Kerr effect cross-phase-modulation between signal and probe beams has been proposed and demonstrated as a means for quantum nondemolition (QND) measurement of the signal beam’s photon number by homodyne detection of the probe beam. Recently, such QND measurements have been suggested as providing a new route to photonic quantum computation. For a signal-beam qubit, whose computational basis is the vacuum and one-photon states, the QND detector’s error probability is shown to be determined by the qubit fidelity after the cross-phase-modulation interaction, with the former increasing from 0 to $\frac{1}{2}$ as the latter increases from $\frac{2}{3}$ to 1. This relationship is shown to hold regardless of the probe beam’s input state. It also applies, without modification, when the cross-phase-modulation interaction is replaced with a more general unitary transformation.

We introduce two two-player quantum pseudotelepathy games based on two recently proposed all-versus-nothing (AVN) proofs of Bell’s theorem [A. Cabello, Phys. Rev. Lett. 95, 210401 (2005); Phys. Rev. A 72, 050101(R) (2005)]. These games prove that Broadbent and Méthot’s claim that these AVN proofs do not rule out local-hidden-variable theories in which it is possible to exchange unlimited information inside the same light cone (quant-ph/0511047) is incorrect.

We treat vibrational excitation of hydrogen by low-energy electrons using an improved nonlocal resonance model. The model is based on accurate ab initio data for the ${}^2\Sigma _u^{+}$ shape resonance and takes full account of the nonlocality of the effective potential for nuclear motion. Integral vibrational excitation cross sections were calculated for numerous initial and final rovibrational states of the hydrogen molecule, and the dependence of the vibrational excitation cross section on the rovibrational initial target state has been investigated. The vibrational excitation cross sections are in very good agreement with measurements for the transitions $v=0\to 1$ and $v=0\to 2$, while for higher vibrational channels the agreement is less satisfactory. However, the oscillatory structures in $v=0\to 4$ vibrational excitation and higher channels predicted by Domcke and collaborators and measured by Allan are described by the present calculation, in very good agreement with the experimental data. A detailed analysis of the origin of the oscillations has been performed. It is shown that the oscillations can be qualitatively understood within the so-called boomerang model of Herzenberg. The resonance contribution to the vibrationally elastic scattering $(v\to v)$ is also discussed. It is found that this cross section is dominated at low energies by the resonance contribution, as predicted by Schulz. The calculated integral vibrational excitation cross sections generally are in good agreement with other theoretical data obtained by different approaches. A comprehensive study of the effect of isotopic substitution has been performed, and an inverse isotope effect in vibrational excitation has been found for certain vibrational levels of the target.

The aim of this paper is to obtain the right expression of the fully nonrelativistic $K$-shell Compton scattering amplitudes and cross sections. Using the Coulomb Green’s function method, we prove that by adequate analytical calculation of the nonrelativistic limit of the second order $S$-matrix element, it is possible to get Compton amplitudes which have no spurious singularities, as the old nonrelativistic result with retardation [M. Gavrila, Phys. Rev. A 6, 1348 (1972)] presents. A pole-free formula for Compton triply differential cross section, giving the right dependence on the angles of both the final electron and photon is obtained. This was possible by introducing relativistic kinematics terms and noticing that some of them cancel the retardation terms that generate the spurious poles. Consequently, the right nonrelativistic limit of the Compton amplitudes should be considered only after the cancellation of these terms. In this way the contributions corresponding to ${\mathbf{A}}^2$ and $\mathbf{p}\bullet \mathbf{A}$ operators present in the nonrelativistic Hamiltonian are correctly revealed. We show that good predictions are obtained for the whole Compton spectrum and any photon scattering angles for incoming photon energies ${\omega }_1$ up to $\alpha Zm$, if relativistic kinematics terms are included. The doubly differential cross section for Compton scattering of unpolarized photons from $K$-shell electrons is obtained by numerical integration over the angles of the final photon. Comparing our exact nonrelativistic formulae predictions for Compton scattering on intermediate and high atomic number targets, with experimental results and fully relativistic numerical evaluation of Bergstrom et al. [Phys. Rev. A 48, 1134 (1993)], a good agreement within 10% is found for the whole spectrum and any scattering angle for incoming photon energy below 200 keV. This shows that spin effects are small for unexpected large incoming photon energies and high $Z$ targets. Also, in the case of $s$ bound states, the nonrelativistic wave function approximates fairly well the Dirac spinor even for large energies if momentum transfer is not too high. A second numerical integration of the doubly differential cross section over scattered photon energies was performed, giving the singly differential cross section. A good agreement with fully relativistic data is found for incoming photon energies up to 300 keV and any atomic target, if relativistic kinematics effects are taken into account. The same is true in the case of Compton scattering on lead at 661 keV for scattering angles less than 60°.

The collisional relaxation of rotationally “hot” OH molecules in He as a buffer gas has been studied as a fully quantum event using an ab initio potential energy surface and the exact dynamical coupling of the relevant angular momenta during the process. The range of energies considered corresponds to the ultralow temperatures of cold traps and the calculations were carried out down to the Wigner regime of cross section behavior. It is shown that the general dependence of the inelastic processes on rotational angular momentum and parity clearly indicates a fairly marked size dependence of the final cross sections on the specific fine structure levels in which the target radical is being prepared to undergo relaxation.

The concept of phase stability in a Stark decelerator ensures that polar molecules can be accelerated, guided, or decelerated without loss; molecules within a certain position and velocity interval are kept together throughout the deceleration process. In this paper the influence of the transverse motion on phase stability in a Stark decelerator is investigated. For typical deceleration experiments—i.e., for high values of the phase angle ${\varphi }_0$—the transverse motion considerably enhances the region in phase space for which phase stable deceleration occurs. For low values of ${\varphi }_0$, however, the transverse motion reduces the acceptance of a Stark decelerator and unstable regions in phase space appear. These effects are quantitatively explained in terms of a coupling between the longitudinal and transverse motion. The predicted longitudinal acceptance of a Stark decelerator is verified by measurements on a beam of OH $(X{}^2\Pi _{3∕2},J=3∕2)$ radicals passing through a Stark decelerator.

We demonstrate that the global-entanglement (GE) measure defined by Meyer and Wallach [J. Math. Phys. 43, 4273 (2002)] is maximal at the critical point for the Ising chain in a transverse magnetic field. Our analysis is based on the equivalence of GE to the averaged linear entropy, allowing an understanding of multipartite entanglement (ME) features through a generalization of GE for bipartite blocks of qubits. Moreover, in contrast to GE, the proposed ME measure can distinguish three paradigmatic entangled states: ${\mathrm{GHZ}}_N$ (Greenberger-Horne-Zeilinger), $W_N$, and ${\mathrm{EPR}}^{\otimes N∕2}$. As such the generalized measure can detect a genuine ME and is maximal at the critical point.

We discuss the characterization and properties of quantum nondemolition (QND) measurements on qubit systems. We introduce figures of merit which can be applied to systems of any Hilbert space dimension, thus providing universal criteria for characterizing QND measurements. The controlled-NOT gate and an optical implementation are examined as examples of QND devices for qubits. We also consider the QND measurement of weak values.

We examine the perfect cloning of nonlocal, orthogonal states using only local operations and classical communication. We provide a complete characterisation of the states that can be cloned under these restrictions, and their relation to distinguishability. We also consider the case of catalytic cloning, which we show provides no enhancement to the set of clonable states.

We derive a proof of security for the differential-phase-shift quantum key distribution protocol under the assumption that Eve is restricted to individual attacks. The security proof is derived by bounding the average collision probability, which leads directly to a bound on Eve’s mutual information on the final key. The security proof applies to realistic sources based on pulsed coherent light. We then compare individual attacks to sequential attacks and show that individual attacks are more powerful.

We introduce a family of linear maps which are positive but not completely positive. We exhibit examples of nondecomposable maps and $2^N\otimes 2^N$, $N⩾2$, bound entangled states—e.g., nondistillable bipartite states of $N+N$ qubits. Such states, as the standard Bell diagonal states, are diagonal in a maximally entangled basis and, apart remaining positive under partial transposition, are not detected by the realignment criterion.

We have calculated total energies of atoms and diatomic molecules from the Luttinger-Ward functional, using self-energy approximations to second order as well as the $GW$ approximation. In order to assess the variational quality of this functional, we have also solved the Dyson equation self-consistently. The Luttinger-Ward functional is compared to the variational functional due to Klein, and we demonstrate that the variational property of the latter functional is inferior to that of the Luttinger-Ward functional. We also show how to obtain variational density functionals from the functionals of the Green function. These orbital functional schemes are important for systems where density-functional theory using local functionals of the density necessarily fails. We derive an optimized effective potential (OEP) scheme that is based on the Luttinger-Ward functional and, unlike the conventional OEP schemes, produces energies in good agreement with the values obtained from the self-consistent Green function. Our calculations show that, when applied to molecules, the Luttinger-Ward functional is more sensitive to the quality of the input Green function than when applied to atoms, but the energies are remarkably close to the self-consistent values when the Hartree-Fock Green function is used as input. This Luttinger-Ward functional is therefore a simple and efficient method for studying the merits of various self-energy approximations while avoiding the computationally demanding task of solving the Dyson equation self-consistently.

Compact Jastrow-Slater-type correlated wave functions for three- and four-electron atoms and ions (Li, ${\mathrm{Be}}^{+}$, ${\mathrm{B}}^{2+}$, ${\mathrm{C}}^{3+}$, Be, ${\mathrm{B}}^{+}$, and ${\mathrm{C}}^{2+}$) are proposed. The Jastrow factor we employed consists of one-body and two-body functions including only two variational parameters in total. We found that a one-body Jastrow function with one variational parameter, which is responsible for the screening effect around the nucleus, is effective for reproducing good total energies of the three- and four-electron atomic systems if hydrogenoid orbitals are adopted in the Slater determinant. On the other hand, a determinant composed of Hartree-Fock orbitals multiplied by the same Jastrow factor was found to give rather worse results than that composed of hydrogenoid orbitals. This result clearly indicates that analytic hydrogenoid orbitals coupled with the one-body Jastrow function are useful for describing simple wave functions and understanding the physical properties of these systems.

Properties of the Hohenberg-Kohn functional are considered. In particular, the Hohenberg-Kohn functional should (a) give correct results in the variational principle and should be (b) continuous, (c) convex, and (d) size consistent. All of these properties are satisfied by the Legendre-transform functional (equivalently, the density matrix constrained search functional) and, moreover, this is the only functional that possesses all these properties. Not only that, but the Legendre-transform functional is determined uniquely by requiring (a), (b), and either (c) or (d). This shows how an “axiomatic” approach to constructing the Hohenberg-Kohn functional leads naturally to the Legendre-transform functional. Among all functionals consistent with the variational principle, the Legendre-transform functional is the smallest. One corollary to this approach is a simple proof of the equivalence of the Legendre-transform and density-matrix constrained search functionals. For completeness, the Appendix shows that ensemble-$v$-representable densities lie dense in the set of $N$-representable densities.

The limit relations for the partial derivatives of the two-electron atomic wave functions at the two-particle coalescence lines have been obtained numerically using accurate correlation function hyperspherical harmonic method wave functions. The asymptotic solutions of the proper two-electron Schrödinger equation have been derived for both electron-nucleus and electron-electron coalescence. It is shown that the solutions for the electron-nucleus coalescence correspond to the ground and singly excited bound states, including triplet ones. The proper solutions at small distances $R$ from the triple coalescence point were presented as the second order expansion on $R$ and $\ln R$. The vanishing of the Fock’s logarithmic terms at the electron-nucleus coalescence line was revealed in the frame of this expansion, unlike the case of electron-electron coalescence. On the basis of the obtained boundary solutions the approximate wave function corresponding to both coalescence lines have been proposed in the two-exponential form with no variational parameters.

Manipulation of infinite-dimensional quantum systems is important to controlling complex quantum dynamics with many practical physical and chemical backgrounds. In this paper, a general investigation is casted to the controllability problem of quantum systems evolving on infinite-dimensional manifolds. Recognizing that such problems are related with infinite-dimensional controllability algebras, we introduce an algebraic mathematical framework to describe quantum control systems possessing such controllability algebras. Then we present the concept of smooth controllability on infinite-dimensional manifolds, and draw the main result on approximate strong smooth controllability. This is a nontrivial extension of the existing controllability results based on the analysis over finite-dimensional vector spaces to analysis over infinite-dimensional manifolds. It also opens up many interesting problems for future studies.

Properties of nitrogen cluster plasmas produced by an intense, ultrashort laser pulse have been investigated numerically and experimentally. The classical dynamics simulations show that on increasing the cluster size a plasma with residual electron energy above $1\mathrm{keV}$ can be created due to collisional heating, which is considerably higher than the value obtained with a conventional low-density gas target. Experimentally, nitrogen gas jets created by two types of nozzles were irradiated with a laser pulse of $55\mathrm{fs}$, up to $1.2\times {10}^{17}\mathrm{W}∕{\mathrm{cm}}^2$. A seeded gas jet consisting of nitrogen and helium was also employed to promote the production of large clusters. The influences of the shape of nozzle, the seeded gas, and the gas jet stagnation pressure on the properties of plasmas were examined by spectroscopic observations. $K$-shell emissions showed that for the gas jet using the conical nozzle the electrons underwent intense collisional heating within the large clusters, resulting in the production of highly charged ions. In contrast, the emissions observed with the capillary nozzle exhibited the characteristics of a cold plasma without suffering substantial electron heating, indicating the absence of large clusters. That is, the differences between the two types of nozzles in the efficiency of electron heating and subsequent residual energies after the passage of the laser pulse, which are strongly dependent upon the cluster size, drastically changed the properties of the produced plasmas. The reason that for the capillary gas jet the plasma density deduced from the recombination spectra was significantly higher than the value obtained using the conical nozzle is also given by the difference in residual electron energy.

The time-dependent Schrödinger equation is solved for a Born-Oppenheimer (static nuclei) three-dimensional $\mathrm{H}_2{}^{+}$ in super intense laser fields ($I=4\times {10}^{18}$, ${10}^{19}$, and $4\times {10}^{19}\mathrm{W}∕{\mathrm{cm}}^2$) at wavelength ${\lambda }_L=45\mathrm{nm}$ and $25\mathrm{nm}$ to assess the influence of nondipolar (magnetic) effects on high order harmonic generation spectra in molecules. It is found that even harmonics appear due to the magnetic field component direction perpendicular to the electric field polarization with intensities about two orders of magnitude less than the odd harmonics emitted along the electric field polarization. The even harmonics exhibit plateaus with cutoffs which exceed in intensity the odd harmonic plateaus and maximum energies predicted by semiclassical electron recollision models. Although the spectra are weak, the wavelength of the recollision electron in the maximum energy regions correspond to subatomic dimensions and the corresponding emitted photons have subnanometer wavelengths.

The wavelength dependence of double ionization of xenon in a 100-fs laser pulse $(2–4\times {10}^{13}\mathrm{W}∕{\mathrm{cm}}^2)$ has been studied using photoelectron imaging and ion time-of-flight spectrometry. In the wavelength ranges between 1150 and $1560\mathrm{nm}$ and 792 and $803\mathrm{nm}$ a pronounced variation of the ratio of ion yields ${\mathrm{Xe}}^{2+}∕{\mathrm{Xe}}^{+}$ is observed. We attribute this variation to the strong influence of a $5s^{2}5p^5\to 5s5p^6$ transition on the dynamics of double ionization.

We investigate the dynamics of a $F=1$ spinor Bose-Einstein condensate of ${}^{87}\mathrm{Rb}$ atoms confined in a quasi-one-dimensional trap both at zero and at finite temperature. At zero temperature, we observe coherent oscillations between populations of the various spin components and the formation of multiple domains in the condensate. We study also finite temperature effects in the spin dynamics taking into account the phase fluctuations in the Bogoliubov-de Gennes framework. At finite $T$, despite complex multidomain formation in the condensate, population equipartition occurs. The length scale of these spin domains seems to be determined intrinsically by nonlinear interactions.