We investigate the nonlinear interaction between two photons in a single-input pulse at an atomic two-level nonlinearity. A one-dimensional model for the propagation of light to and from the atom is used to describe the precise spatiotemporal coherence of the two-photon state. It is shown that the interaction generates spatiotemporal entanglement in the output state similar to the entanglement observed in parametric down-conversion. A method of generating photon pairs from coherent pump light using this quantum-mechanical four-wave mixing process is proposed.

Photon-number-resolving detectors are needed for a variety of applications including linear-optics quantum computing. Here we describe the use of time-multiplexing techniques that allow ordinary single-photon detectors, such as silicon avalanche photodiodes, to be used as photon-number-resolving detectors. The ability of such a detector to correctly measure the number of photons for an incident number state is analyzed. The predicted results for an incident coherent state are found to be in good agreement with the results of a proof-of-principle experimental demonstration.

Vaidman described how a team of three players, each of them isolated in a remote booth, could use a three-qubit Greenberger-Horne-Zeilinger state to always win a game which would be impossible to always win without quantum resources. However, Vaidman’s method requires all three players to share a common reference frame; it does not work if the adversary is allowed to disorientate one player. Here we show how to always win the game, even if the players do not share any reference frame. The introduced method uses a 12-qubit state which is invariant under any transformation $R_a\otimes R_b\otimes R_c$ (where $R_a{=U}_a\otimes U_a\otimes U_a\otimes U_a,$ where $U_j$ is a unitary operation on a single qubit) and requires only single-qubit measurements. A number of further applications of this 12-qubit state are described.

The mean arrival time of free particles is computed using the quantum-mechanical probability current. This is uniquely determined in the nonrelativistic limit of Dirac equation, although the Schrödinger probability current has an inherent nonuniqueness. Since the Dirac probability current contains a spin-dependent term, an arrival time distribution based on the probability current shows an observable spin-dependent effect, even for free particles. This arises essentially from relativistic quantum dynamics, but persists even in the nonrelativistic regime.

We calculate radiative corrections to the Lamb shift of order ${\alpha }^3(Z\alpha {)}^{5}m$ and radiative corrections to hyperfine splitting of order ${\alpha }^3(Z\alpha {)E}_F$ generated by the diagrams with insertions of radiative photons and electron polarization loops in the graphs with two external photons. We also obtain the radiative-recoil correction to hyperfine splitting in muonium generated by the diagrams with the $\tau$ polarization loop.

A simultaneous, contextual experimental demonstration of the two processes of cloning an input qubit $|\Psi 〉$ and of flipping it into the orthogonal qubit $|{\Psi }^{\perp }〉$ is reported. The adopted experimental apparatus, a quantum-injected optical parametric amplifier is transformed simultaneously into a universal optimal quantum cloning machine and into a universal-NOT quantum-information gate. The two processes, indeed forbidden in their exact form for fundamental quantum limitations, were found to be universal and optimal, i.e., the measured fidelity of both processes $F<\mathrm{}1\mathrm{}$ was found close to the limit values evaluated by quantum theory. A contextual theoretical and experimental investigation of these processes, which may represent the basic difference between the classical and the quantum worlds, can reveal in a unifying manner the detailed structure of quantum information. It may also enlighten the yet little explored interconnections of fundamental axiomatic properties within the deep structure of quantum mechanics.

The degree to which a pure quantum state is entangled can be characterized by the distance or angle to the nearest unentangled state. This geometric measure of entanglement, already present in a number of settings [A. Shimony, Ann. NY. Acad. Sci. 755, 675 (1995); H. Barnum and N. Linden, J. Phys. A: Math. Gen. 34, 6787 (2001)], is explored for bipartite and multipartite pure and mixed states. The measure is determined analytically for arbitrary two-qubit mixed states and for generalized Werner and isotropic states, and is also applied to certain multipartite mixed states. In particular, a detailed analysis is given for arbitrary mixtures of three-qubit Greenberger-Horne-Zeilinger, W, and inverted-$W$ states. Along the way, we point out connections of the geometric measure of entanglement with entanglement witnesses and with the Hartree approximation method.

The orientation in space of a Cartesian coordinate system can be indicated by the two vectorial constants of motion of a classical Keplerian orbit: the angular momentum and the Laplace-Runge-Lenz vector. In quantum mechanics, the states of a hydrogen atom that mimic classical elliptic orbits are the coherent states of the SO(4) rotation group. It is known how to produce these states experimentally. They have minimal dispersions of the two conserved vectors and can be used as direction indicators. We compare the fidelity of this transmission method with that of the idealized optimal method.

By looking at quantum data compression in the second quantization, we present a model for the efficient generation and use of variable length codes. In this picture, lossless data compression can be seen as the minimum energy required to faithfully represent or transmit classical information contained within a quantum state. In order to represent information, we create quanta in some predefined modes (i.e., frequencies) prepared in one of the two possible internal states (the information carrying degrees of freedom). Data compression is now seen as the selective annihilation of these quanta, the energy of which is effectively dissipated into the environment. As any increase in the energy of the environment is intricately linked to any information loss and is subject to Landauer’s erasure principle, we use this principle to distinguish lossless and lossy schemes and to suggest bounds on the efficiency of our lossless compression protocol. In line with the work of Bostroem and Felbinger [Phys. Rev. A 65, 032313 (2002)], we also show that when using variable length codes the classical notions of prefix or uniquely decipherable codes are unnecessarily restrictive given the structure of quantum mechanics and that a 1-1 mapping is sufficient. In the absence of this restraint, we translate existing classical results on 1-1 coding to the quantum domain to derive a new upper bound on the compression of quantum information. Finally, we present a simple quantum circuit to implement our scheme.

The range of validity of perturbative calculations of relativistic sum rules is investigated by calculating the second-order relativistic corrections to the Bethe sum rule and its small momentum limit, the Thomas-Reiche-Kuhn (TRK) sum rule. For the TRK sum rule and atomic systems, the second-order correction is found to be less than $0.5\%$ up to about $Z=70.\mathrm{}$ The total relativistic corrections should then be accurate at least through this range of Z, and probably beyond this range if the second-order terms are included. For Rn $\mathrm{}(Z=86\mathrm{}),$ however, the second-order corrections are nearly 1%. The total corrections to the Bethe sum rule are largest at small momentum, never being significantly larger than the corresponding corrections to the TRK sum rule. The first-order corrections to the Bethe sum rule also give better than $0.5\%$ accuracy for $Z<\mathrm{}70,$ and inclusion of the second-order corrections should extend this range, as well.

The general applicability of the basis set and correlation-dependent extrapolation method [J. Chem. Phys. 118, 3035 (2003)], which fits two successive correlation energies with correlation-consistent $\mathrm{cc}-pVXZ$ and $\mathrm{cc}-pV(X+1\mathrm{})Z$ basis sets $[X=D(2),T(3),Q(4\left)\mathrm{}\right]$ by ${\mathrm{}(X+k)\mathrm{}}^{-3}$ with varying k according to basis-set quality and correlation level, was explored by examining the basis-set limit binding energies of the metallic clusters of ${\mathrm{Be}}_n$ and ${\mathrm{Mg}}_n$ $\mathrm{}(n=2,3,4\mathrm{})\mathrm{}$ at the MP2 (second-order Moller-Plesset perturbation theory) and CCSD(T) (single and double coupled cluster method with perturbative triple correction) level. The comparison of the extrapolated basis-set limit estimates with the highly accurate reference basis-set limits suggests that the extrapolation of correlation contributions of binding energies with only $\mathrm{cc}-pVDZ$ and $\mathrm{cc}-pVTZ$ basis sets already yields the basis-set limit estimates close to the reference complete basis-set limits within 1 m-hartree in most cases, signifying the utility of this extrapolation method in the study of larger clusters. The natural extension of this extrapolation method to all electron correlated computations including core electrons with core-valence $\mathrm{cc}-pCVXZ$ basis sets is also made, which shows the similar accuracy of the extrapolated estimates for all electron correlated results as the valence electron only correlated results. The comparison of the MP2 and CCSD(T) basis-set limit binding energies with DFT (density-functional theory) results manifests the capability and limitation of the current DFT methods in studying the binding of such clusters.

By means of a scaling ansatz, we investigate an approximated solution of the Boltzmann-Vlasov equation for a classical gas. Within this framework, we derive the frequencies and the damping of the collective oscillations of a harmonically trapped gas and we investigate its expansion after releasing of the trap. The method is well suited to study the collisional effects taking place in the system and in particular to discuss the crossover between the hydrodynamic and the collisionless regimes. An explicit link between the relaxation times relevant for the damping of the collective oscillations and for the expansion is established.

The properties of noninteracting, low-energy atom waves propagating through circular bends are investigated. Time-independent quantum mechanical calculations using various simple harmonic oscillator based confining potentials explore the transmission, reflection, and mode-transfer probabilities over a range of energies. It is shown that at low energies single-mode wave propagation dominates. At higher energies, however, excitation and transmission of other modes become significant. Notably, reflections generally remain negligible even for sharply curved bends. The behavior near the mode thresholds and their associated resonances is emphasized.

We consider two regimes where a trapped Bose gas behaves as a one-dimensional (1D) system. In the first one the Bose gas is microscopically described by 3D mean-field theory, but the trap is so elongated that it behaves as a 1D gas with respect to low-frequency collective modes. In the second regime we assume that the 1D gas is truly 1D and that it is properly described by the Lieb-Liniger model. In both regimes we find the frequency of the lowest compressional mode by solving the hydrodynamic equations. This is done by making use of a method which allows us to find analytical or quasianalytical solutions of these equations for a large class of models approaching very closely the actual equation of state of the Bose gas. We find an excellent agreement with the recent results of Menotti and Stringari obtained from a sum-rule approach.

We present the results of Bragg spectroscopy performed on an accelerating Bose-Einstein condensate. The Bose-Einstein condensate undergoes circular micromotion in a magnetic time-averaged orbiting potential trap and the effect of this motion on the Bragg spectrum is analyzed. A simple frequency modulation model is used to interpret the observed complex structure, and broadening effects are considered using numerical solutions to the Gross-Pitaevskii equation.

By means of a canonical transformation it is shown how it is possible to recast the equations for molecular nonlinear optics to completely eliminate ground-state static dipole coupling terms. Such dipoles can certainly play a highly important role in nonlinear optical response—but equations derived by standard methods, in which these dipoles emerge only as special cases of transition moments, prove unnecessarily complex. It has been shown that the elimination of ground-state static dipoles in favor of dipole shifts results in a considerable simplification in form of the nonlinear optical susceptibilities. In a fully quantum theoretical treatment the validity of such a procedure has previously been verified using an expedient algorithm, whose defense was afforded only by a highly intricate proof. In this paper it is shown how a canonical transformation method entirely circumvents such an approach; it also affords insights into the formulation of quantum field interactions.

Using the SuperEBIT electron-beam ion trap and a flat-field spectrometer, we observed extreme ultraviolet spectra of highly charged ions of Xe and measured the wavelengths of prominent lines from Li-, Be-, B-, Na-, and Mg-like ions. Our results for Li- and Na-like ions are as precise as the best available elsewhere. The results for Be-, B-, and Mg-like ions are much more precise than available data or extend those available from lower-$Z$ ions and reveal significant shortcomings of the various theoretical predictions.

We present a joint experimental and theoretical study of convoy-electron emission resulting from highly-charged-ion transport through carbon foils at moderately relativistic speeds. Energy spectra of electrons ejected at $0°$ have been measured for 390 MeV/u hydrogen-like ${\mathrm{Ar}}^{17+}$ ions and 460 MeV/u $(\beta =v/c=0.74,\gamma =1.49)$ ${\mathrm{Fe}}^{25+}$ $\mathrm{}\left(1s\right),$ ${\mathrm{Fe}}^{24+}$ ${(1s}^2),$ and ${\mathrm{Fe}}^{23+}$ ${(1s}^{2}2s)$ incident on carbon foils with thicknesses from 25 to $8700\mu {\mathrm{g}/\mathrm{c}\mathrm{m}}^2.$ Due to this unprecedented wide range of thicknesses, the sequential excitation and ionization of initially deeply bound electrons to highly excited states and continuum states can be followed in considerable detail. The analysis of the spectra is aided by simulations based on the classical transport theory which has been extended to relativistic energies and to multielectron projectiles. The motion of the projectile electron inside the solid target is calculated taking into account the Coulomb potential of the projectile ion and the multiple stochastic collisions with target cores and target electrons. Different phases of the convoy-electron emissions can be disentangled: direct ejection to the continuum, the transient buildup of an excited-state wave packet followed by ionization, and postionization modification of the continuum spectrum. We find good agreement between experiment and simulation for the evolution of charge states and the emission spectrum.

The influence of an external electric field on the state dynamics of electronically excited molecules was analyzed. The electric field was shown to affect the $\Delta S=0\mathrm{}$ internal conversion transitions. It was found that in the presence of an external electric field, the lifetime of the acetylene fluorescence decreases, while the emission amplitude remains constant. The theory developed was applied to acetylene excited into single rotational levels of the $(A^1{A}_u{)V}^2{K}^{l=0,1,2\mathrm{}}$ vibronic states, which are below the ground-state dissociative threshold. It was proposed that levels of the $(A^1{A}_u{)V}^2{K}^{l=0,1,2\mathrm{}}$ vibronic states are coupled by a field to “quasiresonance” levels of the $\tilde{X}{}^1{\Sigma }_g^{+}$ electronic ground state. Dynamics of the system evolution over the vibrational energy spectrum of the $\tilde{X}{}^1{\Sigma }_g^{+}$ electronic ground state was investigated using its IR emission kinetics.

In this paper we study the superfluid–Mott-insulator phase transition of ultracold dilute gas of bosonic atoms in an optical lattice by means of Green function method and Bogliubov transformation as well. The superfluid–Mott-insulator phase transition condition is determined by the energy-band structure with an obvious interpretation of the transition mechanism. Moreover the superfluid phase is explained explicitly from the energy spectrum derived in terms of Bogliubov approach.