Given a pure state transformation $\psi \mapsto \varphi$ restricted to entanglement-assisted local operations with classical communication, we determine a lower bound for the dimension of a catalyst allowing that transformation. Our bound is stated in terms of the generalized concurrence monotones (the usual concurrence of two qubits is one such monotone). We further provide tools for deriving further conditions upon catalysts of pure state transformations.

It is shown that the principal results of a recent work by Alvarez-Thon et al. [Phys. Rev. A 77, 034502 (2008)] are in conflict with earlier work of the present authors [JETP Lett. 73, 35 (2001)] and also with a well known result concerning magnetic properties, NMR, and Jahn-Teller effect in the systems possessing even number of $d$ electrons. This can be attributed to the fact that Alvarez-Thon et al. did not account for the influence of ${}^{19}\text{F}$ and ${}^{195}\text{P}\text{t}$ nuclear magnetic moments and vibronic interactions on the wave function of ${\text{PtF}}_6$ molecules.

It is shown that the comments of Gabuda and Kozlova [Phys. Rev. A 79, 056501 (2009)] are in conflict with their earlier work [S. P. Gabuda et al., JETP Lett. 73, 35 (2001)], where they stated that there is no indication of the structural distortions in ${\text{PtF}}_6$. In their original publication they also stated that qualitative electrostatic considerations suggest that the electronic $5d^4$ configuration remains spin paired as the ground state in the octahedral field.

We study the effect of decoherence on the sub-Planck scale structures of the vibrational wave packet of a molecule. The time evolution of these wave packets is investigated under the influence of a photonic or phononic environment. We determine the master equation describing the reduced dynamics of the wave packet and analyze the sensitivity of the sub-Planck structures against decoherence in the case of a hydrogen iodide (HI) molecule.

With the quantum state filtering as a known example, it has been shown that the unambiguous discrimination between subsets of nonorthogonal quantum states is possible with a certain possibility of success. In present work, besides reconsidering the known case of quantum state filtering, we also ask what happens if parts of the states are shared by both the subsets or if there are more than two subsets. The procedure, which is designed to find the optimal way for quantum set discrimination, contains two steps. For each case, we at first construct a one-photon interferometer (OPI) to realize the unambiguous discrimination in an enlarged Hilbert space according to the Neumark’s theorem. The awards from the OPI are double: an optical experiment and the operators in terms of positive operator-valued measures. Then, with the operators from its corresponding OPI and the given a priori probability for each state, we are able to find out the optimal operators which can discriminate the subsets in an optimal way. It is shown that the OPIs, which have been discussed in present work, can be constructed by taking the quantum state filtering as their elementary process. This fact indicates that the problem of quantum set discrimination can be reduced to the known problem of quantum state filtering.

The transmission of 18-keV ${\text{O}}^{-}$ ions through ${\text{Al}}_2{\text{O}}_3$ nanocapillaries with 50 nm in diameter and $12\mu \text{m}$ in length is studied in this work. By measuring angular distribution of transmitted particles when capillaries were tilted with respect to incident ion beam, two peaks were observed. It is distinguished that one of them is composed by direct transmitted ions and another one is composed by scattered ions. A phenomenon referred to as guiding effect, as found for highly charged ions and low-energy electrons, was observed. When negative ions (18-keV ${\text{O}}^{-}$) are transmitted through nanocapillaries, most of them were ionized to neutral atoms and even positive ions. The intensity of transmitted particles (${\text{O}}^{-}$, ${\text{O}}^0$, and ${\text{O}}^{+}$) decreased when the tilt angle increased. In transmitted particles, the fraction of ${\text{O}}^{-}$ declined but that of ${\text{O}}^0$ and ${\text{O}}^{+}$ ions grew when the tilt angle grew. Both elastic collision and electrostatic scattering were found in scattered ions.

We investigate theoretically the behavior of a one-dimensional interacting Bose-Fermi mixture with equal masses and equal repulsive interactions between atoms at finite temperature in the scheme of thermodynamic Bethe ansatz. Combining the Yang-Yang thermodynamic formalism with local-density approximation in a harmonic trap, we calculate the density distribution of bosons and fermions numerically by treating the radially and axially excited states as discrete and continuous ones, respectively. Our result from exactly solvable solutions may be used as a touchstone for one-dimensional interacting Bose-Fermi mixture for experimental data fitting where mean-field theoretical approaches fail.

We use quantum Monte Carlo simulations to obtain zero-temperature state diagrams for strongly correlated lattice bosons in one and two dimensions under the influence of a harmonic confining potential. Since harmonic traps generate a coexistence of superfluid and Mott insulating domains, we use local quantities such as the quantum fluctuations of the density and a local compressibility to identify the phases present in the inhomogeneous density profiles. We emphasize the use of the “characteristic density” to produce a state diagram that is relevant to experimental optical lattice systems, regardless of the number of bosons or trap curvature and of the validity of the local-density approximation. We show that the critical value of $U/t$ at which Mott insulating domains appear in the trap depends on the filling in the system, and it is in general greater than the value in the homogeneous system. Recent experimental results by Spielman et al. [Phys. Rev. Lett. 100, 120402 (2008)] are analyzed in the context of our two-dimensional state diagram, and shown to exhibit a value for the critical point in good agreement with simulations. We also study the effects of finite, but low $\left(T\le t/2\right)$, temperatures. We find that in two dimensions they have little influence on our zero-temperature results, while their effect is more pronounced in one dimension.

We propose an efficient method for spatial filtering of light beams by propagating them through two-dimensional (also three dimensional) chirped photonic crystals, i.e., through the photonic structures with fixed transverse lattice period and with the longitudinal lattice period varying along the direction of the beam propagation. We prove the proposed idea by numerically solving the paraxial propagation equation in refraction-index–modulated media and we evaluate the efficiency of the process by harmonic-expansion analysis. The technique can be also applied for filtering (for cleaning) of the packages of atomic waves (Bose condensates), also to improve the directionality of acoustic and mechanical waves.

A rigorous solution (generalized Lorenz-Mie theory) and an approximate solution (geometrical optics) are developed for the optical stress distribution on the surface of a homogeneous sphere. Demonstration calculations are made for plane-wave and Gaussian-beam illuminations. The influence of diffracted waves, surface waves, interference effects, caustic points, beam width, and refractive index on the stress is analyzed. The Debye series is used to evaluate the validity of geometrical optics and provides a quantitative analysis of the contribution of rays of different orders.

We demonstrate that a Doppler-broadened two-level medium can be made transparent to a laser pulse by an appropriate adiabatic variation in the laser field amplitude and its nominal detuning. This technique of adiabatic self-induced transparency (ASIT) is compared with the well-known self-induced transparency phenomenon, showing that the adiabatic method is much more robust against variations in the system parameters. We also discuss a possible experimental implementation of ASIT using ${}^{87}\text{R}\text{b}$ atoms.

An electromagnetic realization of Landau-Zener (LZ) tunneling is experimentally demonstrated in femtosecond-laser written waveguide couplers with a cubically bent axis. Quantitative measurements of light evolution inside the coupler, based on fluorescence imaging, enable to trace the detailed dynamics of the LZ process. The experimental results are in good agreement with the theoretical LZ model for linear crossing of energy levels with constant coupling of finite duration.

We present a theoretical method for the efficient analysis of quantum nonlinear dynamics of correlated photons. Since correlated photons can be regarded as a superposition of uncorrelated photons, semiclassical analysis can be applied to this problem. The proposed method is demonstrated for a V-type three-level atom as a nonlinear optical system.

We show that an appropriate choice of the potential parameters in one-dimensional quantum systems allows for unity transmission of the tunneling particle at all incident tunneling energies, except at controllable exceedingly small incident energies. The corresponding dwell time and the transmission amplitude are indistinguishable from those of a free particle in the unity-transmission regime. This implies the possibility of designing quantum systems that are invisible to tunneling by a passing wave packet.

We propose a quantum algorithm for the purification of a generic mixed state $\rho$ of a $n$-qudit system by using an ancillary $n$-qudit system. The algorithm is optimal in that (i) the number of ancillary qudits cannot be reduced, (ii) the number of parameters which determine the purification state $|\Psi ⟩$ exactly equals the number of degrees of freedom of $\rho$, and (iii) $|\Psi ⟩$ is easily determined from the density matrix $\rho$. Moreover, we introduce a quantum circuit in which the quantum gates are unitary transformations acting on a $2n$-qudit system. These transformations are determined by parameters that can be tuned to generate, once the ancillary qudits are disregarded, any given mixed $n$-qudit state.

The multiconfiguration Dirac-Hartree-Fock model has been employed to calculate the expectation values for the hyperfine splittings of the $5d^{9}6s^2{{}^{2}D}_{3/2}$ and $5d^{9}6s^2{{}^{2}D}_{5/2}$ levels of atomic gold. One-, two-, and three-body electron correlation effects involving all 79 electrons have been included in a systematic manner. The approximation employed in this study is equivalent to a complete-active-space approach. Calculated electric field gradients, together with experimental values of the electric quadrupole hyperfine-structure constants, allow us to extract a nuclear electric quadrupole moment $Q\left({}^{197}\text{A}\text{u}\right)=521.5\left(5.0\right)\text{mb}$.

Quasiresonance is a general effect that may arise from the coupling between approximately resonant degrees of freedom in a system perturbed by some transient interaction. In a process induced by a slowly switching on and off of the coupling interaction, quasiresonance is characterized by the existence of significant ranges of initial states in the perturbed system over which some very specific and efficient transfer of energy between the approximately resonant degrees of freedom occurs. This work presents a classical and quantum analysis of quasiresonant processes in grazing incident angle atom-surface collisions. The momentum transfer between the normal components to an index direction is investigated. For fast atoms with grazing angle of incidence there is an interval of azimuthal angles around the index directions, the quasiresonance region, in which the energy transfer can be very efficient. This effect is reflected in quantum diffraction patterns with large nonspecular peaks, associated with the parallel to the surface and normal to the index direction momentum component. We demonstrate the essentially classical underlying mechanism for the persistence of a pattern of diffraction peak intensities for incidence close to an index direction. The analysis also shows that the size of the quasiresonance region is approximately equal to the spectral width of the diffraction pattern.

The Ginzburg-Landau theory of a trapped Fermi gas with a BEC-BCS crossover is derived by the path-integral method. In addition to the standard Ginzburg-Landau equation, a second equation describing the total atom density is obtained. These two coupled equations are necessary to describe both homogeneous and inhomogeneous systems. The Ginzburg-Landau theory is valid near the transition temperature $T_c$ on both sides of the crossover. In the weakly interacting BEC region, it is also accurate at zero temperature where the Ginzburg-Landau equation can be mapped onto the Gross-Pitaevskii (GP) equation. The applicability of GP equation at finite temperature is discussed. On the BEC side, the fluctuation of the order parameter is studied and the renormalization to the molecule coupling constant is obtained.

We discover an inherent mechanism for entanglement swap associated with sequential superradiance from an atomic Bose-Einstein condensate. Based on careful examinations with both analytical and numerical approaches, we conclude that as a result of the swap mechanism, Einstein-Podolsky-Rosen-type quantum correlations can be detected among the scattered light pulses.

Spatial orientation of molecules is a pervasive issue in chemical physics and, by breaking inversion symmetry, has major consequences in nonlinear optics. In this paper, we propose and analyze an approach to molecular orientation. This extracts from an ensemble of aligned diatomic molecules (equally $AB$ and $BA$, relative to the $\mathcal{E}$ vector) a subensemble that is oriented (mostly $AB$ or $BA$). Subjecting an aligned molecule to a tailored infrared (ir) laser pulse creates a pair of coherent wave packets that correlate vibrational phase with the $AB$ or $BA$ orientation. Subsequent, suitably phased ultraviolet (uv) or visible pulses dissociate one of these vibrational wave packets, thereby “weeding out” either $AB$ or $BA$ but leaving intact the other orientation. Molecular orientation has significant implications for coherent Raman spectroscopy. In the absence of orientation, coherence between vibrational levels is generated by a pair of laser pulses off which a probe pulse is scattered to produce a signal. Orientation allows direct one-photon ir excitation to achieve (in principle) maximal Raman coherence.