Bose-Einstein condensation (BEC) in cold gases can be turned on and off by an external potential, such as that presented by an optical lattice. We present a model of this phenomenon which we are able to analyze rigorously. The system is a hard core lattice gas at half of the maximum density and the optical lattice is modeled by a periodic potential of strength $\lambda$. For small $\lambda$ and temperature, BEC is proved to occur, while at large $\lambda$ or temperature there is no BEC. At large $\lambda$ the low-temperature states are in a Mott insulator phase with a characteristic gap that is absent in the BEC phase. The interparticle interaction is essential for this transition, which occurs even in the ground state. Surprisingly, the condensation is always into the $\mathbf{p}=\mathbf{0}$ mode in this model, although the density itself has the periodicity of the imposed potential.

The production of pairs of fast atoms leads to a pronounced loss of atoms during upward ramps of Feshbach resonance levels in dilute Bose-Einstein condensates. We provide comparative studies on the formation of these bursts of atoms containing the physical predictions of several theoretical approaches at different levels of approximation. We show that, despite their very different description of the microscopic binary physics during the passage of a Feshbach resonance, all approaches lead to virtually the same prediction on the total loss of condensate atoms, provided that the ramp of the magnetic field strength is purely linear. We give the reasons for this remarkable insensitivity of the remnant condensate fraction to the microscopic physical processes and compare the theoretical predictions with recent Feshbach resonance crossing experiments on ${}^{23}\mathrm{Na}$ and ${}^{85}\mathrm{Rb}$.

We present a theoretical study of ghost imaging based on correlated beams arising from parametric down-conversion, and which uses balanced homodyne detection to measure both the signal and idler fields. We analytically show that the signal-idler correlations contain the full amplitude and phase information about an object located in the signal path, both in the near-field and the far-field case. To this end we discuss how to optimize the optical setups in the two imaging paths, including the crucial point regarding how to engineer the phase of the idler local oscillator as to observe the desired orthogonal quadrature components of the image. As is well known, the near-field image resolution is inherently linked to the far-field bandwidth of the image, determined by the bandwidth of the source of the correlated beams. We show how to circumvent this limitation by using a spatial averaging technique which dramatically improves the imaging bandwidth of the far-field correlations as well as speeds up the convergence rate. The results are backed up by numerical simulations taking into account the finite size and duration of the pump pulse.

The optical-model approach has been used to investigate positronium (Ps) formation in $e^{+}\text{‐}\mathrm{Na}$ collision at low impact energies $(0.1–20.0\mathrm{eV})$. A complex equivalent local polarization potential is obtained to describe the rearrangement process. The Ps formation cross section is excellently reproduced by this potential. The results for the Ps $(n=1)$ and Ps $(n=2)$ formation cross sections are reported and compared with the experimental measurements and other close-coupling calculations.

We study the constraints imposed on the population and phase relaxation rates by the physical requirement of completely positive evolution for open $N$-level systems. The Lindblad operators that govern the evolution of the system are expressed in terms of observable relaxation rates, explicit formulas for the decoherence rates due to population relaxation are derived, and it is shown that there are additional, nontrivial constraints on the pure dephasing rates for $N>2$. Explicit, experimentally testable inequality constraints for the decoherence rates are derived for three- and four-level systems, and the implications of the results are discussed for generic ladder, $\Lambda$, and V systems and transitions between degenerate energy levels.

In this work we analyze the coherence dynamics and estimate decoherence times of quantum states in a network composed of $N$ coupled dissipative quantum oscillators. We assume a symmetric network where all oscillators are coupled to each other with the same coupling strength. Master equations are derived for regimes of both weak and strong coupling between the oscillators. The strong coupling regime is characterized by the coupling strength between the oscillators or by the number of oscillators in the network. The decoherence times of particular states of the network are computed and the results are clarified by analyzing the processes of state swap and recurrence of reduced states of the network together with the linear entropies of the joint and reduced systems.

In this work we analyze the coherence dynamics and estimate decoherence times of quantum states in a network where a central dissipative oscillator is coupled with $N-1$ peripheral noninteracting dissipative oscillators. The results obtained here are compared with those in part I of this work where a symmetric network was considered. This comparison helps us to understand the influence of the topology of a network on the coherence dynamics of quantum superposition states. As in part I, master equations are derived for regimes of both weak and strong coupling between the oscillators. Decoherence times of particular states of the network are computed and the results are analyzed in the light of state swap and recurrence processes of reduced states of the network. The linear entropies of the joint and reduced systems are also analyzed.

Entanglement-changing power of an arbitrary two-qubit operation, including increasing and decreasing power, is investigated in this paper. We consider the maximal entanglement $C_{\max }$ and the minimal entanglement $C_{\min }$ of the states obtained by a given two-qubit unitary operation $U_d$ acting on arbitrary pure states with fixed entanglement $C_0$. We give the condition that the maximal entanglement $C_{\max }$ of the obtained states can be $1$ and the minimal entanglement $C_{\min }$ can be $0$. When the maximal entanglement $C_{\max }$ cannot be $1$, we give the maximal value it can reach. When the minimal entanglement $C_{\min }$ cannot be $0$, we give the minimal value it can reach. We think $C_{\max }$ and $C_{\min }$ represent the entanglement-changing power of two-qubit unitary operations.

Quantum estimation theory provides optimal observations for various estimation problems for unknown parameters in the state of the system under investigation. However, the theory has been developed under the assumption that every observable is available for experimenters. Here, we generalize the theory to problems in which the experimenter can use only locally accessible observables. For such problems, we establish a Cramér-Rao-type inequality by obtaining an explicit form of the Fisher information as a reciprocal lower bound for the mean-square errors of estimations by locally accessible observables. Furthermore, we explore various local quantum estimation problems for composite systems, where nontrivial combinatorics is needed for obtaining the Fisher information.

The minimum Rényi and Wehrl output entropies are found for bosonic channels in which the signal photons are either randomly displaced by a Gaussian distribution (classical-noise channel), or coupled to a thermal environment through lossy propagation (thermal-noise channel). It is shown that the Rényi output entropies of integer orders $z⩾2$ and the Wehrl output entropy are minimized when the channel input is a coherent state.

We present a way to teleport multiqubit quantum information from a sender to a distant receiver via the control of many agents in a network. We show that the original state of each qubit can be restored by the receiver as long as all the agents collaborate. However, even if one agent does not cooperate, the receiver cannot fully recover the original state of each qubit. The method operates essentially through entangling quantum information during teleportation, in such a way that the required auxiliary qubit resources, local operation, and classical communication are considerably reduced for the present purpose.

In pair density-functional theory, the only unknown piece of the energy is the kinetic energy $T$ as a functional of the pair density $P(x_1,x_2)$. Although $T\left[P\right]$ has a simpler structure than the Hohenberg-Kohn functional of conventional density-functional theory, computational requirements are still moderate. In the present work, a particularly convenient model system to represent many-electron pair densities is introduced. This “boson pair model” (BPM) approximately treats electron pairs as noninteracting bosons. The resulting explicit model for the kinetic energy $T_2\left[P\right]$ is shown to be exact for two-electron systems and a lower bound to $T\left[P\right]$ for more than two electrons. The one- and two-particle density matrices obtained from the BPM yield upper bounds for the corresponding many-electron quantities. This suggests a partitioning $T\left[P\right]=T_2\left[P\right]+T_{\mathrm{eff}}\left[P\right]$, where only the remainder $T_{\mathrm{eff}}\left[P\right]⩾0$ needs to be approximated. If the BPM is constrained to yield the exact ground-state pair density, a two-electron Schrödinger equation with an effective local two-particle potential results; the latter is identified as a sum of the bare Coulomb interaction and the functional derivative of $T_{\mathrm{eff}}\left[P\right]$. This self-consistent scheme to minimize the energy with respect to $P$ is more efficient than previous procedures. Further information on the functional derivative of $T_{\mathrm{eff}}\left[P\right]$ is derived from a contracted Schrödinger equation. Since $T_{\mathrm{eff}}\left[P\right]$ is explicitly known in the two-electron and noninteracting (Hartree-Fock) limits, the present method provides an alternative to density-matrix functional theories, which can be exact in the same limits and are similar in computational cost.

Angle- and spin-resolved photoelectron spectroscopy with circularly and linearly polarized synchrotron radiation were used to study the electronic structure of the hydrogen sulfide molecule. A strong effect of the molecular environment appears in the spin-resolved measurements and, although less clearly, in the angular distribution of the sulfur $2p$ photoelectrons. The anisotropy and spin parameters of the three main spectral components have been obtained. The validity of simple atomic models in explaining the results is discussed.

Photodetachment of the outer shells of the ground ${}^{4}S^o$ state of ${\mathrm{C}}^{-}$ using an augmented $R$-matrix theoretical methodology has been studied from threshold to $13\mathrm{eV}$. Total and partial cross sections and photoelectron angular distribution asymmetry parameters have been obtained. Excellent agreement between length and velocity formulations is found. The results resolve a discrepancy among earlier calculations, and a new shape resonance, $1s^{2}2s^{2}2p3s3p$ ${}^{4}P$, at a photon energy of $8.588\mathrm{eV}$ is predicted.

Extending recent work to finite temperatures, we calculate the Landau damping of a Bogoliubov excitation in an optical lattice, due to the coupling to a thermal cloud of such excitations. For simplicity, we consider a one-dimensional Bose-Hubbard model and restrict ourselves to the first energy band. For energy conservation to be satisfied, the excitations in the collision processes must exhibit “anomalous dispersion,” analogous to phonons in superfluid ${}^4\mathrm{He}$. This leads to the disappearance of all damping processes when $U{n}^{\mathrm{c}0}⩾6J$, where $U$ is the on-site interaction, $J$ is the hopping matrix element, and $n^{\mathrm{c}0}\left(T\right)$ is the number of condensate atoms at a lattice site. This phenomenon also occurs in two-dimensional and three-dimensional optical lattices. The disappearance of Beliaev damping above a threshold wave vector is noted.

We investigate the effect of the dipole-dipole interaction on the quantum jump statistics of three atoms. This is done for three-level systems in a $\mathsf{V}$ configuration and in what may be called a $\mathsf{D}$ configuration. The transition rates between the four different intensity periods are calculated in closed form. Cooperative effects are shown to increase by a factor of 2 compared to two of either three-level systems. This results in transition rates that are, for distances of about one wavelength of the strong transition, up to 100% higher than for independent systems. In addition the double and triple jump rates are calculated from the transition rates. In this case cooperative effects of up to 170% for distances of about one wavelength and still up to 15% around 10 wavelengths are found. Nevertheless, for the parameters of an experiment with ${\mathrm{Hg}}^{+}$ ions the effects are negligible, in agreement with the experimental data. For three ${\mathrm{Ba}}^{+}$ ions this seems to indicate that the large cooperative effects observed experimentally cannot be explained by the dipole-dipole interaction.

An experimental demonstration of an optical field ionization short-wavelength laser driven in a gas-filled capillary-discharge waveguide is described in detail. Guiding of high-intensity laser pulses has previously been demonstrated with this type of waveguide for capillary discharges in hydrogen. For the present experiments xenon gas was mixed with the hydrogen, and strong lasing on the $4d^{9}5d\text{−}4d^{9}5p$ transition in ${\mathrm{Xe}}^{8+}$ at $41.8\mathrm{nm}$ was observed. Under optimum conditions the short-wavelength laser output achieved with the waveguide was found to be greater than that from a Xe gas cell. Measurements of the transmission of the pump laser pulses through the waveguide show that the short-wavelength laser signal was greatest under conditions for which the pump laser pulses were well guided. Simulations of the propagation of the pump laser radiation are presented for a range of initial plasma conditions, and these indicate that the laser-plasma interaction length achieved was greatly increased compared to that which can be achieved in a gas cell.

We study the interaction of a weak probe field, having two orthogonally polarized components, with an optically dense medium of four-level atoms in a tripod configuration. In the presence of a coherent driving laser, electromagnetically induced transparency is attained in the medium, dramatically enhancing its linear as well as nonlinear dispersion while simultaneously suppressing the probe field absorption. We present the semiclassical and fully quantum analysis of the system. We propose an experimentally feasible setup that can induce large Faraday rotation of the probe field polarization and therefore be used for ultrasensitive optical magnetometry. We then study the Kerr nonlinear coupling between the two components of the probe, demonstrating a novel regime of symmetric, extremely efficient cross-phase modulation, capable of fully entangling two single-photon pulses. This scheme may thus pave the way to photon-based quantum information applications, such as deterministic all-optical quantum computation, dense coding, and teleportation.

We report on the formation of translationally cold $\mathrm{NaCs}$ molecules starting from a laser-cooled atomic vapor of $\mathrm{Na}$ and $\mathrm{Cs}$ atoms. Colliding atoms are transferred into bound molecular states in a two-step photoactivated process in which the atoms are first photoassociated by trap photons into an excited state molecular complex and then allowed to decay into a bound molecular ground state. Time-of-flight measurements show a translational temperature $T=260\pm 130\mu \mathrm{K}$ that reflects the measured temperature of the initial atomic gas.

A parametric source of polarization-entangled photon pairs with striking spatial characteristics is reported. The distribution of the output electromagnetic $\mathbf{k}$ modes excited by spontaneous parametric down-conversion and coupled to the output detectors can be very broad. Using these states realized over a full entanglement ring output distribution, the nonlocal properties of the generated entanglement have been tested by standard Bell measurements and by Ou-Mandel interferometry. A “mode-patchwork” technique based on the quantum superposition principle is adopted to synthesize in a straightforward and reliable way any kind of mixed state, of large conceptual and technological interest in modern quantum information. Tunable Werner states and maximally entangled mixed states have indeed been created by this technique and investigated by quantum tomography. A study of the entropic and nonlocal properties of these states has been undertaken experimentally and theoretically, by a unifying variational approach.