Based on a perturbative approach, a series expansion in susceptibility function of the medium is obtained for the Casimir force between arbitrarily shaped objects immersed in a scalar or vector fluctuating field in arbitrary dimensions. Finite-temperature corrections are derived, and the results are compared in first order with the weak-coupling regime in the scattering method. The generalization to a massive vector field is also investigated.

The VUV-induced photofragmentation of ${\mathrm{As}}_4$ clusters was studied using photoelectron-photoion-coincidence (PEPICO) spectroscopy. The fragmentation pathways subsequent to outer and inner valence photoionization and resonant photoexcitation were studied by examining the cationic production as a function of electron energy. In addition, regular photoelectron spectroscopy and partial ion yield absorption spectroscopy were employed. In order to enhance the weak signal from the inner valence states, resonant core $3d$ excitation was used in the PEPICO experiment. The fragmentation pathways were inspected with the aid of ab initio and thermochemical calculations. The many-electron effects were found to play a major role in the observed inner valence structure and resulting photofragmentation.

We present efficient theoretical tools for describing the optical pumping of atoms by light propagating at arbitrary directions with respect to an external magnetic field, at buffer-gas pressures that are small enough for velocity-selective optical pumping (VSOP) but large enough to cause substantial collisional relaxation of the velocities and the spin. These are the conditions for the sodium atoms at an altitude of about 100 km that are used as guidestars for adaptive optics in modern ground-based telescopes to correct for aberrations due to atmospheric turbulence. We use spin and velocity relaxation modes to describe the distribution of atoms in spin space (including both populations and coherences) and velocity space. Cusp kernels are used to describe velocity-changing collisions. Optical pumping operators are represented as a sum of poles in the complex velocity plane. Signals simulated with these methods are in excellent agreement with previous experiments and with preliminary experiments in our laboratory.

We investigate an ensemble of atoms which can be excited into a Rydberg state. Using a disordered quantum Ising model, we perform a numerical simulation of the experimental procedure and calculate the probability distribution function $P\left(M\right)$ to create a certain number of Rydberg atoms $M$, as well as their pair-correlation function. Using the latter, we identify the critical interaction strength above which the system undergoes a phase transition to a Rydberg crystal. We then show that this phase transition can be detected using $P\left(M\right)$ alone.

We report the demonstration of a magnetometer with noise-floor reduction below the shot-noise level. This magnetometer, based on a nonlinear magneto-optical rotation effect, is enhanced by the injection of a squeezed vacuum state into its input. The noise spectrum shows squeezed noise reduction of about $2\pm 0.35$ dB spanning from close to 100 Hz to several megahertz. We also report on the observation of two different regimes of operation of such a magnetometer: one in which the detection noise is limited by the quantum noise of the light probe only, and one in which we see additional noise originating from laser noise which is rotated into the vacuum polarization.

We compute the design parameters that maximize the cooperative decay rate (CDR) from a nanosphere of identical two-level atoms phased to radiate coherently (Dicke enhancement), encased in a shell of a noble metal (Purcell effect), the whole suspended for mechanical support in a dielectric medium extending to infinity. Both the radiating core and the metallic shell are described internally by their respective frequency-dependent dielectric functions. (In previous papers one or the other medium was given a fixed dielectric constant.) The solution is noticeably altered, and the enhancement increased, when both media respond interactively to one another.

The coincidence rate in two detectors that register signal and idler photons in parametric down-conversion is calculated using a quantum description of the radiation field that extends the semiclassical theory to the resonance regime. The signal is given by a sum over paths in the joint field plus matter space, each involving a pair of sites (molecules) and six radiation field modes. It may not be factorized into amplitudes representing one-site, three-mode paths. All effects of multiple vacuum modes are accounted for by theses paths without adding a Langevin noise source. The molecular information is given by a time-ordered superoperator Green's function rather than the susceptibility ${\chi }^{\left(2\right)}$ used in the semiclassical theory.

We apply the stochastic master equations (quantum filter) derived by Gough et al. (Proc. 50th IEEE Conference on Decision and Control, 2011) to a system consisting of a cavity driven by a multimode single photon field. In particular, we analyse the conditional dynamics for the problem of cross phase modulation in a doubly resonant cavity. Through the exact integration of the stochastic equations, our results reveal features of the problem unavailable from previous models.

We investigate a class of optical mesh periodic structures that are discretized in both the transverse and longitudinal directions. These networks are composed of waveguide arrays that are discretely coupled, while phase elements are also inserted to discretely control their effective potentials and can be realized both in the temporal and the spatial domain. Their band structure and impulse response are studied in both the passive and parity-time ($\mathcal{PT}$)-symmetric regime. The possibility of band merging and the emergence of exceptional points, along with the associated optical dynamics, are considered in detail both above and below the $\mathcal{PT}$-symmetry breaking point. Finally, unidirectional invisibility in $\mathcal{PT}$-synthetic mesh lattices is also examined, along with possible superluminal light transport dynamics.

One of the main challenges for the manipulation and storage of multipartite entanglement is its fragility under noise. We present a simple recipe for the systematic enhancement of the resistance of multipartite entanglement against any local noise with a privileged direction in the Bloch sphere. For the case of exact local dephasing along any given basis, and for all noise strengths, our prescription grants full robustness: Even states with exponentially decaying entanglement are mapped to states whose entanglement is constant. In contrast to previous techniques resorting to complex logical-qubit encodings, such enhancement is attained simply by performing local-unitary rotations before the noise acts. The scheme is therefore highly experimentally friendly, as it brings no overhead of extra physical qubits to encode logical ones. In addition, we show that, apart from entanglement, the resiliences of the relative entropy of quantumness and the usefulness as resources for practical tasks such as metrology and nonlocality-based protocols are equivalently enhanced.

We consider multiple entanglement swappings performed on a chain of bipartite states. Each state does not violate Clauser-Horne-Shimony-Holt (CHSH) inequality. We show that before some critical number of entanglement swappings is achieved the output state does not violate this inequality either. However, if this number is achieved, then for some results of Bell measurements obtained in the protocol of entanglement swapping the output state violates CHSH inequality. Moreover, we show that for different states we have different critical numbers for which CHSH inequality is activated.

Building on the recent experimental achievements obtained with scanning electron microscopy on ultracold atoms, we study one-dimensional Bose gases in the crossover between the weakly (quasicondensate) and the strongly interacting (Tonks-Girardeau) regime. We measure the temporal two-particle correlation function and compare it with calculations performed using the time-evolving block decimation algorithm. More pronounced antibunching is observed when entering the more strongly interacting regime. Even though this mimics the onset of a fermionic behavior, we highlight that the exact and simple duality between one-dimensional bosons and fermions does not hold when such a dynamical response is probed. The onset of fermionization is also reflected in the density distribution, which we measure in situ to extract the relevant parameters and to identify the different regimes. Our results show agreement between experiment and theory and give insight into the dynamics of strongly correlated many-body systems.

We develop a perturbative method of computing spectral singularities of a Schrödinger operator defined by a general complex potential that vanishes outside a closed interval. These can be realized as zero-width resonances in optical gain media and correspond to a lasing effect that occurs at the threshold gain. Their time-reversed copies yield coherent perfect absorption of light that is also known as antilasing. We use our general results to establish the exactness of the $n$th-order perturbation theory for an arbitrary complex potential consisting of $n$ delta functions, obtain an exact expression for the transfer matrix of these potentials, and examine spectral singularities of complex barrier potentials of arbitrary shape. In the context of optical spectral singularities, these correspond to inhomogeneous gain media.

We consider the class of ($N+1$)-partite states suitable for protocols where there is a powerful party, the authority, and the other $N$ parties play the same role, namely, the state of their system lies in the symmetric Hilbert space. We show that, within this scenario, there is a “maximally entangled state” that can be transform by a local operations and classical communication protocol into any other state. In addition, we show how to use the protocol efficiently, including the construction of the state, and discuss security issues for possible applications to cryptographic protocols. As an immediate consequence we recover a sequential protocol that implements the 1-to-$N$ symmetric cloning.

We present expressions demonstrating that collisional decoherence of ultracold atoms or molecules in a coherent superposition of nondegenerate quantum states is suppressed when both the real and imaginary parts of the scattering lengths for the states in the coherent superposition are equal. We show that the rate of collisional decoherence can be enhanced or suppressed by varying an external magnetic field near a Feshbach resonance. For some resonances, the suppression is very dramatic. We propose a method for measuring the scattering length of ultracold particles in excited quantum states exhibiting Feshbach resonances.

Photoionization cross-section calculations are performed on the ground state ([Ne]3$s^2$3$p^6$4$s$ ${}^2{S}_{1/2}^e$) and the first two excited states ([Ne]3$s^2$3$p^6$3$d$ ${}^2{D}_{3/2}^e$ and [Ne]3$s^2$3$p^6$3$d$ ${}^2{D}_{5/2}^e$) of Ca${}^{+}$ ions for photon energies from threshold to 45.0 eV using the relativistic (Breit-Pauli) $R$-matrix method. The discrete Ca${}^{2+}$ orbitals are generated using the computer program autostructure; 30 configurations are included in the configuration-interaction calculation for the states of Ca${}^{2+}$. The prominent 3$p$ → 3$d$ giant resonances are analyzed and identified, and our results are compared with experimental results, and rather good agreement is found. Using results of our previous photoionization calculations on Sc${}^{2+}$ and Ti${}^{3+}$ ions, the strongest and broadest resonances in the photoionization cross section of those three ions (Ca${}^{+}$, Sc${}^{2+}$, and Ti${}^{3+}$), in terms of width and oscillator strengths, are compared to show the evolution as a function of nuclear charge.

The nonequilibrium dynamics of a rapidly quenched spin-1 Bose gas with spin-orbit coupling is studied. By solving the stochastic projected Gross-Pitaevskii equation, we show that crystallization of half-skyrmions (merons), can occur in a spinor condensate of ${}^{87}$Rb. The stability of such a crystal structure is analyzed. Likewise, inverted half-skyrmions can be created in a spin-polarized spinor condensate of ${}^{23}$Na. Our studies provide a chance to explore the fundamental properties of skyrmionlike matter.

The flow of a uniform Bose gas at speeds greater than the Landau critical velocity $v_c$ does not necessarily destroy superfluidity, but rather needs only to lead to a decrease of the superfluid mass density ${\rho }_s$. Analyzing a weakly interacting Bose gas with a finite-range interparticle interaction that leads to a Landau critical velocity at nonzero quasiparticle momentum, we explicitly construct the (nonuniform) condensate for fluid flow faster than $v_c$ and calculate the accompanying decrease in ${\rho }_s$. We briefly comment on the relation of the physics to other problems in superfluids, e.g., solitons and vortices in Bose-Einstein condensates, and critical currents in superconductors.

We study both Bose and Fermi gases at finite temperature and density in an approximation that sums an infinite number of many-body processes that are reducible to two-body scatterings. This is done for arbitrary negative scattering length, which interpolates between the ideal and unitary gas limits. In the unitary limit, we compute the first four virial coefficients within our approximation. The second virial coefficient is exact, and we extend the previously known result for fermions to bosons and also for both bosons and fermions for the upper branch on the other side of unitarity (infinitely large positive scattering length). Assuming bosons can exist in a metastable state before undergoing mechanical collapse, we map out the critical temperatures for strongly coupled Bose-Einstein condensation as a function of scattering length.

We study models of itinerant spinless fermions with random long-range interactions. We motivate such models from descriptions of fermionic atoms in multimode optical cavities. The solution of an infinite-range model yields a metallic phase, which has glassy charge dynamics, and a localized glass phase with suppressed density of states at low energies. We compare these phases to the conventional disordered Fermi liquid, and the insulating electron glass of semiconductors. Prospects for the realization of such glassy phases in cold-atom systems are discussed.