We consider equilibrium canonical-ensemble fluctuations of the Bose-Einstein condensate (BEC) in a trap using the particle-number conserving operator formalism of Girardeau and Arnowitt [Phys. Rev. 113, 755 (1959)] and the concept of the canonical-ensemble quasiparticles. We find explicit expressions for the characteristic function and all cumulants of the ground-state occupation statistics both for the dilute weakly interacting and ideal Bose gases. We present analytical formulas for the moments of the ground-state occupation fluctuations in the weakly interacting and ideal Bose gases in a box (“homogeneous gas”) as well as in the ideal Bose gas in an arbitrary power-law trap, in particular, in an arbitrary harmonic trap. We calculate the effect of Bogoliubov coupling between quasiparticles on suppression of the ground-state occupation fluctuations at moderate temperatures and their enhancement at very low temperatures. We clarify a crossover between ideal-gas and weakly interacting gas statistics, which is governed by a pair-correlation, squeezing mechanism. The important conclusion is that in most cases the ground-state occupation fluctuations are anomalously large and are not Gaussian even in the thermodynamic limit.

In this paper we employ the hydrodynamic quantization approach to studying the macroscopic state occupation of a bosonic system. We propose that the condensed state is a coherent state of the phase field component associated with the quantized field operator. By making Ansätze on functional states, we transform the problem of finding the phase and density associated with the condensate into a variational problem. We also discuss some properties of the condensed state, like superfluidity. In close analogy with Bose-Einstein condensation in the $\overrightarrow{p}=0\mathrm{}$ state, we propose some possible wave functions for the excited states of a condensed system.

We consider peculiarities of the light propagation in electro-optical crystals with the rotating optical “indicatrix” (index ellipsoid). Eigenmodes in such a medium have right- and left-hand circularly polarized components propagating with different phase velocities. We consider spatial and temporal optical solitons in crystals with second- and third-order nonlinearity. We discuss the problem of the frequency superposition by the transition to a frame connected with the axes of the rotating indicatrix, and phenomena suitable for the observation of effects caused the nonlinear superposition law.

The polarization eigenmodes of vertical-cavity surface-emitting lasers (VCSELs) are investigated theoretically. The study is based on a first-principles theory and includes a microscopic model for the optically active quantum well and a vectorial solution of the VCSEL cavity mode problem. The theory is evaluated for an anisotropically strained GaAs quantum well structure, interacting with two orthogonally polarized VCSEL eigenmodes. The dependence of the calculated input-output characteristics and polarization stability criteria on microscopic input parameters such as the value of the strain are discussed for various levels of sophistication of the microscopic many-body effects used in the analysis. The results of the stability analysis are consistent with recent experimental observations of polarization switching, suggesting that anisotropic strain of the active quantum well may be a dominant factor in those observations.

We find the analytic expressions and obtain plots of the Wigner distribution function for the bound eigenstates of the Morse potential on quantum phase space.

We investigate the behavior of a coupled atom-cavity system (a collection of two-level atoms inside a high-Q cavity) driven by a strong external resonant pulse. A different effect is predicted: parametric instability of a coupled atom-cavity system appears if the atomic number density in a cavity exceeds the threshold value that is proportional to the strong driving field. The increment of this instability is proportional to the atom-cavity coupling constant.

On the basis of a nonperturbative ab initio calculation for a hydrogen molecule in an electric field within a fully correlated, three-dimensional description, it is found that the ionization rate exhibits a pronounced enhancement at a specific internuclear distance. A general quantum-mechanical explanation for this enhancement is presented that is based on (diabatic) curve crossings and should be applicable to most diatomic molecules.

We report on a theoretical approach to the calculation of wave functions, energies $E,$ and widths $\Gamma$ of high-lying resonances of ${\mathrm{H}}^{-},$ with application to the identification of 76 states of ${}^1{P}^o,$ ${}^1{D}^o,$ and ${}^1{F}^o$ symmetries up to the $n=4\mathrm{}$ threshold, with widths down to about $1\times {10}^{-8}$–$1\times {10}^{-10}\mathrm{a}.\mathrm{u}.\mathrm{},$ depending on symmetry and threshold. The overwhelming majority of these resonances have not been detected experimentally. Previous calculations by different methods allowed the identification of 35 of these states, with only very few cases having a level of accuracy comparable to the one of the present work. We suggest that the measurement of these resonances might become possible via two-step excitation mechanisms using ultrasensitive techniques capable of dealing with the problems of very small widths and preparation cross-sections. In this work, the ${}^{1}D$ state at $10.872\mathrm{eV}$ above the ${\mathrm{H}}^{-}{1s}^2{}^{1}S$ ground state, already prepared and measured by electron scattering as well as by two-photon absorption, is considered as the stepping stone for the possible probing of resonances of ${}^1{P}^o,$ ${}^1{D}^o,$ and ${}^1{F}^o$ symmetries via absorption of tunable radiation of high resolution. By classifying the results according to the Gailitis-Damburg model of dipole resonances (a product of a ${1/r}^2$-like potential) we find that there are unperturbed as well as perturbed series, in analogy with the Rydberg spectra of neutrals and positive ions (a product of a $1/r$-like potential). For the former, the agreement with the Gailitis-Damburg predictions as to the relationship of the extent of the outer orbital and of the energies and widths of states is excellent. The perturbed series result from interchannel coupling and the remaining electron correlation. One of the effects is the existence of overlapping resonances. For example, for two ${}^1{P}^o$ states below the $n=3\mathrm{}$ threshold there is degeneracy on the energy axis ${(E}_1=-0.0555763612\mathrm{a}.\mathrm{u}.\mathrm{}$ and $E_2=-0.0555763099\mathrm{a}.\mathrm{u}.\mathrm{})$ but the widths differ $({\Gamma }_1=1.14\mathrm{}\times {10}^{-4}\mathrm{eV}$ and ${\Gamma }_2=5.45\mathrm{}\times {10}^{-6}\mathrm{eV}).\mathrm{}$ We also comment on whether consideration of the relativistic Lamb shift splitting of the hydrogen thresholds is sufficient for deciding the truncation of the resonance series. Our calculations were carried out by implementing previously published theories, whereby the resonance $E\mathrm{’}\mathrm{s}$ and Γ’s are determined from properly selected complex eigenvalues of non-Hermitian Hamiltonian matrices constructed in terms of physically relevant square integrable real and complex function spaces representing the localized and asymptotic parts of the resonance eigenfunctions. For the ${\mathrm{H}}^{-}$ series of resonances, the physical relevance of the real functions implies the systematic construction of basis sets with average $〈r〉$ extending to thousands of atomic units, in order to account for the extreme diffuseness of the outer orbital as each threshold is approached. The complex one-electron basis sets are Slater-type orbitals of a complex coordinate ${\mathrm{re}}^{-i\theta }.$ Their inclusion into the overall calculation and their optimization via the variation of nonlinear parameters (including θ) accounts for the contribution of the asymptotic part of the resonance, and for the energy width and shift beyond the real energy $E_o$ of the localized part.

The resonance spectrum of ${\mathrm{H}}^{-}$ for ${}^{1}S$ and ${}^{1}D$ symmetries up to the $n=4\mathrm{}$ threshold has been computed by solving the corresponding complex eigenvalue Schrödinger equation in terms of basis functions of real and complex coordinates. These functions are chosen and optimized judiciously and systematically in order to account for the specific details of electronic structure, electron correlation, and multistate and multichannel couplings characterizing the problem. Large sets of Slater orbitals, extending in a regular manner to about 8000 atomic units, were employed in order to describe properly the full range and especially the large-$r$ behavior of the localized part of these resonances, as their energy approaches their corresponding threshold. Energies, widths, and wave-function characteristics are presented for $33{}^{1}S$ states and $37{}^{1}D$ states having widths down to about $1\times {10}^{-9}\mathrm{a}.\mathrm{u}.\mathrm{}$ Of this total of 70 states, only 32 have been identified before via the application of different theoretical approaches, or, for very few of them, in scattering experiments. By adopting the Gailitis-Damburg model of dipole resonances as the relevant zero order model, we identify unperturbed and perturbed spectral series, in analogy with the well-known spectra of neutral atoms or positive ions, where the zero-order model is based on the Rydberg spectrum of the $1/r$ Coulomb potential. For perturbed spectra, only rough correspondence can be made with the smooth series predictions of the zero-order model. By achieving many-digit numerical precision for our results, we demonstrate the occasional presence of unique irregularities associated with each threshold, such as the existence of overlapping resonances and of “loner” resonances (i.e., not belonging to any series) below and above threshold. An example for the latter is a ${}^{1}D$ shape resonance above the $n=3\mathrm{}$ threshold. This state was already identified by Ho and Bhatia [Phys. Rev. A 48, 3720 (1993)]. However, our values for the energy above threshold $(\Delta E=0.49497\mathrm{}\mathrm{meV})$ and for the width $(\Gamma =8.632\mathrm{}\mathrm{meV})$ differ significantly from theirs $(\Delta E=116.94\mathrm{}\mathrm{meV}$ and $\Gamma =157\mathrm{}\mathrm{meV}).\mathrm{}$

Wavelengths have been measured for x-ray transitions from the excited states with strong configuration mixing between ${(2p}_{1/2}^{-1}{3s)}_{J=1\mathrm{}}$ and ${(2p}_{3/2}^{-1}{3d}_{5/2}{)}_{J=1\mathrm{}}$ to the ground states in neonlike ${\mathrm{I}}^{43+},$ ${\mathrm{Cs}}^{45+},$ and ${\mathrm{Ba}}^{46+}.$ The measurements were made with a flat crystal spectrometer on the Tokyo electron beam ion trap. The experimental wavelengths are compared to theoretical values calculated with the multiconfigurational Dirac-Fock method and other existing theoretical results. Using the present results, the degree of mixing in the wave functions between the two excited electronic configurations is investigated. The present investigation gives a clear demonstration for strong configuration mixing in highly charged ions through observation of an avoided crossing.

In this paper we report an experimental and theoretical study of the joint effect of two types of longitudinal gain nonuniformity (partial cavity filling by an active medium and the exponential absorption of pump intensity along the active element) on competitive interaction of longitudinal modes. A justification of the approach to the description of solid-state laser dynamics with gain nonuniformity, where the dimension of the model is the same as in a simple case of uniform longitudinal gain distribution, is presented. A detailed comparison of different approaches to the problem of describing the longitudinal gain nonuniformity is made.

Various aspects of nonlocality of a quantum wave are discussed. In particular, the question of the possibility of extracting information about the relative phase in a quantum wave is analyzed. It is argued that there is a profound difference in the nonlocal properties of the quantum wave between fermion and boson particles. The phase of the boson quantum state can be found from correlations between results of measurements in separate regions. These correlations are identical to the Einstein-Podolsky-Rosen (EPR) correlations between two entangled systems. An ensemble of results of measurements performed on fermion quantum waves does not exhibit the EPR correlations and the relative phase of fermion quantum waves cannot be found from these results. The existence of a physical variable (the relative phase) that cannot be measured locally is the nonlocality aspect of the quantum wave of a fermion.

We consider the problem of the optimal compression rate in the case of a source producing mixed signal states within the visible scheme (where Alice, who is to compress the signal, can know the identities of the produced states). We show that a simple strategy based on replacing the signal states with their extensions gives optimal compression. As a result we obtain a considerable simplification of the formula for an optimal compression rate within a visible scheme.

The basis generator method is used to propagate effective single-particle equations for ion-atom collisions to provide a mean-field description for the proton-oxygen collision system. The pure capture and ionization as well as transfer ionization cross sections are calculated using two alternative prescriptions to extract the physical information from the propagated orbitals. The sensitivity of the resonant single capture cross section to the effective single-particle potential for atomic oxygen is tested. Cross sections are calculated for 1–2000 keV proton impact and good overall agreement is found with available experiments, while some of the results are at variance with a recent model calculation. The single-particle excitation amplitudes are combined in the LS coupling scheme to obtain excitation cross sections for particular atomic oxygen configurations. The latter are compared with recent measurements for proton and electron impact. Reasonable agreement is found for many one-electron excitations and some two-electron processes.

Closed-orbit theory is a semiclassical technique for explaining the spectra of Rydberg atoms in external fields. We derive an alternative version of closed-orbit theory that applies when the external fields are time dependent. We compare the results of this theory with experiments on lithium atoms in a weak oscillating electric field.

A scheme for generating quantum superpositions of macroscopically distinguishable states of the vibrational motion of a bidimensionally trapped ion is reported. We show that these states possess highly nonclassical properties controllable by an adjustable parameter simply related to the initial condition of the confined system

We investigate the interaction of a two-dimensional model atom with an intense, high-frequency circularly polarized laser pulse. As the laser intensity is increased, the ionization rate initially increases, then decreases dramatically, with the electron wave function developing an asymmetric ring form which rotates with the electric field. We provide evidence that this wave form is due to localization of the electron onto nonlinear classical structures.

Discontinuous initial wave functions, or wave functions with a discontinuous derivative and a bounded support, arise in a natural way in various situations in physics, in particular in measurement theory. The propagation of such initial wave functions is not well described by the Schrödinger current which vanishes on the boundary of the support of the wave function. This propagation gives rise to a unidirectional current at the boundary of the support. We use path integrals to define current and unidirectional current, and to provide a direct derivation of the expression for current from the path-integral formulation for both diffusion and quantum mechanics. Furthermore, we give an explicit asymptotic expression for the short-time propagation of an initial wave function with compact support for cases of both a discontinuous derivative and a discontinuous wave function. We show that in the former case the probability propagated across the boundary of the support in time $\Delta t$ is $O\left(\Delta t^{3/2}\right),$ and the initial unidirectional current is $O\left(\Delta t^{1/2}\right).\mathrm{}$ This recovers the Zeno effect for continuous detection of a particle in a given domain. For the latter case the probability propagated across the boundary of the support in time $\Delta t$ is $O\left(\Delta t^{1/2}\right),$ and the initial unidirectional current is $O\left(\Delta t^{-1/2}\right).\mathrm{}$ This is an anti-Zeno effect. However, the probability propagated across a point located at a finite distance from the boundary of the support is $O\left(\Delta t\right).\mathrm{}$ This gives a decay law.

Consider three qubits A, B, and C which may be entangled with each other. We show that there is a trade-off between A’s entanglement with B and its entanglement with C. This relation is expressed in terms of a measure of entanglement called the concurrence, which is related to the entanglement of formation. Specifically, we show that the squared concurrence between A and B, plus the squared concurrence between A and C, cannot be greater than the squared concurrence between A and the pair BC. This inequality is as strong as it could be, in the sense that for any values of the concurrences satisfying the corresponding equality, one can find a quantum state consistent with those values. Further exploration of this result leads to a definition of an essential three-way entanglement of the system, which is invariant under permutations of the qubits.

The exchange interaction between identical qubits in a quantum-information processor gives rise to unitary two-qubit errors. It is shown here that decoherence-free subspaces (DFSs) for collective decoherence undergo Pauli errors under exchange, which, however, do not take the decoherence-free states outside of the DFS. In order to protect DFSs against these errors it is sufficient to employ a recently proposed concatenated DFS quantum-error-correcting code scheme [D. A. Lidar, D. Bacon, and K.B. Whaley, Phys. Rev. Lett. 82, 4556 (1999)].