We describe the construction of a conditional quantum control-NOT (CNOT) gate from linear optical elements following the program of Knill, Laflamme, and Milburn [Nature 409, 46 (2001)]. We show that the basic operation of this gate can be tested using current technology. We then simplify the scheme significantly.

We demonstrate a class of optimum detection strategies for extracting the maximum information from sets of equiprobable real symmetric qubit states of a single photon. These optimum strategies have been predicted by Sasaki et al. [Phys. Rev. A 59, 3325 (1999)]. The peculiar aspect is that the detections with at least three outputs suffice for optimum extraction of information regardless of the number of signal elements. The cases of ternary (or trine), quinary, and septenary polarization signals are studied where a standard von Neumann detection (a projection onto a binary orthogonal basis) fails to access the maximum information. Our experiments demonstrate that it is possible with present technologies to attain about 96% of the theoretical limit.

This paper addresses quantum statistical estimation of operators $U\in \mathrm{SU}\left(2\right)\mathrm{}$ acting on $C{P}^3$ as $\psi \mapsto (U\otimes I)\psi$ where $\psi \in C^2\otimes C^2.$ This is regarded as a continuous analog of the dense coding. We first prove that the quantum Cramér-Rao lower bound takes the minimum, and is achievable, if and only if ψ is a maximally entangled state. We next show that an SU(2) orbit on $C{P}^3$ equipped with the standard Riemannian structure is isometric to $\mathrm{SU}\left(2\right)\mathrm{}/\{\pm I\}\cong \mathrm{SO}\left(3\right)\mathrm{}$ if and only if ψ is a maximally entangled state. These results provide an alternative view for the optimality of the use of a maximally entangled state.

The spectrum of resonance states of ${\mathrm{H}}^{-}$ of ${}^3{P}^o$ symmetry up to the $n=5\mathrm{}$ Hydrogen threshold has been resolved by identifying all the complex eigenvalues of the corresponding Schrödinger equation with widths down to about ${10}^{-9}$ a.u. In order to achieve this spectral resolution inside the continuous spectrum, we employed the previously described polyelectronic complex-eigenvalue Schrödinger-equation theory, with special choices of large trial two-electron spaces, constructed in terms of real and complex one-electron Slater-type orbitals. Electron correlation and multistate and multichannel couplings characteristic to the problem were accounted for with high numerical accuracy. The basis set of real orbitals constituting the localized part of the resonances, were chosen systematically so as to cover in a regular manner the configuration space from 3 a.u. up to about ${10}^4$ a.u. In this way, both the inner and the outer (very diffuse) orbitals as well as the possible cases of medium-range intrashell states were represented reliably. Energies, widths, and wave-function characteristics were computed and analyzed for 83 resonances below the $n=2,$ 3, 4, and 5 Hydrogen levels. The essence of these results is presented numerically as well as in special figures, whose purpose is to demonstrate the degree to which these complex eigenvalues fall into series according to the Gailitis-Damburg theory of dipole resonances. The existence of series of dipole resonances with characteristic energy and width scaling is used as the zero-order reference model. We found that, in general, the resonances indeed follow the regularity predicted by the Gailitis-Damburg model. At the same time, there are a few irregularities, caused by interseries perturbations. They appear especially strongly in regions where overlapping resonances exist. Using our previous results for the resonance spectrum of ${}^1{P}^o$ symmetry, similarities and differences are discussed. Finally, the existence of a shape resonance lying above the $n=3\mathrm{}$ threshold, which has been predicted in earlier work, is confirmed. On the contrary, our calculations did not confirm the appearance of a shape resonance above the $n=2\mathrm{}$ threshold, which has also been predicted before in the literature.

The HCl inner-valence photoelectron band at 26 eV binding energy has been recorded at high resolution. Discrete peaks arising from at least two separate vibrational progressions are superimposed on the broad continuum. Fano profiles are visible in one of the progressions. This indicates interference between superimposed electronic states, where weak avoided crossing allows two adiabatic states to couple. In the isotopic DCl molecular spectrum, the discrete lines are less pronounced, due to slower dissociation and therefore less coupling between the continuum and the bound state.

The vibrationally resolved photoelectron spectra of HCl and DCl in the 25–28 eV region were computed using a time-dependent approach for the nuclear dynamics. The spectral features cannot be understood without including a nonadiabatic coupling between the dissociative $3^2{\Sigma }^{+}$ state and the bound $4{}^2{\Sigma }^{+}$ state in the adiabatic picture. Alternatively, in the diabatic picture a dissociative two-hole–one-particle state interacts with a bound one-hole state. The molecular system is of intermediate coupling strength, i.e., it cannot be described by a single potential-energy curve. The interaction between a bound and a dissociative state leads to Fano resonances superimposed on a broad background, as observed in the experimental spectra [Burmeister et al., Phys. Rev. A 64, 012704 (2001)]. From modified potential-energy curves, all features of the experimental spectra, including Fano resonance parameters and lifetimes, were reproduced. From the simulations we observe that two additional peaks in the experimental DCl spectra should appear if the resolution were to be enhanced to around 10 meV.

A rigorous full quantum-mechanical wave-packet calculation is carried out to study the protonium formation $\overline{p}+\mathrm{H}\to \overline{p}p+e.\mathrm{}$ The present paper directly solves the time-dependent Schrödinger equation for the heavy particle Coulomb collision system. A discrete-variable-representation technique is used to evaluate the action of the Hamiltonian operator on the wave packet. The cross sections for the protonium formation are obtained at center-of-mass translational energies up to 10 eV. The present quantum-mechanical results are compared with those of previous studies based on classical trajectory Monte Carlo and semiclassical methods. Applicability of the adiabatic molecular picture to the protonium formation is also discussed.

We explore the nonlinear coupling of the three scissors modes of an anisotropic Bose-Einstein condensate. We show that only when the frequency of one of the scissors modes is twice the frequency of another scissors mode, these two modes can be resonantly coupled and a down-conversion can occur. We perform the calculation variationally using a gaussian trial wave function. This enables us to obtain simple analytical results that describe the oscillation and resonance behavior of the two coupled modes.

Classical optical interference experiments correspond to a measurement of the first-order correlation function of the electromagnetic field. The converse of this statement: experiments that measure the first-order correlation functions do not distinguish between the quantum and classical theories of light, does not always hold. A counterexample is given.

Optical bistability and dynamic instability are experimentally observed and studied in a system consisting of three-level $\Lambda$-type rubidium atoms in an optical ring cavity. The bistable behavior and self-pulsing frequency are experimentally manipulated by changing the controlling and cavity field parameters (power and frequency). These nonlinear effects are influenced by the enhanced Kerr nonlinearity due to atomic coherence in such a system.

In this paper we propose two surprisingly simple optical systems that display Bell-type correlations between the continuous variables of their subsystems. We first discuss how these two systems may be used to construct Bell-type correlations from two bright, amplitude-squeezed sources. Then the experimental viability of these systems is analyzed. Issues such as the conditions under which the systems display Bell correlations, sources of nontechnical as well as technical noise, signal-to-noise ratio and losses are discussed. Based on this discussion, we conclude that both of these systems are currently experimentally viable.

Motivated by the recently demonstrated ability to attach quantum dots to polymers at well-defined locations, we propose a condensed-phase analog of the ion-trap quantum computer: a scheme for quantum computation using chemically assembled semiconductor nanocrystals attached to a linear support. The linear support is either a molecular string (e.g., DNA) or a nanoscale rod. The phonon modes of the linear support are used as a quantum-information bus between the dots. Our scheme offers greater flexibility in optimizing material parameters than the ion-trap method, but has additional complications. We discuss the relevant physical parameters, provide a detailed feasibility study, and suggest materials for which quantum computation may be possible with this approach. We find that Si is a potentially promising quantum-dot material, already allowing a 5–10-qubit quantum computer to operate with an error threshold of ${10}^{-3}.$

We present a construction for quantum error correcting codes. The basic ingredients are a graph and a finite Abelian group, from which the code can explicitly be obtained. We prove necessary and sufficient conditions for the graph such that the resulting code corrects a certain number of errors. This allows a simple verification of the one-error correcting property of codes of length 5 in any dimension. As examples, we construct a large class of maximum distance separable codes, i.e. codes saturating the Singleton bound, as well as a code of length 10 detecting three errors.

The dynamics of a generic quantum XOR gate operation involving two interacting qubits being coupled to a bath of quantum harmonic oscillators is explored. By use of the formally exact quasiadiabatic-propagator path-integral methodology we study the time-resolved evolution of this interacting and decohering two-qubit system in presence of time-dependent external fields. The quality of the XOR gate operation is monitored by evaluating the four characteristic gate quantifiers: fidelity, purity, the quantum degree, and the entanglement capability of the gate. Two different types of errors for the XOR operation have been modeled, i.e., (i) bit-flip errors and (ii) phase errors. The various quantifiers are systematically investigated vs the strength of the interqubit coupling and vs both, the environmental temperature and the (Ohmic-like) bath-interaction strength. Our main findings are that these four gate quantifiers depend only very weakly on temperature, but are extremely sensitive to the bath-interaction strength. Interestingly enough, however, we find that the XOR gate operation deteriorates only weakly upon decreasing the interqubit coupling strength. This generic case study yields lower bounds on the quality of realistic XOR gate operations.

Although it is impossible for a bit commitment protocol to be both arbitrarily concealing and arbitrarily binding, it is possible for it to be both partiallyconcealing and partiallybinding. This means that Bob cannot, prior to the beginning of the unveiling phase, find out everything about the bit committed, and Alice cannot, through actions taken after the end of the commitment phase, unveil whatever bit she desires. We determine upper bounds on the degrees of concealment and bindingness that can be achieved simultaneously in anybit commitment protocol, although it is unknown whether these can be saturated. We do, however, determine the maxima of these quantities in a restricted class of bit commitment protocols, namely, those wherein all the systems that play a role in the commitment phase are supplied by Alice. We show that these maxima can be achieved using a protocol that requires Alice to prepare a pair of systems in an entangled state, submit one of the pair to Bob at the commitment phase, and the other at the unveiling phase. Finally, we determine the form of the trade off that exists between the degree of concealment and the degree of bindingness given various assumptions about the purity and dimensionality of the states used in the protocol.

We utilize the Sturmian expansion of the Dirac-Coulomb Green function [R. Szmytkowski, J. Phys. B 30, 825 (1997)] to obtain components of the dynamic dipole polarizability tensor of the relativistic hydrogenlike atom in the ground state. It is found that the tensor may be expressed in terms of two independent quantities: a scalar polarizability and a vector polarizability, the latter being of the relativistic origin. In the static and nonrelativistic limits the previously known expressions for the scalar polarizability are recovered.

We consider the process of double photoionization (DPI) in a rare-gas atom as a two-step process, namely, (i) photoionization in an inner shell followed by (ii) the emission of an Auger electron from an outer shell. An angular correlation function for the two emitted electrons is defined by analogy with the theory of angular correlation in nuclear physics. An expression is obtained for this angular correlation function by a statistical method that makes use of the density and efficiency operators. The latter takes care of the attenuation of the probability of detection of an electron due to the geometrical properties of the detector. Theoretical values of the angular correlation function are obtained for DPI in xenon and these are shown to be in good agreement with the experimental results given by Kämmerling and Schmidt [J. Phys. B 26, 1141 (1993)].

A very elemental method of observing the motion of the nucleus in molecules or solids is described. The observations for copper, graphite, and formvar films can be understood assuming that the electrons scatter from a moving target (vibrating atoms). The method is the complete electron analog for neutron Compton scattering. The nuclear motion causes a doppler shift in the energy of elastically scattered electrons. It is rather unusual among the methods of studying vibrations (e.g., molecular vibrations in individual molecules or phonons in solids) in that the information obtained is directly related to the momentum distribution of the probed atoms, rather than the energy difference between different vibrational states. The application of the semiclassical picture described here could fail to describe more detailed measurements. Gas-phase experiments may be more suitable for fully quantitative measurements. Indeed the experiment could be used to study the breakup of molecules after a well-defined perturbation.

We demonstrate that the presence of excited states in sputtered surface atoms after ion bombardment affects the measured ion yield of a subsequent post multiphoton-ionization processes. This effect was investigated using an advanced time-of-flight mass-spectroscopic technique. This work reports a comparison of two-photon ionization spectra of metallic atoms obtained from solid samples via sputtering and thermal evaporation that reveals the role of excited states. Furthermore we experimentally determine the cross sections for the two photon ionization processes of evaporated Mg, Zn, and In through quantitative ion yield measurement. Numerical configuration interaction calculations for Mg and Zn are presented and the resulting theoretical two-photon ionization cross sections are compared with the measured ones.

The relaxation time of optical excitations in simple metal clusters is calculated. The relaxation mechanism arises from electron-phonon transitions from the optically excited electron state to all possible excited states. The electronic excitations are described in the random-phase approximation with exchange within the jellium model. The phonon spectrum is associated with the thermal fluctuations of the ionic background, which is described in the liquid drop model. Calculated relaxation times are in a good agreement with available experimental data. The asymptotic limit of these rates in very large clusters is estimated within an analytical model that describes the decay, into particle-hole excitations, of the dipole collective state associated with the center-of-mass motion.