We present a detailed study of an atom interferometer which can be realized in a double-well potential. We assume that the interferometric phase is imprinted in the presence of coherent tunneling between the wells. We calculate the ultimate bounds for the estimation sensitivity and show how they relate to the precision of the Mach-Zehnder interferometer. The interferometer presented here allows for sub-shot-noise sensitivity when fed with spin-squeezed states with either a reduced relative population imbalance or a reduced relative phase. We also calculate the precision of the estimation from the population imbalance and show that it overcomes the shot-noise limit when the entangled squeezed states are used at the input.

We present a detailed numerical and theoretical analysis of the recently discovered phenomenon of coherent forward scattering. This effect manifests itself as a macroscopic interference peak in the forward direction of the momentum distribution of a matter wave launched with finite velocity in a random potential. Focusing on the two-dimensional case, we show that coherent forward scattering generally arises due the confinement of the wave in a finite region of space, and explain under which conditions it can be seen as a genuine signature of Anderson localization.

We connect explicitly the classical $\text{O}\left(2\right)$ model in $1+1$ dimensions, a model sharing important features with $\text{U}\left(1\right)$ lattice gauge theory, to physical models potentially implementable on optical lattices and evolving at physical time. Using the tensor renormalization-group formulation, we take the time continuum limit and check that finite-dimensional projections used in recent proposals for quantum simulators provide controllable approximations of the original model. We propose two-species Bose-Hubbard models corresponding to these finite-dimensional projections at strong coupling and discuss their possible implementations on optical lattices using a ${}^{87}\mathrm{Rb}$ and ${}^{41}\mathrm{K}$ Bose-Bose mixture.

We study a system of two bosons of one species and a third atom of a second species in a one-dimensional parabolic trap at zero temperature. We assume contact repulsive inter- and intraspecies interactions. By means of an exact diagonalization method we calculate the ground and excited states for the whole range of interactions. We use discrete group theory to classify the eigenstates according to the symmetry of the interaction potential. We also propose and validate analytical Ansätze gaining physical insight over the numerically obtained wave functions. We show that, for both approaches, it is crucial to take into account that the distinguishability of the third atom implies the absence of any restriction over the wave function when interchanging this boson with any of the other two. We find that there are degeneracies in the spectra in some limiting regimes, that is, when the interspecies and/or the intraspecies interactions tend to infinity. This is in contrast with the three-identical boson system, where no degeneracy occurs in these limits. We show that, when tuning both types of interactions through a protocol that keeps them equal while they are increased towards infinity, the systems's ground state resembles that of three indistinguishable bosons. Contrarily, the systems's ground state is different from that of three-identical bosons when both types of interactions are increased towards infinity through protocols that do not restrict them to be equal. We study the coherence and correlations of the system as the interactions are tuned through different protocols, which permit us to build up different correlations in the system and lead to different spatial distributions of the three atoms.

Using a three-path contrast interferometer (CI) geometry and laser-pulse diffraction gratings, we create a matter-wave interferometer with ytterbium (Yb) atoms. We present advances in contrast interferometry relevant to high-precision measurements. By comparing to a traditional atom interferometer, we demonstrate the immunity of the CI to vibrations for long interaction times ($>20\mathrm{ms}$). We characterize and demonstrate control over the two largest systematic effects for a high-precision measurement of the fine-structure constant via photon recoil with our interferometer: diffraction phases and atomic interactions. Diffraction phases are an important systematic for most interferometers using large-momentum transfer beam splitters; atomic interactions are a key concern for any Bose-Einstein condensate (BEC) interferometer. Finally, we consider the prospects for a future subpart per billion photon recoil measurement using a Yb CI.

We report on the realization of Bose-Einstein condensation of metastable helium-4. After exciting helium to its metastable state in a novel pulse-tube cryostat source, the atomic beam is collimated and slowed. We then trap several ${10}^8$ atoms in a magneto-optical trap. For subsequent evaporative cooling, the atoms are transferred into a magnetic trap. Degeneracy is achieved with typically a few ${10}^6$ atoms. For detection of atomic correlations with high resolution, an ultrafast delay-line detector has been installed. Consisting of four quadrants with independent readout electronics that allow for true simultaneous detection of atoms, the detector is especially suited for quantum correlation experiments that require the detection of correlated subsystems. We expect our setup to allow for the direct demonstration of momentum entanglement in a scenario equivalent to the Einstein-Podolsky-Rosen gedanken experiment. This will pave the way to matter-wave experiments exploiting the peculiarities of quantum correlations.

We investigate the effect of dipolar interactions in one-dimensional systems in connection with the possibility of observing exotic many-body effects with trapped atomic and molecular dipolar gases. By combining analytical and numerical methods, we show how the competition between short- and long-range interactions gives rise to frustrating effects which lead to the stabilization of spontaneously dimerized phases characterized by a bond ordering. This genuine quantum order is sharply distinguished from Mott and spin-density-wave phases, and can be unambiguously probed by measuring nonlocal order parameters via in situ imaging techniques.

In this article, we illustrate the scaling properties of a family of solutions for $N$ attractive bosonic atoms in the limit of large $N$. These solutions represent the quantized dynamics of solitonic degrees of freedom in atomic droplets. In dimensions lower than two, or $d=2-\epsilon$, we demonstrate that the number of isotropic droplet states scales as $N^{3/2}/{\epsilon }^{1/2}$, and for $\epsilon =0$, or $d=2$, scales as $N^2$. The ground-state energies scale as $N^{2/\epsilon +1}$ in $d=2-\epsilon$, and when $d=2$, scale as an exponential function of $N$. We obtain the universal energy spectra and the generalized Tjon relation; their scaling properties are uniquely determined by the asymptotic freedom of quantum bosonic fields at short distances, a distinct feature in low dimensions. We also investigate the effect of quantum loop corrections that arise from various virtual processes and show that the resultant lifetime for a wide range of excited states scales as $N^{\epsilon /2}{E}^{1-\epsilon /2}$.

The orbital angular momentum (OAM) of light is potentially interesting for astronomical study of rotating objects such as black holes, but the effect of reduced spatial coherence of astronomical light sources like stars is largely unknown. In a laboratory-scale experiment, we find that the detected OAM spectrum depends strongly on the position of the light-twisting object along the line of sight. We develop a simple intuitive model to predict the influence of reduced spatial coherence on the propagating OAM spectrum for, e.g., astronomical observations. Further, we derive equations to predict the effect of line-of-sight misalignment and the received intensity in higher-order OAM modes for limited-size detectors such as telescopes.

We present a scheme for high-precision three-dimensional (3D) localization by the measurement of the atomic-level population. The scheme is applied to a four-level tripod-type atom coupled by three strong standing waves and a probe running wave. As a result, the atom can be localized in volumes that are substantially smaller than a cubic optical wavelength, which is achieved by the increase of standing-wave intensities. The upper-level distribution depends crucially on the atom-field coupling and it forms 3D periodic structures composed of spheres, hourglasses, bowls, donuts, or deformed barrels.

We study the effects of the quantum vacuum on the propagation of a Gaussian laser beam in vacuum. By means of a double perturbative expansion in paraxiality and quantum vacuum terms, we provide analytical expressions for the self-induced transverse mode mixing, rotation of polarization, and third harmonic generarion. We discuss the possibility of searching for the self-induced, spatially dependent phase shift of a multipetawatt laser pulse, which may allow the testing of quantum electrodynamics and new physics models, such as Born-Infeld theory and models involving new minicharged or axion-like particles, in parametric regions that have not yet been explored in laboratory experiments.

We have recently developed a position-dependent quantization scheme for describing the ladder and effective photon-number operators associated with the electric field to analyze quantum optical energy transfer in lossy and dispersive dielectrics [Phys. Rev. A 89, 033831 (2014)]. While having a simple connection to the thermal balance of the system, these operators only described the electric field and its coupling to lossy dielectric bodies. Here we extend this field quantization scheme to include the magnetic field and thus to enable description of the total electromagnetic field and discuss conceptual measurement schemes to verify the predictions. In addition to conveniently describing the formation of thermal balance, the generalized approach allows modeling of the electromagnetic pressure and Casimir forces. We apply the formalism to study the local steady-state field temperature distributions and electromagnetic force density in cavities with cavity walls at different temperatures. The calculated local electric and magnetic field temperatures exhibit oscillations that depend on the position as well as the photon energy. However, the effective photon number and field temperature associated with the total electromagnetic field is always position independent in lossless media. Furthermore, we show that the direction of the electromagnetic force varies as a function of frequency, position, and material thickness.

Quadrupole shifts for three prominent clock transitions, $\left[4f^{14}6s\right]{}^2{S}_{1/2}\to \left[4f^{14}5d\right]{}^2{D}_{3/2},\left[4f^{14}6s\right]{}^2{S}_{1/2}\to \left[4f^{14}5d\right]{}^2{D}_{5/2}$, and $\left[4f^{14}6s\right]{}^2{S}_{1/2}\to \left[4f^{13}6s^2\right]{}^2{F}_{7/2}$, in the ${\mathrm{Yb}}^{+}$ ion are investigated by calculating values of the quadrupole moment $\left(\Theta \right)$ for the $5d_{3/2,5/2}$ and $4f_{7/2}$ states using the relativistic coupled-cluster (RCC) methods. We find an order of magnitude difference in the $\Theta$ value of the $4f_{7/2}$ state between our calculation and the experimental result, but our result concurs with that of other calculations carried out using many-body methods different from ours. However, our $\Theta$ value of the $5d_{3/2}$ state is in good agreement with the available experimental result and is highly precise. This enables us to estimate the quadrupole shift of the $\left[4f^{14}6s\right]{}^2{S}_{1/2}\to \left[4f^{14}5d\right]{}^2{D}_{3/2}$ clock transition more accurately. To justify the accuracies in our calculations, we evaluate the hyperfine structure constants of the $6s_{1/2},5d_{3/2,5/2}$, and $4f_{7/2,5/2}$ states of the ${}^{171}\mathrm{Yb}^{+}$ ion using the same RCC methods and compare the results with the experimental values. We also determine the lifetime of the $5d_{3/2}$ state to address a discrepancy between conflicting values given by recent experiments.

Exciton sizes and electron-hole binding energies, which are central properties of excited states in extended systems and crucial to the design of modern electronic devices, are readily defined within a quasiparticle framework but are quite challenging to understand in the molecular-orbital picture. The intent of this work is to bridge this gap by providing a general way of extracting the exciton wave function out of a many-body wave function obtained by a quantum chemical excited-state computation. This methodology, which is based on the one-particle transition density matrix, is implemented within the ab initio algebraic diagrammatic construction scheme for the polarization propagator and specifically the evaluation of exciton sizes, i.e., dynamic charge separation distances, is considered. A number of examples are presented. For stacked dimers it is shown that the exciton size for charge separated states corresponds to the intermolecular separation, while it only depends on the monomer size for locally excited states or Frenkel excitons. In the case of conjugated organic polymers, the tool is applied to analyze exciton structure and dynamic charge separation. Furthermore, it is discussed how the methodology may be used for the construction of a charge-transfer diagnostic for time-dependent density-functional theory.

We propose an approach for describing the effective electronic states of atoms in compounds to study the properties of molecules and condensed matter, which are circumscribed by the operators heavily concentrated in atomic cores. Among the properties are hyperfine structure, space parity (P) and time reversal invariance (T) nonconservation effects, chemical shifts of x-ray emission lines (XES), Mössbauer effect, etc. An advantage of the approach is that a good quantitative agreement of predicted and experimental data can be attained even for such difficult cases as XES chemical shifts providing correct quantum-mechanical interpretation of the experimental data. From the computational point of view the method can be quite efficient being implemented in the framework of the relativistic pseudopotential theory [A. V. Titov and N. S. Mosyagin, Int. J. Quantum Chem. 71, 359 (1999)] and procedures of recovering the wave functions in heavy-atom cores [A. V. Titov, N. S. Mosyagin, A. N. Petrov, and T. A. Isaev, Int. J. Quantum Chem. 104, 223 (2005)] after a molecular, cluster or periodic structure calculation performed on the basis of pseudo-orbitals smoothed near the nuclei within the pseudopotential approximation. We report results of our studies of a number of atomic and molecular systems to demonstrate the capabilities of the approach.

We performed charge-exchange experiments with the electron-beam ion trap and an x-ray calorimeter spectrometer at the Lawrence Livermore National Laboratory. We compare the relative strength of the high-$n$ Lyman series emission for different combinations of ions and neutral gases. Theoretical predictions show good agreement with experimental data on the relative capture cross section as a function of principal quantum number $n$; however, the few published predictions of the distribution of captures as a function of orbital angular momentum $l$ do not agree with experiments. Our experimental results show that the relative strength of high-$n$ Lyman series emission varies more widely than previous experiments have found and models predict. We find that hardness ratios from charge exchange with helium and molecular hydrogen are more disparate than charge exchange with many-electron neutral species, which is likely due to differences in the relative importance of multielectron capture. We also find that there is no clear scaling of the hardness ratio with the ionization potential of the neutral species, the number of valence electrons in the neutral species, or the atomic number of the ion.

The dynamics of a vortex dipole in a spin-1 Bose-Einstein condensate in which magnetic phases are spatially distributed is investigated. When a vortex dipole travels from the ferromagnetic phase to the polar phase, or vice versa, it penetrates the phase boundary and transforms into one of the various spin vortex dipoles, such as a leapfrogging ferromagnetic-core vortex dipole and a half-quantum vortex dipole. Topological connections of spin wave functions across the phase boundary are discussed.

We investigate the interaction energy and the possibility of itinerant ferromagnetism in a strongly interacting Fermi gas at zero temperature in the absence of molecule formation. The interaction energy is obtained by summing the perturbative contributions of Galitskii-Feynman type to all orders in the gas parameter. It can be expressed by a simple phase-space integral of an in-medium scattering phase shift. In both three and two dimensions (3D and 2D), the interaction energy shows a maximum before reaching the resonance from the Bose-Einstein condensate side, which provides a possible explanation of the experimental measurements of the interaction energy. This phenomenon can be theoretically explained by the qualitative change of the nature of the binary interaction in the medium. The appearance of an energy maximum has significant effects on the itinerant ferromagnetism. In 3D, the ferromagnetic transition is reentrant and itinerant ferromagnetism exists in a narrow window around the energy maximum. In 2D, the present theoretical approach suggests that itinerant ferromagnetism does not exist, which reflects the fact that the energy maximum becomes much lower than the energy of the fully polarized state.