For systems of two and three spins $1∕2$ it is known that the second moment of the Husimi function can be related to entanglement properties of the corresponding states. Here, we generalize this relation to an arbitrary number of spins in a pure state. It is shown that the second moment of the Husimi function can be expressed in terms of the lengths of the concurrence vectors for all possible partitions of the $N$-spin system in two subsystems. This relation implies that the phase space distribution of an entangled state is less localized than that of a nonentangled state. As an example, the second moment of the Husimi function is analyzed for an Ising chain subject to a magnetic field perpendicular to the chain axis.

We investigate the use of continuously applied external fields to maximize the fidelity of quantum logic operations performed on a decohering qubit. Assuming a known error operator and an environment represented by a scalar boson field at a finite temperature, we show how decoherence during logical operations can be efficiently reduced by applying a superposition of two external vector fields: one rotating orthogonally to the direction of the other, which remains static. The required field directions, frequency of rotation, and amplitudes to decouple noise dynamically are determined by the coupling constants and the desired logical operation. We illustrate these findings numerically for a Hadamard quantum gate and an environment with ohmic spectral density.

It is well known that variational optimization of the energy using approximate density functionals can give results below the true ground-state energy. This can be attributed to the fact that many approximate density functionals are not $N$-representable. This paper presents a general method for deriving $N$-representability conditions in density-functional theory and presents specific results for the kinetic energy, the electron-electron interaction energy, the Hohenberg-Kohn functional, and the exchange-correlation energy functional. The method can be extended to energy densities, and specific results are presented for two different choices of the kinetic-energy density. Max-min variational principles for minimizing the energy subject to $N$-representability constraints are presented. Some constraints on exchange-correlation density functionals are among our secondary findings. In particular, we construct an exact meta-generalized-gradient-approximation (meta-GGA) functional using a Legendre transform and use this expression to show that (a) meta-GGAs should be convex functionals of the kinetic-energy density and (b) the sum of the Coulomb energy and the meta-GGA exchange-correlation energy should be a convex functional of the electron density.

We report an experimental observation of simultaneous rotational and vibrational collinear Raman generation in low pressure cooled deuterium gas, with only two narrow-band laser pulses applied at the input of the molecular cell. Only the fundamental vibrational transition $Q_1$ (0) is driven strongly in this experiment. However, in addition to efficient vibrational Raman generation we observe generation of a large number of rotational sidebands (more than 100) corresponding to $S_0$ (0) transition. We notice that fine-tuning of the frequency difference of the driving fields near the vibrational Raman resonance changes dramatically the aspects of the generated spectrum and the efficiency of rotational generation: from complete suppression of a self-starting stimulated rotational Raman generation to a strong enhancement of two orders of magnitude. We conduct a numerical analysis that allows us to attribute this behavior to quantum interference among the probability amplitudes of the three molecular states involved.

Calculations of the resonance part of the cross section of elastic electron scattering with $\mathrm{DI}$ molecule at energies below the dissociative attachment threshold based on the use of the nonlocal resonance model of Horáček, Nakamura and Domcke [Z. Phys. D 42, 181 (1997)] reveal a series of sharp peaks of giant amplitudes of several thousands of ${\mathrm{\AA }}^2$. These structures are interpreted as demonstrations of outer well resonances in the negative molecular ion state potential and should be observable experimentally provided the energy resolution of the beam is in the range of few meV.

Coherent responses of resonance atom layer to short optical pulse excitation are numerically considered. The inhomogeneous broadening of one-photon transition, the local field effect, and the substrate dispersion are involved into analysis. For a certain intensity of incident pulses a strong coherent interaction in the form of sharp spikes of superradiation is observed in transmitted radiation. The Lorentz field correction and the substrate dispersion weaken the effect, providing additional spectral shifts. Specific features of photon echo in the form of multiple responses to a double or triple pulse excitation is discussed.

The Hamiltonian for a small number $N⩽11$ of bosons in a rapidly rotating harmonic trap, interacting via a short range (contact potential) or a long range (Coulomb) interaction, is studied via an exact diagonalization in the lowest Landau level. Our analysis shows that, for both low and high fractional fillings, the bosons localize and form rotating boson molecules (RBMs) consisting of concentric polygonal rings. Focusing on systems with the number of trapped atoms sufficiently large to form multiring bosonic molecules, we find that, as a function of the rotational frequency and regardless of the type of repulsive interaction, the ground-state angular momenta grow in specific steps that coincide with the number of localized bosons on each concentric ring. Comparison of the conditional probability distributions (CPDs) for both interactions suggests that the degree of crystalline correlations appears to depend more on the fractional filling $\nu$ than on the range of the interaction. The RBMs behave as nonrigid rotors, i.e., the concentric rings rotate independently of each other. At filling fractions $\nu <1∕2$, we observe well developed crystallinity in the CPDs (two-point correlation functions). For larger filling fractions $\nu >1∕2$, observation of similar molecular patterns requires consideration of even higher-order correlation functions.

A direct configuration-interaction (CI) approach for studies of Bose-Einstein condensates has been developed and implemented. The reference state is obtained by solving the Hartree-Fock equation in a nonorthogonal Gaussian basis. The CI problem is solved by diagonalizing the Hamiltonian constructed in a many-body basis generated using the orthogonal canonical orbital basis obtained in a Hartree-Fock calculation. For Hamiltonian matrices, which are too large for full diagonalization, a direct iterative diagonalization scheme is employed for obtaining the lowest-lying eigenstates. The computational methods were tested by applications to Bose-Einstein condensates using various isotropic and anisotropic trap geometries.

The probe absorption-dispersion spectrum of a double V-type four-level atom in a double-band photonic crystal is investigated. In the model used, the double V-type transitions are, respectively, coupled by the free vacuum modes and the photonic band gap modes, leading to the two possible types of quantum interference. Three types of zero absorption (transparency) appear in this model. In the first type, there exist two zeroes at the band edge frequencies in the case of isotropic photonic band gap. In the second type, a zero emerges at the middle frequency of two upper levels in the case that the quantum interference takes place in both V-type transitions. Finally, in the third type, a zero occurs at or around the middle frequency of two upper levels in the case that the quantum interference takes place only in the V-type transitions coupled to the free vacuum modes. Ultimately, the probe absorption-dispersion spectrum in the case of the single-band photonic band gap reservoirs compared to those of the double-band photonic band gap reservoirs. The results show that the dispersion property of the system depends on the two types of the quantum interference and the density of states of the photonic band gap reservoir.

We consider the effect of classical noise applied to the geometric quantum phase of a spin $1∕2$ in a revolving magnetic field. The Berry phase shows some sensitivity to the noise because the Bloch vector cannot return to its original direction, and the variance caused by noise is proportional to the evolution time.

The quadrupole channel of two-photon double ionization of He exhibits two distinctly different modes of correlated motion of the photoelectron pair. The kinematics of the mode associated with the center-of-mass motion favors large total momenta maximized at parallel emission where the interelectron repulsion is strong. In contrast, the mode associated with the relative motion favors large relative momenta maximized at antiparallel emission where the interelectron repulsion is relatively weak. This difference in the interelectron repulsion allows for much wider angular correlation width in the relative motion mode as compared to the center-of-mass mode.

We give an explicit procedure based on entangled input states for estimating a $\mathrm{SU}\left(d\right)$ operation $U$ with rate of convergence $1∕N^2$ when sending $N$ particles through the device. We prove that this rate is optimal. We also evaluate the constant $C$ such that the asymptotic risk is $C∕N^2$. However, other strategies might yield a better constant $C$.

We propose a general formalism for analytical description of multiatomic ensembles interacting with a single-mode quantized cavity field under the assumption that most atoms remain unexcited on average. By combining the obtained formalism with the nilpotent technique for the description of multipartite entanglement we are able to overview in a unified fashion different probabilistic control scenarios of entanglement among atoms or examine atomic ensembles. We then apply the proposed control schemes to the creation of multiatom states useful for quantum information.

The presence of an electric field converts the intermediate autoionizing Rydberg $n\ell$ states, through which dielectronic recombination passes, into $nk$ Stark states, which have autoionization and capture rates in excess of the radiative decay rates and contribute to dielectronic recombination. In zero field the high $\ell$ states do not contribute to dielectronic recombination, but the conversion to Stark states makes it possible and raises the dielectronic recombination rate. However, an electric field can also result in coupling to loss channels which locally reduce the dielectronic recombination rate. We have observed holes in the spectrum of dielectronic recombination from the Ba $6p_{3∕2}8g$ continuum of finite bandwidth via the intermediate $6p_{1∕2}ng$ states. The holes appear when an electric field is applied, and we attribute them to interaction with rapidly decaying $6p_{3∕2}8\ell$ states, which diverts flux from dielectronic recombination.

A quantum master equation model for the interaction between a two-level system and whispering-gallery modes (WGMs) of a microdisk cavity is presented, with specific attention paid to current experiments involving a semiconductor quantum dot (QD) embedded in a fiber-coupled ${\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ microdisk cavity. In standard single mode cavity QED, three important rates characterize the system: the QD-cavity coupling rate $g$, the cavity decay rate $\kappa$, and the QD dephasing rate ${\gamma }_{\perp }$. A more accurate model of the microdisk cavity includes two additional features. The first is a second cavity mode that can couple to the QD, which for an ideal microdisk corresponds to a traveling wave WGM propagating counter to the first WGM. The second feature is a coupling between these two traveling wave WGMs, at a rate $\beta$, due to backscattering caused by surface roughness that is present in fabricated devices. We consider the transmitted and reflected signals from the cavity for different parameter regimes of $\{g,\beta ,\kappa ,{\gamma }_{\perp }\}$. A result of this analysis is that even in the presence of negligible roughness-induced backscattering, a strongly coupled QD mediates coupling between the traveling wave WGMs, resulting in an enhanced effective coherent coupling rate $g=\sqrt{2}{g}_0$ corresponding to that of a standing wave WGM with an electric field maximum at the position of the QD. In addition, analysis of the second-order correlation function of the reflected signal from the cavity indicates that regions of strong photon antibunching or bunching may be present depending upon the strength of coupling of the QD to each of the cavity modes. Such intensity correlation information will likely be valuable in interpreting experimental measurements of a strongly coupled QD to a bimodal WGM cavity.

The statistical properties of light emitted by a three-level laser are theoretically investigated. In the model considered the three-level medium is coherently excited by another laser having arbitrary photon statistics. It is shown that under certain conditions the photon statistics of the three-level laser is determined by that of the exciting laser. This feature is referred to as induced photon statistics. It is proposed to use this phenomenon to analyze the statistics of a laser involved in a feedback process. Arranging an experiment in a way such that the laser of interest serves as a coherent pump for the probe three-level laser one is able to directly observe the statistics of the feedback-controlled laser by simply detecting the induced photon statistics in the three-level probe system. The analysis of the operation of such two-laser system presented demonstrates, in particular, that the feedback itself is unable to produce a nonclassical state of light which is in complete agreement with the conclusion of Wiseman and Milburn [Phys. Rev. A 49, 1350 (1994)].

Two protocols of quantum direct communication with authentication [Phys. Rev. A 73, 042305 (2006)] were recently proposed by Lee, Lim, and Yang. In this paper we will show that in the two protocols the authenticator Trent should be prevented from knowing the secret message. The first protocol can be eavesdropped on by Trent using the intercept-measure-resend attack, while the second protocol can be eavesdropped on by Trent using a simple single-qubit measurement. To fix these leaks, we revise the original versions of the protocols by using the Pauli $Z$ operation ${\sigma }_z$ instead of the original bit-flip operation $X$. As a consequence, the attacks we present can be prevented and accordingly the protocol securities are improved.

The noise decoupling problem is investigated for general $N$-level Markovian open quantum systems. First, the concept of Cartan decomposition of the Lie algebra $\mathrm{su}\left(N\right)$ is introduced as a tool of designing control Hamiltonians. Next, under certain assumptions, it is shown that a part of variables of the coherence vector of the system density matrix can be asymptotically decoupled from the environmental noises. The resulting noise decoupling scheme is applied to one-qubit, qutrit, and two-qubit quantum systems, by which the coherence evolution of the one-qubit and qutrit systems can always be asymptotically preserved, while, for two-qubit systems, our findings indicate that evolution of some variables can be preserved only for some initial states.

We report an experimental demonstration of remote preparation of an arbitrary pure qutrit state. A qutrit is encoded in a two-photon (biphoton) polarization state. Prepared states are characterized by quantum state tomography. Experimental imperfection is discussed and evaluated by an experimentally obtained density matrix. The present scheme can develop into generation of an arbitrary two-photon triplet state and accordingly to an essential multiparty quantum communication protocol. Generalization to higher order which enables remote preparation of an arbitrary qudit state and several typical multiphoton entangled states is also shown.

X-ray resonant Raman scattering (RRS) spectra of Al, ${\mathrm{Al}}_2{\mathrm{O}}_3$, Si, and $\mathrm{Si}{\mathrm{O}}_2$ were measured at the European Synchrotron Radiation Facility, using a high-resolution Bragg-type curved crystal spectrometer. The x-ray RRS spectra were collected at several beam energies tuned below the $1s$ absorption thresholds of Al and Si. Differences in the spectral features between the elemental samples and the oxide ones were clearly observed. The data were interpreted using the second-order perturbation theory within the Kramers-Heisenberg (KH) approach. It is shown that, using the KH formalism, oscillator strengths that are similar to the ones deduced from x-ray absorption measurements can be extracted from emission x-ray RRS spectra. The total cross sections for the x-ray RRS process were derived for the different photon beam energies and compared with theoretical predictions. For elemental silicon, the weak $1s\text{−}3p$ excitation was observed and found to be consistent with results of density of states calculations.