic passage (STIRAP) used for molecule association. We also characterize and model STIRAP, providing insights into its limitations. Our work shows that significant molecule association efficiencies can be achieved even for atomic species or mixtures that lack Feshbach resonances suitable for magnetoassociation.

The determination of the electron mass from Penning-trap measurements with ${}^{12}\mathrm{C}^{5+}$ ions and from theoretical results for the bound-electron $g$ factor is described in detail. Some recently calculated contributions slightly shift the extracted mass value. Prospects of a further improvement of the electron mass are discussed both from the experimental and from the theoretical points of view. Measurements with ${}^4\mathrm{He}^{+}$ ions will enable a consistency check of the electron-mass value, and in the future an improvement of the ${}^4\mathrm{He}$ nuclear mass and a determination of the fine-structure constant.

We investigate both analytically and numerically a two-component ultracold atom system in one spatial dimension. The model features a tachyonic instability, which incorporates characteristic aspects of the mechanisms for particle production in early universe inflaton models. We establish a direct correspondence between measurable macroscopic growth rates for occupation numbers of the ultracold Bose gas and the underlying microscopic processes in terms of Feynman loop diagrams. We analyze several existing ultracold atom setups featuring dynamical instabilities and propose optimized protocols for their experimental realization. We demonstrate that relevant dynamical processes can be enhanced using a seeding procedure for unstable modes and clarify the role of initial quantum fluctuations and the generation of a nonlinear secondary stage for the amplification of modes.

We compare failure distributions of quantum error correction circuits for stochastic errors and coherent errors. We utilize a fully coherent simulation of a fault-tolerant quantum error correcting circuit for a $d=3$ Steane and surface code. We find that the output distributions are markedly different for the two error models, showing that no simple mapping between the two error models exists. Coherent errors create very broad and heavy-tailed failure distributions. This suggests that they are susceptible to outlier events and that mean statistics, such as pseudothreshold estimates, may not provide the key figure of merit. This provides further statistical insight into why coherent errors can be so harmful for quantum error correction. These output probability distributions may also provide a useful metric that can be utilized when optimizing quantum error correcting codes and decoding procedures for purely coherent errors.