We perform fully quantum mechanical calculations in the binary approximation of the emission and absorption profiles of the sodium $3s\text{−}3p$ and potassium $4s\text{−}4p$ resonance lines under the influence of a helium perturbing gas. We use carefully constructed potential energy surfaces and transition dipole moments to compute the emission and absorption coefficients at temperatures from $158\text{to}3000\mathrm{K}$. Contributions from quasibound states are included. The resulting red and blue wing profiles agree well with previous theoretical calculations and with experimental measurements.

An exact analytical classical solution for the electronic terms of circular Rydberg states (CRS) in the presence of a magnetic field $B$ is obtained for two-Coulomb-center systems. The classical electronic terms are shown to be significantly affected by the magnetic field. In particular, a sufficiently strong magnetic field is shown to cause the appearance of CRS above the ionization threshold. These CRS are the classical molecular counterparts of the quantal atomic quasi-Landau levels (resonances). Study of the stability of the nuclear motion in this system reveals that the system in CRS is, in the absence of the magnetic field, not really a molecule, but only a quasimolecule with antibonding molecular orbitals. We also find that the magnetic field creates a deep minimum in one of the branches of the effective potential of the relative motion of the nuclei, and thereby stabilizes the nuclear motion. We have therefore shown that a magnetic field can transform the quasimolecule into a real, classically described molecule where one of the molecular orbitals becomes bonding. This result reveals a phenomenon—the magnetically controlled stabilization of the quasimolecules in CRS—which is appropriate for future experimental studies.

Molecular quantum electrodynamics is employed to calculate a generalized formula for the energy shift between a pair of molecules that have electric polarizability of arbitrary multipole order and are in the presence of an intense electromagnetic field. In contrast to a previous calculation of the dipole-dipole contribution, which required fourth-order time-dependent perturbation theory for its evaluation, the present approach involves calculating the interaction between the multipole moments induced at each center by the incident beam and the resonant multipole-multipole coupling tensor together with the average value of the spatial correlation function of the displacement field for an $N$-photon state. The theory developed applies to the situation where the molecular pair is held fixed relative to the direction of propagation of the radiation field or is allowed to be completely randomly oriented. Explicit results are obtained for dipole-quadrupole and quadrupole-quadrupole polarizable molecules. For oriented systems the energy shift for linear and circular polarizations is examined for incident radiation propagating in directions parallel and perpendicular to the intermolecular join, and the asymptotic behavior is obtained at the limits of short and large separation distance. After performing a pair orientation average, the energy shift in the near zone is found to exhibit an $R^{-1}$ power-law behavior with separation distance, while the far zone has a modulated $R^{-2}$ dependence in all of the cases considered. None of the energy shifts obtained display discriminatory characteristics, with respect to either the handedness of the incident beam or the individual species.

We investigate the equilibrium properties of a hybrid atomic and molecular Bose-Einstein condensate in the context of the Feshbach-resonant quantum many-body model. We analyze fully the mean-field solutions of the system for a general choice of interaction parameters. The quantum fluctuations of the system are obtained from the Bogoliubov theory that characterizes the quasiparticle excitations of the system. In particular we find that the excitation energies have two branches: a Goldstone mode and a second one containing a gap. Both gap energy and phonon velocities are functions of the composition, and our analysis indicates that for a large range of parameter space the system is unstable near a Feshbach resonance.

The behavior of high-$n$ Rydberg atoms subject to a periodic sequence of short half-cycle pulses (HCPs) that alternate in sign is reexamined. Each HCP delivers an impulsive momentum transfer or “kick” to the electron and the net average field it experiences is zero. The data show that the excited electron energy distribution initially moves toward the continuum, i.e., toward states of higher $n$, but then becomes transiently trapped near the edge of the continuum leading to sizable overall survival probabilities. The physical mechanisms responsible for this are discussed with the aid of classical trajectory Monte Carlo simulations.

Coupling the output of a source quantum system into a target quantum system is easily treated by cascaded systems theory if the intervening quantum channel is dispersionless. However, dispersion may be important in some transfer protocols, especially in solid-state systems. In this paper we show how to generalize cascaded systems theory to treat such dispersion, provided it is not too strong. We show that the technique also works for fermionic systems with a low flux, and can be extended to treat fermionic systems with large flux. To test our theory, we calculate the effect of dispersion on the fidelity of a simple protocol of quantum state transfer. We find good agreement with an approximate analytical theory that had been previously developed for this example.

Four-qubit bound entangled Smolin states are generalized with help of the Hilbert-Schmidt formalism to any even number of qubits. They are shown to maximally violate simple correlation Bell inequalities and, as such, to reduce communication complexity, although they do not admit quantum security. They are also shown to serve for remote quantum information concentration, as in the case of the original four-qubit states. It is proven that the latter effect allows us to unlock some entanglement measures and classical correlations. Also the possibility of quantum secret sharing by the considered state is pointed out.

We comment on the recent suggestion to use a family of local uncertainty relations as a standard way of quantifying entanglement in two-qubit systems. Some statements made on the applicability of the proposed “measures” are overly optimistic. We exemplify how these specific measures fall short, and present a minor modification of the general theory which uses the same experimentally gathered information, but in a slightly different, better way.

The total cross sections of electron-impact single-$K$-shell ionization of 14 atomic targets ranging from H to U $(1⩽Z⩽92)$ are calculated using a modified version of the BELI formula [Bell et al., J. Phys. Chem. Ref. Data 12, 891 (1983)] by incorporating both ionic and relativistic corrections in it. The proposed modified Bell model with a single set of parameters is found to provide an excellent description of the experimental data in the reduced energy range $1⩽E∕I_K⩽{10}^6$ ($E$ and $I_K$ are, respectively, the incident energy and ionization potential) with a performance level at least as good as any of the existing methods and models.

We describe quantum controllability under the influences of the quantum decoherence induced by the quantum control itself. It is shown that, when the controller is considered as a quantum system, it will entangle with its controlled system and then cause quantum decoherence in the controlled system. In competition with this induced decoherence, the controllability will be limited by some uncertainty relation in a well-armed quantum control process. In association with the phase uncertainty and the standard quantum limit, a general model is studied to demonstrate the possibility of realizing a decoherence-free quantum control with a finite energy within a finite time. It is also shown that if the operations of quantum control are to be determined by the initial state of the controller, then due to the decoherence which results from the quantum control itself, there exists a low bound for quantum controllability.

We propose a scheme for squeezing vibrational wave packets in the ground (or excited) states of diatomic molecules that uses pulse sequences of strong nonresonant short pulses. The physical mechanism of the scheme is a two step process involving adiabatic and diabatic transformations of the wave packet. The first step is the adiabatic stretching of the wave packet on a light-induced potential, and the second step is dynamic squeezing by free evolution after ultrashort (i.e., diabatic) population transfer. We show that this sequence of transformations can be performed very efficiently with a simple two pulse sequence with slow switch on and fast switch off pulse shapes, and we analyze the required physical resources that are needed. We test the scheme on a model of harmonic oscillators and on the ${\mathrm{Rb}}_2$ dimer. Finally, different possible generalizations are proposed.

We investigate collective spin excitations in two-component fermion condensates with special consideration of unequal populations of the two components. The frequencies of monopole and dipole modes are calculated using Thomas-Fermi theory and the scaling approximation. As the fermion-fermion coupling is varied, the system shows various phases of the spin configuration. We demonstrate that spin oscillations have more sensitivity to the spin phase structures than the density oscillations.

We study the rotational properties of an attractively interacting Bose gas in an anharmonic potential. Low-energy excitations for the two possible rotational ground-state configurations (vortex and the center-of-mass rotating state) are analyzed. The vortex excitation spectrum is all positive for weak couplings, but as the interactions become stronger, the energy of the lowest mode decreases rapidly to a negative value. The broken rotational symmetry involved in the center-of-mass rotating state induces the appearance of an extra zero-energy mode in the Bogoliubov spectrum. The excitations of the center-of-mass rotational state also demonstrate the coupling between the center of mass and relative motions.

It is shown that a Bose-Fermi mixture of a degenerate gas of spin-polarized fermions, whose number significantly exceeds the number of bosons, embedded in a strongly anisotropic trap, is described by the one-dimensional coupled nonlinear Schrödinger equation for the boson component and the wave equation with external source for the fermion component. Depending on the type of boson-fermion interaction, the system may display modulational instability and the existence of solitons in the fermion and boson components, respectively. Such solitons represent either a local decrease (increase) of the density of both the components or a decrease of the density in one component and an increase of the density in the other component. It is shown that the type of the effective interactions can be easily managed by varying the trap geometry or by means of Feshbach resonance.

We study properties of excited states of an elongated Fermi superfluid along the Bose-Einstein-condensate–BCS crossover including the unitarity limit. Analytic expressions for the sound velocity in an inhomogeneous as well as homogeneous Fermi superfluid along the crossover are obtained on the basis of the hydrodynamic theory. The complete excitation spectrum of axial quasiparticles with various discrete radial nodes is presented. We discuss the feasibility of measuring the sound velocity and the multibranch Bogoliubov spectrum experimentally.

We consider a rapidly rotating Bose-condensed gas in a harmonic-plus-quartic trap. At sufficiently high rotation rates, the condensate acquires an annular geometry with the superposition of a vortex lattice. With increasing rotation rate, the lattice evolves into a single ring of vortices. Of interest is the transition from this state to the giant vortex state in which the circulation is carried by only a central vortex. By analyzing the Gross-Pitaevskii energy functional variationally, we have been able to map out the phase boundary between these two states as a function of the rotation rate and the various trapped gas parameters. For strong interactions, the transition is first order. Our variational results are in good qualitative agreement with those obtained by means of a direct numerical solution of the Gross-Pitaevskii equation.

We present a theoretical model for formation of molecules in an optical lattice well where a resonant coupling of atomic and molecular states is provided by small oscillations of a magnetic field in the vicinity of a Feshbach resonance. As opposed to an adiabatic sweep over the full resonance, this provides a coherent coupling with a frequency that can be tuned to meet resonance conditions in the system. The effective Rabi frequencies for this coupling are calculated and simulations show perfect Rabi oscillations. Robust production of molecules with an adiabatic sweep of the modulation frequency is demonstrated. For very large oscillation amplitudes, the Rabi oscillations are distorted but still effective and fast association is possible.

We identify the specific polarizations for the two components of a bichromatic field, which produce pure superposition states of atoms with a specific magnetic quantum number $m$ via coherent population trapping. The superposition states are composed of two Zeeman substates magnetic quantum number $m$ of the two ground-state hyperfine levels with arbitrary angular momenta $F_1$ and $F_2$. It is established that in the general case of $m\ne 0$, optical fields with elliptical polarizations are needed for the preparation of such a pure state. It is shown analitically that a unique advantage of the $D1$ line (over the $D2$ line) of alkali-metal atoms is the possibility that pure $m\text{−}m$ states may be generated even if the excited-state hyperfine levels are not spectrally resolved.

We formulate continuous time quantum walks (CTQW) in a discrete quantum mechanical phase space. We define and calculate the Wigner function (WF) and its marginal distributions for CTQWs on circles of arbitrary length $N$. The WF of the CTQW shows characteristic features in phase space. Revivals of the probability distributions found for continuous and for discrete quantum carpets do manifest themselves as characteristic patterns in phase space.

An experimental setup for testing quantum nonlocality of $N$ qubits is proposed. This method is a generalization of the optical setup proposed by Banaszek and Wódkiewicz [Phys. Rev. Lett. 82, 2009 (1999)]. The quantum nonlocality of $N$ qubits can be obtained through its violation of $N$-qubit Bell inequalities. The correlation function measured in the experiment is described by the Wigner function. The effect of inefficient detector is also considered.