We show that the dependence of high-order harmonic generation (HHG) on the molecular orientation can be understood within a theoretical treatment that does not involve the strong field of the laser. The results for ${\mathrm{H}}_2$ show excellent agreement with time-dependent strong-field calculations for model molecules, and this motivates a prediction for the orientation dependence of HHG from the ${\mathrm{N}}_2$ $3{\sigma }_g$ valence orbital. For both molecules, we find that the polarization of recombination photons is influenced by the molecular orientation. The variations are particularly pronounced for the ${\mathrm{N}}_2$ valence orbital, which can be explained by the presence of atomic $p$ orbitals.

We discuss the differences between one- and two-channel descriptions of fermionic gases with arbitrarily tunable attractive interactions; these two cases correspond to whether molecular bosonic degrees of freedom are omitted or included. We adopt the standard ground state wave function for the fermionic component associated with the BCS to BEC crossover problem: for weak attraction the system is in the BCS state while it crosses over continuously to a Bose-Einstein-condensed (BEC) state as the interaction strength is increased. Our analysis focuses on the BEC and near-BEC limit where the differences between the one- and two-channel descriptions are most notable, and where analytical calculations are most tractable. Among the differences we elucidate are the equations of state at general $T$ below $T_c$ and related particle density profiles. We find a narrowing of the density profile in the two-channel problem relative to the one-channel analog. Importantly, we infer that the ratio between bosonic and fermionic scattering lengths depends on the magnetic detuning and is generally smaller than its one-channel counterpart. Future experiments will be required to determine to what extent this ratio varies with magnetic fields, as predicted here.

We propose to use quantum tomography to characterize the state of a perturbed Bose-Einstein condensate. We assume knowledge of the number of particles in the zero-wave-number mode and of density distributions in space at different times, and we treat the condensate in the Bogoliubov approximation. For states that can be treated with the Gross-Pitaevskii equation, we find that the reconstructed density operator gives excellent predictions of the second moments of the atomic creation and annihilation operators, including the one-body density matrix. Additional inclusion of the momentum distribution at one point of time enables somewhat reliable predictions to be made for the second moments for mixed states, making it possible to distinguish between coherent and thermal perturbations of the condensate. Finally, we find that with the observation of the zero-wave-number mode anomalous second moment $⟨{\widehat{a}}_0{\widehat{a}}_0+{\widehat{a}}_0^{†}{\widehat{a}}_0^{†}⟩$, the reconstructed density operator gives reliable predictions of the second moments of locally amplitude squeezed states.

For quantum systems described by finite matrices, linear and affine maps of matrices are shown to provide equivalent descriptions of evolution of density matrices for a subsystem caused by unitary Hamiltonian evolution in a larger system; an affine map can be replaced by a linear map, and a linear map can be replaced by an affine map. There may be significant advantage in using an affine map. The linear map is generally not completely positive, but the linear part of an equivalent affine map can be chosen to be completely positive and related in the simplest possible way to the unitary Hamiltonian evolution in the larger system.

We explore entanglement loss along renormalization group trajectories as a basic quantum information property underlying their irreversibility. This analysis is carried out for the quantum Ising chain as a transverse magnetic field is changed. We consider the ground-state entanglement between a large block of spins and the rest of the chain. Entanglement loss is seen to follow from a rigid reordering, satisfying the majorization relation, of the eigenvalues of the reduced density matrix for the spin block. More generally, our results indicate that it may be possible to prove the irreversibility along renormalization group trajectories from the properties of the vacuum only, without need to study the whole Hamiltonian.

In this paper, we report on the observation of channel competition following double ionization of NO molecules in femtosecond strong laser fields. We show that slight variations of two parameters of laser light, intensity and polarization, lead to dramatic change in the branching ratio between the metastable and dissociation channels of doubly ionized NO molecules. The difference of electronic configuration between the metastable and dissociation channels indicates that our observation results from the competing processes of sequential and nonsequential double ionization of NO. This study suggests that multielectron collective effects may be utilized in obtaining a desirable final state among several competing channels.

In this paper, we report on an apparently anomalous observation in the dissociation channels of singly ionized nitric oxide (NO) molecules. We observe that the NO molecules, when oriented perpendicular to the laser polarization, appear to preferentially dissociate into the ${\mathrm{N}}^{+}+\mathrm{O}$ channel rather than the $\mathrm{N}+{\mathrm{O}}^{+}$ channel, despite the fact that the latter channel is more energetically favorable. A careful examination of the unique electronic structure of the NO molecule suggests that this observation is most likely due to the influence of the detailed electronic structure of NO on its strong-field ionization dynamics, which leads $\mathrm{N}{\mathrm{O}}^{+}$ created in strong fields to dissociate differently from that in weak fields. This study reinforces our understanding of the fundamental differences between ionization dynamics in strong fields versus weak fields.

We put forward a method to suppress distinguishing information contained in the frequency spectrum of entangled photon pairs generated in spontaneous parametric down-conversion. The distinguishing information is shown to be suppressed by employing achromatic phase-matching techniques to tailor the group velocities of the generated signal and idler photons, and thus tuning their spectral properties. The method can be implemented in materials and frequency bands where conventional solutions do not hold, and it can benefit from the dispersion cancellation inherent to entangled photons featuring frequency correlation or anticorrelation. The generation of polarization Bell states is discussed.

This study proposes quantum secret sharing protocols using product states. The first two protocols adopt the quantum key distribution protocol using product states [Guo et al.Phys. Rev. A 64, 042301 (2001)]. In these two protocols, the sender does not reveal any information about the qutrits until confirming that each receiver has received a qutrit. This study also considers the security and some possible eavesdropping strategies. In the third proposed protocol, three-level Bell states are exploited for qutrit preparation via nonlocality swapping.

In this paper, we consider a simplified error-correcting problem: for a fixed encoding process, to find a cascade connected quantum channel such that the worst fidelity between the input and the output becomes maximum. With the use of the one-to-one parametrization of quantum channels, a procedure finding a suboptimal error-correcting channel based on a semidefinite programming is proposed. The effectiveness of our method is verified by an example of the bit-flip channel decoding.

The problem of dipole transition-matrix element calculation for optical transitions in multiply charged one-electron diatomic quasimolecules with unequal nuclear charges $Z_1$ and $Z_2$ has been stated and solved. The quasimolecule $Z_{1}e{Z}_2$ is a unique example of a two-center system for which the energy terms and dipole transition moments have been calculated precisely in the frame of a nonrelativistic approach. Particular examples for the optical transitions with $Z_1=1.5,2,2.5,3$ and $Z_2=1$ and with the principal quantum number of the united ion $n_u=1,2,3,4$ have been tabulated. The scaling rules make it possible to determine the matrix elements for quasimolecules having nuclear charge ratios such as 2:1, 3:1, 3:2, and 5:2. Zeros at intermediate $R$ and zero limiting values at large $R$ are the highlighted features of the matrix elements. The heteronucleus case generates a large number of asymptotically forbidden transitions corresponding to transitions of an electron from one ion to another.

A spin-dependent density-functional approach for the calculation of highly and multiply excited state of atomic system is proposed based on the localized Hartree-Fock density-functional method and Slater’s diagonal sum rule. In this approach, electron spin orbitals in an electronic configuration are obtained first by solving the Kohn-Sham equation with an exact nonvariational spin-dependent localized Hartree-Fock exchange potential. Then a single-Slater-determinant energy of the electronic configuration is calculated by using these electron spin orbitals. Finally, a multiplet energy of an excited state is evaluated from the single-Slater-determinant energies of the electronic configurations involved in terms of Slater’s diagonal sum rule. This approach has been applied to the calculation of singly, doubly, and especially triply excited Rydberg states of He- and Li-like ions. The total energies obtained from the calculation with an exchange-only ($X$-only) potential are surprisingly close to those of Hartree-Fock method and the total energies from the calculation with exchange-correlation potential are in overall agreement with available theoretical and experimental data. The presented procedure provides a simple and computationally efficient scheme for the accurate calculation of highly and multiply excited Rydberg states of an atomic system within density-functional theory.

Motivated by the recent experimental achievements in the work with Bose-Einstein condensates (BECs), we consider bright matter-wave solitons, in the presence of a parabolic magnetic trap and a spatially periodic optical lattice (OL), in the attractive BEC. We examine pinned states of the soliton and their stability by means of perturbation theory. The analytical predictions are found to be in good agreement with numerical simulations. We then explore possibilities to use a time-modulated OL as a means of stopping and trapping a moving soliton, and of transferring an initially stationary soliton to a prescribed position by a moving OL. We also study the emission of radiation from the soliton moving across the combined magnetic trap and OL. We find that the soliton moves freely (without radiation) across a weak lattice, but suffers strong loss in deeper OLs.

We present a quantum phase-space model of the Bose-Einstein condensate (BEC) in a double-well potential. In a quantum two-mode approximation we examine the eigenvectors and eigenvalues and find that the energy correlation diagram indicates a transition from a delocalized to a fragmented regime. Phase-space information is extracted from the stationary quantum states using the Husimi distribution function. We show that the mean-field phase-space characteristics of a nonrigid physical pendulum arises from the exact quantum states, and that only 4–8 particles per well are needed to reach the semiclassical limit. For a driven double-well BEC, we show that the classical chaotic dynamics is manifest in the dynamics of the quantum states. Phase-space analogy also suggests that a $\pi$ phase-displaced wave packet put on the unstable fixed point on a separatrix bifurcates to create a superposition of two pendulum rotor states—a macroscopic superposition state of BEC. We show that the choice of initial barrier height and ramping, following a $\pi$ phase imprinting on the condensate, can be used to generate controlled entangled number states with tunable extremity and sharpness.

The chirp of the xuv supercontinuum generated by a polarization gating is investigated by comparing three-dimensional nonadiabatic numerical simulations with classical calculations. The origin of the chirp is the dependence of the energy gain by an electron on the return time. The chirp is positive and its value is almost the same as that when a linearly polarized laser is used. Although the $250\text{−}\mathrm{eV}$-wide supercontinuum corresponds to a single attosecond pulse, the shortest duration of the pulse is limited by the chirp. By compensating the positive chirp with the negative group velocity dispersion of a Sn filter, it is predicted that a single $58\text{−}\mathrm{as}$ pulse can be generated.

It is demonstrated that for very thin or very shallow rectangular barriers the transmission amplitude possesses an antibound pole situated very close to threshold energy. The transmission coefficient and the delay time at very low incidence energies may be expressed analytically in terms of the antibound pole contribution, which accounts, respectively, for the enhancement of the transmittivity to almost a unity value and for the large delay time exhibited by these systems. The large delay time caused by the antibound pole represents a type of “trapping” mechanism different from that of resonant tunneling.

Controlling the dynamics of a dipolar coupled spin system is critical to the development of solid-state spin-based quantum information processors. Such control remains challenging, as every spin is coupled to a large number of surrounding spins. Here we demonstrate that in an ensemble of spin pairs it is possible to decouple the weaker interactions (weak coupling ${\omega }_D^w$) between different pairs and extend the coherence lifetimes within the two-spin system from $19\mu \mathrm{s}\text{to}11.1\mathrm{ms}$, a factor of 580. This is achieved without decoupling the stronger interaction (strong coupling ${\omega }_D^S$) between the two spins within a pair. An amplitude modulated rf field is applied on resonance with the Larmor frequency of the spins, with amplitude ${\omega }_1$, and frequency of the modulation matched to the strong coupling. The spin pairs appear isolated from each other in the regime where the rf power satisfies ${\omega }_D^w⪡{\omega }_1⪡{\omega }_D^S$.

We construct an explicit Wigner function for the $N$-mode squeezed state. Based on a previous observation that the Wigner function describes correlations in the joint measurement of the phase-space displaced parity operator, we investigate the nonlocality of the multipartite entangled state by the violation of the Żukowski-Brukner $N$-qubit Bell inequality. We find that quantum predictions for such a squeezed state violate these inequalities by an amount that grows with the number $N$.

The fine structure of high-angular-momentum $n=9$ and 10 Rydberg states of barium has been measured precisely, using the resonant excitation Stark ionization spectroscopy method. Optical transitions corresponding to $(n,n^{\prime })=(10,30)$, (9,17), and (9,20) were induced with a Doppler-tuned ${\mathrm{CO}}_2$ laser, determining the fine-structure energies corresponding to all $n=9$ and 10 levels with $L⩾6$. The pattern of these fine-structure energies conforms closely with an effective potential model, by comparison with which the dipole and quadrupole polarizabilities of ${\mathrm{Ba}}^{+}$ can be determined. Combining our data with earlier measurements made it possible to deduce, in addition, the portion of ${\alpha }_2$ due to the lowest excited $D$ state of ${\mathrm{Ba}}^{+}$. Our best estimates of these three properties are ${\alpha }_1=124.30\left(16\right)a_0^3$, ${\alpha }_2=2462\left(361\right)a_0^5$, and ${\alpha }_2^0=1828\left(88\right)a_0^5$.

The experimental $\mathrm{N}\left(1s\right)$ near-edge x-ray-absorption fine-structure spectrum of the benzonitrile molecule in the gas phase shows well separated double peaks with different vibrational profiles. Hybrid density-functional theory calculations reveal that such a separation is a result of the conjugation effect on the nitrogen $2p$ orbitals and the double spectral peaks can be assigned as the $\mathrm{N}\left(1s\right)-\pi *$ out-of-plane and in-plane resonances. The vibrational profiles have been analyzed using a combined transition state theory and linear coupling model. Each profile consists of two different vibrational progressions corresponding to stretching modes and a broad continuum of bending excited states. The use of transition state theory allows identifying the dynamics of the N $1s$ core excitation. It is found that upon core excitations the $\mathrm{C}\mathrm{N}$ bond of the benzonitrile molecule can go from initial linear to final bent structures through different paths. The calculated spectrum is in excellent agreement with experiment.