We present a perturbation theory for non-Markovian quantum-state diffusion (QSD), the theory of diffusive quantum trajectories for open systems in a bosonic environment [Phys. Rev. A 58, 1699 (1998)]. We establish a systematic expansion in the ratio between the environmental correlation time and the typical system time scale. The leading order recovers the Markov theory, so here we concentrate on the next-order correction corresponding to first-order non-Markovian master equations. These perturbative equations greatly simplify the general non-Markovian QSD approach, and allow for efficient numerical simulations beyond the Markov approximation. Furthermore, we show that each perturbative scheme for QSD naturally gives rise to a perturbative scheme for the master equation which we study in some detail. Analytical and numerical examples are presented, including the quantum Brownian motion model.

We consider the problem of the bound states of a $\mathrm{s}\mathrm{p}\mathrm{i}\mathrm{n}-1/2$ chargeless particle in a given Aharonov-Casher configuration. To this end we recast the description of the system in a supersymmetric form. Then the basic physical requirements for unbroken supersymmetry are established. We comment on the possibility of neutron confinement in this system.

Exterior complex scaling enables one to compute the outgoing wave portion of the wave function for three charged particles without explicitly imposing the asymptotic boundary condition for three-body breakup. This technique is used in connection with a high-order finite difference scheme to provide numerically accurate single-differential ionization cross sections for the Temkin-Poet (s-wave) model of $e-\mathrm{H}$ scattering. These benchmark values are compared with results obtained from several recent close-coupling approaches that employ pseudostates to discretize the ionization continuum, but use a strictly two-body scattering formalism.

We have determined the Fano parameters and oscillator strengths of the triply photoexcited Li ${2s}^{2}2p$ ${}^2{P}^o$ autoionizing resonance in the ${\mathrm{Li}}^{+}$ and ${\mathrm{Li}}^{2+}$ partial photoion yields. Using monochromatized photons we observed an asymmetric resonance profile not only in the ${\mathrm{Li}}^{+}$ but also in the ${\mathrm{Li}}^{2+}$ partial cross section. The interaction between the triply excited state and the double-photoionization continuum takes place via a one-step double autoionization, since a two-step autoionization of the discrete state is energetically not possible. Our theoretical calculations using an $R$-matrix method for both the ${\mathrm{Li}}^{+}$ and ${\mathrm{Li}}^{2+}$ partial cross sections show resonance profiles in good agreement with experimental result.

The distorted-wave approximation is used to calculate doubly and triply differential cross sections for the electron-impact ionization of hydrogen molecules for incident energies of 100 and 250 eV. In the present model, the wave function of the incoming electron is calculated in the static-exchange (SE) potential field generated by a neutral ${\mathrm{H}}_2$ molecule, whereas those of the two outgoing electrons are calculated in the SE field of the ${\mathrm{H}}_2^{+}$ ion. The Schwinger variational iterative method was used in the calculation of these distorted waves. Comparison of the present calculated results with experimental data available in the literature is encouraging.

There are significant differences in the multielectron dissociative ionization (MEDI) of ${\mathrm{N}}_2$ by 100-fs-long laser pulses (intensity ${10}^{15}{\mathrm{W}\mathrm{}\mathrm{cm}}^{-2})$ using linearly and circularly polarized light, with substantial suppression of ionization in the latter case. Enhanced ionization occurs in both instances at an internuclear distance (r) of ∼2.2 Å, with an increased propensity for MEDI at larger r values with circularly polarized light.

We derive a simple formula for the heating rate that arises from quantum-diffractive background gas collisions in atom traps. This result appears to explain the residual heating rates reported for recent experiments with a Cs vapor-loaded, far-detuned optical trap at $\simeq {10}^{-9}$ Torr [Phys. Rev. Lett. 81, 5768 (1998)]. Diffractive collisions may determine the minimum heating rates achievable in shallow all-optical or magnetic atom traps operating at low temperature and high density.

We study the absorption and dispersion properties of a Λ-type atom that decays spontaneously near the edge of a photonic band gap (PBG). Using an isotropic PBG model, we show that the atom can become transparent to a probe laser field, even when other dissipative channels are present. This transparency originates from the square-root singularity of the density of modes of the PBG material at threshold.

We report a two-photon interference effect, in which the entangled photon pairs are generated from two laser pulses well separated in time. In a single pump pulse case, interference effects did not occur in our experimental scheme. However, by introducing a second pump pulse delayed in time, quantum interference was then observed. The visibility of the interference fringes shows a dependence on the delay time between two laser pulses. The results are explained in terms of indistinguishability of biphoton amplitudes that originates from two temporally separated laser pulses.

An analysis using classical stochastic processes is used to construct a consistent system of quantum counterfactual reasoning. When applied to a counterfactual version of Hardy’s paradox, it shows that the probabilistic character of quantum reasoning together with the “one framework” rule prevents a logical contradiction, and there is no evidence within this approach for any nonlocal influences. Counterfactual reasoning can support a realistic interpretation of standard quantum theory (measurements reveal what is actually there) under appropriate circumstances.

The usefulness of a scale-independent approach to identify Efimov states in three-body systems is shown by comparing such an approach with a realistic calculation in the case of three helium atoms. We show that the scaling limit is realized in practice in this case, and suggest its application to study other similar systems, including the case where two kinds of atoms are mixed. We also consider the observed large scattering length of $\mathrm{the}{\hspace{0.5em}}^{87}\mathrm{Rb}$ dimer to estimate the critical value of the ground-state energy of the corresponding trimer $(>~1.5\hspace{0.5em}\mathrm{mK})$, in order to allow for one Efimov state above the ground state.

The methods used to determine the reduced density matrix (RDM) of the ground and excited states, the finite-temperature systems, and the large systems without using the wave function by solving the density equation were discussed. We examined the foundations to reconstruct the higher-order RDMs of the ground and excited states and the finite-temperature systems in terms of the lower-order RDMs. We presented the equation to determine the RDMs of the finite-temperature systems directly and showed that only the exact RDMs satisfy the equation. Our previous approximation for third- and fourth-order RDMs of the ground state [H. Nakatsuji and K. Yasuda, Phys. Rev. Lett. 76, 1039 (1996)] was reformulated, and the accuracy of this approximation for the excited states was examined. The structure of the $n\mathrm{th}$ order energy density matrix $(n$-EDM) was analyzed, and the calculation method which sums up the Parquet diagram of the 2-EDM without explicitly constructing the third- and fourth-order RDMs was reported. This approximation is more accurate than the previous second-order approximation and also includes the infinite series of bubble and ladder Green’s function diagrams. Such a method is necessary to apply the density-equation method to large systems, such as polymers, metals, and semiconductors. The new approximation together with the density equation was applied to the ground states of some molecules including CO, ${\mathrm{C}}_2{\mathrm{H}}_2,$ ${\mathrm{C}}_3{\mathrm{H}}_8$, and ${\mathrm{C}}_4{\mathrm{H}}_{10},$ and the excited states of the Be atom and ${\mathrm{Li}}_2$ molecule. The calculated energies were as accurate as the exact or coupled-cluster single and double excitations with triples included noniteratively, and the energy errors of the second-order approximation were significantly reduced. The calculated 2-RDMs almost satisfied important representability conditions while the 1-RDMs were exactly ensemble representable. These results demonstrate that the density equation offers a new quantitative method for treating electron correlations. The relationship between the iterative procedure and the finite-temperature density-equation method was discussed.

Long-distance Bell-type experiments are presented. The different experimental challenges and their solutions in order to maintain the strong quantum correlations between energy-time entangled photons over more than 10 km are reported and the results analyzed from the point of view of tests of fundamental physics as well as from the more applied side of quantum communication, especially quantum key distribution. Tests using more than one analyzer on each side are also presented.

A method of reconstructing a wave function from part of the Q function in a pure state of light is proposed. This method involves the use of a noniterative phase-retrieval method based on Gaussian filtering, which allows one to determine a convolution of the wave function with a known Gaussian function for the vacuum state from measured data of the Q function along only two parallel lines in phase space. By using a deconvolution process, the wave function is reconstructed from the convolution, provided that the resolution of the reconstructed wave function is limited by the extent of the Fourier transform of the Gaussian function. Numerical simulations demonstrate the applicability of this method to the reconstruction of the wave function from the Q function obtained from the photoelectric counting statistics in unbalanced homodyne detection.

In earlier classical, semiclassical, and quantum electrodynamical treatments of the Compton scattering in strong fields the strong component of the radiation remained unchanged or forward scattered during interaction with the electron. In our analysis, along with the Compton scattering of a single photon the simultaneous nonforward elastic scattering of the other photons of the intense radiation is also taken into account, resulting in changed kinematical relations that enable the electron to absorb or emit a larger amount of energy up to the ponderomotive energy, in agreement with the experimental results.

We show how it is possible to suppress decoherence using tailored external forcing acting as pulses. In the limit of infinitely frequent pulses decoherence and dissipation are completely frozen; however, a significant decoherence suppression is already obtained when the frequency of the pulses is of the order of the reservoir typical frequency scale. This method could be useful in particular to suppress the decoherence of the center-of-mass motion in ion traps.

In this paper the relativistic quantum mechanics (QM) is considered in the framework of the nonstandard synchronization scheme, which preserves the Poincaré covariance but (at least formally) distinguishes an inertial frame. This enables one to avoid the problem with a strong formulation of local causality related to the breaking of Bell’s inequalities in QM. Our analysis has been focused mainly on the problem of the existence of a proper position operator for massive particles. We have proved that in our framework such an operator exists for particles with arbitrary spin. This operator is Hermitian and covariant, it has commuting components, and its eigenvectors (localized states) are covariant too. We have found an explicit form of the position operator and demonstrated that it coincides with the Newton-Wigner one in the preferred frame. We have also defined a covariant spin operator and constructed an invariant spin squared operator. Moreover, full algebra of observables consisting of position, four-momentum, and spin operators is manifestly Poincaré covariant in this framework. Our results support expectations of other authors [J. S. Bell, in Quantum Gravity, edited by C. J. Isham, R. Penrose, and D. W. Sciama (Oxford University Press, Oxford, 1981), p. 611; P. H. Eberhard, Nuovo Cimento B 46, 392 (1978)] that a consistent formulation of quantum mechanics demands the existence of a preferred frame.

We identify what ideal correlated photon number states are required to maximize the discrepancy between local realism and quantum mechanics when a quadrature homodyne phase measurement is used. Various Bell-inequality tests are considered.

A method for generating two entangled macroscopic ensembles of atoms via interaction with Einstein-Podolsky-Rosen-correlated light is proposed. The method is directly applicable for creating entanglement between, e.g., two distant atom traps. The proposed special type of partial entanglement is analyzed.

We analyze the problem of distillation of entanglement of mixed states in higher-dimensional compound systems. Employing the positive maps method [M. Horodecki et al., Phys. Lett. A 223, 1 (1996)] we introduce and analyze a criterion of separability that relates the structures of the total density matrix and its reductions. We show that any state violating the criterion can be distilled by suitable generalization of the two-qubit protocol that distills any inseparable two-qubit state. In particular, this means that any state $\varrho$ of two N-level systems with $〈{\psi }_{+}|\varrho |{\psi }_{+}〉>1/N$ can be distilled $({\psi }_{+}$ is the singlet state generalized to higher dimension). The criterion also singles out all the states that can be distilled by a class of protocols. The proof involves construction of the family of states that are invariant under transformation $\overrightarrow{\varrho }U\otimes U^{*}\varrho U^{†}\otimes U^{*†},$ where U is a unitary transformation and the asterisk denotes complex conjugation. The states are related to the depolarizing channel generalized to the nonbinary case.