We propose a microscopic approach describing the interaction of an ideal gas of hydrogenlike atoms with a weak electromagnetic field. This approach is based on the Green-function formalism and an approximate formulation of the method of second quantization for quantum many-particle systems in the presence of bound states of particles. The dependencies of the propagation velocity and damping rate of electromagnetic pulses on the microscopic characteristics of the system are studied for a gas of hydrogenlike atoms. For a Bose-Einstein condensate of alkali-metal atoms we find the conditions when the electromagnetic waves of both the optical and microwave regions are slowed. In the framework of the proposed approach, the influence of an external homogeneous and static magnetic field on the slowing phenomenon is studied.

We have studied the nonlinear Faraday effect with intense linear polarized light in an optically thick atomic rubidium vapor. We demonstrate that the polarization rotation rate (rotation angle per unit magnetic field, in the limit of low field) has a maximum value as the intensity and density are increased. We also show that the optimal sensitivity of an optical magnetometer based on this system reaches a saturation value as the intensity and density are increased.

We show that extremely narrow beams (of the width of few wavelengths) can be used for second-harmonic generation in quadratic-nonlinear photonic crystals, tuned to the subdiffractive (self-collimating) regime simultaneously for both fundamental and second-harmonic waves. We prove second-harmonic generation numerically by means of finite-difference time-domain numerical integration.

The multipolar solution of the electromagnetic field is useful in light-matter interactions. Here is presented a method to control the superpositions of multipolar electromagnetic fields using paraxial beams. This is applied to orbital angular momentum paraxial modes, which allow us to calculate their total angular momentum. This quantity plays an important role in the control of electronic transitions in atoms and molecules. The results here can easily be extended to highly focused laser beams.

We show that single-photon entangled states of the form $\mid 0⟩\mid 1⟩+\mid 1⟩\mid 0⟩$ can be purified with a simple linear-optics-based protocol, which is eminently feasible with current technology. Besides its conceptual interest, this result is relevant for attractive quantum repeater protocols.

With the goal of gaining a deeper understanding of quantum nonlocality, we decompose quantum correlations into more elementary nonlocal correlations. We show that the correlations of all pure entangled states of two qubits can be simulated without communication, hence using only no-signaling resources. Our simulation model works in two steps. First, we decompose the quantum correlations into a local and a nonlocal part. Second, we present a model for simulating the nonlocal part using only no-signaling resources. In our model partially entangled states require more nonlocal resources than maximally entangled states, but the less the state is entangled, the less frequently must the nonlocal resources be used.

We show that it is possible to modify the stationary state by a feedback control in a two-level dissipative quantum system. Based on the geometric control theory, we also analyze the effect of the feedback on the time-optimal control in the dissipative system governed by the Lindblad master equation. These effects are reflected in the functions ${\Delta }_A\left(\vec{x}\right)$ and ${\Delta }_B\left(\vec{x}\right)$, which characterize the optimal trajectories, as well as the switching functions $\Phi \left(t\right)$ and $\theta \left(t\right)$, which characterize the switching point in time for the time-optimal trajectory.

We obtain exponential decay laws for solutions of density-matrix master equations in the weak-coupling limit: after comparing with results already present in the literature and developing the necessary techniques, we study the crucial aspect of complete positivity under fairly general conditions. We propose a time average that guarantees complete positivity and approximates, in Markovian fashion, the exact dynamics for a plethora of physical applications, no matter which are the spectral properties of the subsystem, or its dimensions. We shall comment on some interesting examples, such as a quantum version of the celebrated Fermi’s “golden rule” and some recently proposed entangling projections.

Probabilistic quantum filtering is proposed to properly adapt sequential independent quantum channels in order to stop sudden death of entanglement. In the adaptation, the quantum filtering does not distill or purify more entanglement, it rather properly prepares an entangled state to the subsequent quantum channel. In particular, the quantum adaptation probabilistically eliminates the sudden death of entanglement of a two-qubit entangled state with isotropic noise injected into separate amplitude damping channels. The result has an application in quantum key distribution through noisy channels.

We report on two optical realizations of the $1\to 2$ asymmetric phase-covariant cloning machines for polarization states of single photons. The experimental setups combine two-photon interference and tunable polarization filtering, which enables us to control the asymmetry of the cloners. The first scheme involves a special unbalanced bulk beam splitter exhibiting different splitting ratios for vertical and horizontal polarizations, respectively. The second implemented scheme consists of a balanced fiber coupler where photon bunching occurs, followed by a free-space part with polarization filters. With this latter approach we were able to demonstrate very high cloning fidelities which are above the universal cloning limit.

Entanglement is believed to be crucial in macroscopic physical systems for understanding the collective quantum phenomena such as quantum phase transitions. We start from and solve exactly a Yang-Baxter spin-$1∕2$ chain model with inhomogeneous and anisotropic short-range interactions. For the ground state, we show the behavior of neighboring entanglement in the parameter space and find that the inhomogeneous coupling strengths affect entanglement in a distinctive way from the homogeneous case, but this would not affect the coincidence between entanglement and quantum criticality.

Inelastic collisions of sodium due to low-energy helium are investigated using the quantum-mechanical molecular-orbital coupled-channel method. The calculations adopt adiabatic potentials and nonadiabatic radial and rotational couplings obtained with the multireference single- and double-excitation configuration interaction approach. The potentials are fitted to long-range dispersion coefficients and adjusted with a model interaction in the van der Waals well region. Collisional cross sections for energies between $0.001\mathrm{eV}$ and $10\mathrm{eV}$ and rate coefficients as a function of temperature between $10\mathrm{K}$ and $10000\mathrm{K}$ are obtained for $\mathrm{Na}(3p\to 3s)$ quenching and $\mathrm{Na}(3s\to 3p)$ excitation. The results are relevant to modeling non-LTE effects in Na D absorption lines in extrasolar planets and brown dwarfs.

We study collisions of para-${\mathrm{H}}_2$ with five rare-gas atomic species (He, Ne, Ar, Kr, and Xe) over the range from $1\mathrm{K}\text{to}1\mu \mathrm{K}$ and evaluate the feasibility of sympathetic cooling ${\mathrm{H}}_2$ with ultracold ground state rare-gas atoms co-trapped within a deep optical trap. Collision cross sections over this large temperature range show that all of these species could be used to cool ${\mathrm{H}}_2$ to ultracold temperatures and that argon and helium are the most promising species for future experiments. A simple yet accurate method for calculating the microscopic observables needed in the present analysis is also described, as well as the sensitivity of the calculated cross sections to the potential energy surface used.

The x-ray mass-attenuation coefficient of copper was measured at 108 energies between 5 and $20\mathrm{keV}$ using synchrotron radiation. The measurements are accurate to between 0.09 and 4.5 %, with most measurements being accurate to better than 0.12%. The imaginary component of the form factor of copper was also determined after subtracting the attenuation contribution due to scattering. Measurements were made over an extended range of experimental parameter space, allowing us to correct for several systematic errors present in the data. These results represent the most extensive and accurate dataset of their type for copper in the literature and include the important and widely studied region of the $K$-edge and x-ray absorption fine structure. The results are compared with current theoretical tabulations as well as previous experimental measurements and expose inadequacies in both.

We introduce the exterior complex scaling transformed $B$-spline basis sets into the Floquet theory to study the ionization dynamics of symmetric and asymmetric linear molecular ion $\mathrm{H}_3{}^{2+}$ in dc and intense low-frequency laser fields. For several lowest electronic states, the double-peak structure of the ionization rate as a function of the internuclear distance is observed. We explore the insights of the charge-resonance-enhanced multiphoton ionization of the symmetric and asymmetric $\mathrm{H}_3{}^{2+}$ at some critical internuclear distances $R_c$ by the Floquet theory. A detailed analysis of the behavior of the quasienergy states corresponding to the lowest three electronic states is presented. For the purpose of comparison, the total ionization rate is also calculated by numerically solving the full-dimensional time-dependent Schrödinger equation. Very good agreement is achieved between the results obtained by these two different methods.

The excitation spectra of the radial quadrupole and scissors modes of ultracold Fermi gases in elongated traps are studied across the BCS superfluid-normal phase transition in the framework of a transport theory for quasiparticles. In the limit of zero temperature, this theory reproduces the results of superfluid hydrodynamics, while in the opposite limit, above the critical temperature, it reduces to the collisionless Vlasov equation. In the intermediate temperature range, the excitation spectra have two or three broad peaks, respectively, which are roughly situated at hydrodynamic and collisionless frequencies, and whose strength is shifted from the hydrodynamic to the collisionless modes with increasing temperature. By fitting the time-dependent quadrupole deformation with a damped oscillation of a single frequency, we can understand the “jump” of the frequency of the radial quadrupole mode as a function of interaction strength which has recently been reported by the Innsbruck group.

We propose a potentially practical scheme, in combination with the Bell-state analyzer [X. L. Zhang et al., Phys. Rev. A 73, 014301 (2006)], to generate Bell states for two electron spins confined, respectively, to two distant ${\mathrm{C}}_{60}$ fullerenes. To this end, we consider the endohedral fullerenes staying in single-walled carbon nanotubes and employ auxiliary mobile electrons and selective microwave pulses. The application and the experimental feasibility of our scheme are discussed.

We formulate a general method and provide an iteration scheme for quantitative two-dimensional imaging of pure phase objects using an arbitrary shift-invariant linear optical imaging system. This is a very general method that may be applicable to phase retrieval in shift-invariant linear optical imaging systems, in particular light and electron optics, given a single distorted image obtained from such an imperfect system. The efficacy of the method has been demonstrated using simulated data in the presence of noise.

Detection of quantum light in the presence of dark counts and background radiation noise is considered. The corresponding positive operator-valued measure is obtained and photocounts statistics of quantum light in the presence of noise is studied.