We investigate the experimental spectrum of excited NO molecules in the diamagnetic regime and develop a quantitative semiclassical framework to account for the results. We show the dynamics can be interpreted in terms of classical orbits provided that in addition to the geometric orbits, diffractive effects are appropriately taken into account. We also show how individual orbits can be extracted from the experimental signal and use this procedure to reveal the first experimental manifestation of inelastic diffractive orbits.

Do diffusive non-Markovian stochastic Schrödinger equations (SSEs) for open quantum systems have a physical interpretation? In a recent paper [Phys. Rev. A 66, 012108 (2002)] we investigated this question using the orthodox interpretation of quantum mechanics. We found that the solution of a non-Markovian SSE represents the state the system would be in at that time if a measurement was performed on the environment at that time, and yielded a particular result. However, the linking of solutions at different times to make a trajectory is, we concluded, a fiction. In this paper we investigate this question using the modal (hidden variable) interpretation of quantum mechanics. We find that the noise function $z\left(t\right)\mathrm{}$ appearing in the non-Markovian SSE can be interpreted as a hidden variable for the environment. That is, some chosen property (beable) of the environment has a definite value $z\left(t\right)\mathrm{}$ even in the absence of measurement on the environment. The non-Markovian SSE gives the evolution of the state of the system “conditioned” on this environment hidden variable. We present the theory for diffusive non-Markovian SSEs that have as their Markovian limit SSEs corresponding to homodyne and heterodyne detection, as well as one which has no Markovian limit.

We establish a mapping between a continuous-variable (CV) quantum system and a discrete quantum system of arbitrary dimension. This opens up the general possibility to perform any quantum information task with a CV system as if it were a discrete system. The Einstein-Podolsky-Rosen state is mapped onto the maximally entangled state in any finite-dimensional Hilbert space and thus can be considered as a universal resource of entanglement. An explicit example of the map and a proposal for its experimental realization are discussed.

The interaction between particles and the electromagnetic field induces decoherence generating a small suppression of fringes in an interference experiment. We show that if a double-slit-like experiment is performed in the vicinity of a conducting plane, the fringe visibility depends on the position (and orientation) of the experiment relative to the conductor’s plane. This phenomenon is due to the change in the structure of vacuum induced by the conductor and is closely related to the Casimir effect. We estimate the fringe visibility both for charged and for neutral particles with a permanent dipole moment. The presence of the conductor may tend to increase decoherence in some cases and to reduce it in others. A simple explanation for this peculiar behavior is presented.

The N-qubit states of the W class, for $N>\mathrm{}10,$ lead to more robust (against noise admixture) violations of local realism, than the Greenberger-Horne-Zeilinger (GHZ) states. These violations are most pronounced for correlations for a pair of qubits, conditioned on specific measurement results for the remaining $N-2$ qubits. The considerations provide us with a qualitative difference between the W state and GHZ state in the situation when they are separately sent via depolarizing channels. For sufficiently high amount of noise in the depolarizing channel, the GHZ states cannot produce a distillable state between two qubits, whereas the W states can still produce a distillable state in a similar situation.

We investigate the inverse problem concerning the evolution of a qubit system, specifically we consider how one can establish the Hamiltonians that account for the evolution of a qubit along a prescribed path in the projected Hilbert space. For a given path, there are infinite Hamiltonians which can realize the same evolution. A general form of the Hamiltonians is constructed in which one may select the desired one for implementing a prescribed evolution. This scheme can be generalized to higher dimensional systems.

The dynamics of a quantum system driven by an external field is well described by a unitary transformation generated by a time-dependent Hamiltonian. The inverse problem of finding the field that generates a specific unitary transformation is the subject of study. The unitary transformation which can represent an algorithm in a quantum computation is imposed on a subset of quantum states embedded in a larger Hilbert space. Optimal control theory is used to solve the inversion problem irrespective of the initial input state. A unified formalism based on the Krotov method is developed leading to a different scheme. The schemes are compared for the inversion of a two-qubit Fourier transform using as registers the vibrational levels of the $X{}^1{\Sigma }_g^{+}$ electronic state of ${\mathrm{Na}}_2.$ Raman-like transitions through the $A{}^1{\Sigma }_u^{+}$ electronic state induce the transitions. Light fields are found that are able to implement the Fourier transform within a picosecond time scale. Such fields can be obtained by pulse-shaping techniques of a femtosecond pulse. Of the schemes studied, the square modulus scheme converges fastest. A study of the implementation of the Q qubit Fourier transform in the ${\mathrm{Na}}_2$ molecule was carried out for up to five qubits. The classical computation effort required to obtain the algorithm with a given fidelity is estimated to scale exponentially with the number of levels. The observed moderate scaling of the pulse intensity with the number of qubits in the transformation is rationalized.

Energy denominators occurring in perturbation theory can be factorized if one writes them as exponentials using Laplace transformation. This idea is especially useful if weak interaction between large many-electron systems is to be described at many points in the configuration space. The expensive part of the calculation has to be performed only once, while the interaction at various geometrical arrangements is calculated by a simple site-site formula facilitating a linear scaling, $O\left(n\right)\mathrm{}$ technique. The interaction between the layers of a 300 Å long double-wall chiral nanotube is computed to illustrate the formalism. The results indicate a slight preference of heterochiral (6,4)@(11,9) double-wall nanotube as compared to the homochiral one.

A model has been proposed to investigate theoretically, the simultaneous electron capture and the ejection of another electron by which a bare hydrogen ion and a positronium atom (Ps) are produced in a single collision between a positron and a negative hydrogen ion $\left({\mathrm{H}}^{-}\right).\mathrm{}$ The angular distributions of the scattered Ps atom as well as of the ejected electron are studied in the intermediate- and high-energy regimes (40–200 eV) with respect to the threshold energy for this particular transfer ionization (TI) process. The electron-electron correlation effect that mainly governs such two-electron transition processes in this energy regime has been taken into account in both the initial and final channels. The long-range Coulomb attraction between the incident positron and the negative hydrogen ion in the initial channel has also been incorporated properly. Signature of the so-called Thomas peak (a double-peak structure) predicted for charge-transfer or transfer-ionization process for heavy-particle projectiles in the high-energy regime has also been noted in the present TI process (for light projectile $e^{+})$ and could be attributed to the correlated $e^{+}-e-e$ scattering mechanism. In addition, the fully differential (triple) cross sections for different kinematics reveal some structures unusual for a pure transfer or a pure ionization process which are to be verified by the future experiments.

In a recent paper [Phys. Rev. D 63, 111101 (2001)] we reported a new limit on CPT (charge, parity, and time reversal) and Lorentz violation of the proton by using a hydrogen maser to search for a sidereal variation of the $F=1,$ $\Delta m_F=\pm 1$ Zeeman frequency in atomic hydrogen. Here we discuss the theoretical interpretation of this recent experiment, the operating principles of the maser, and the double-resonance technique used to measure the Zeeman frequency. We also describe the characterization of systematic effects and details of the data analysis. We conclude by comparing our result to other recent experiments, and discussing potential improvements to the hydrogen maser double-resonance technique.

A linear 50-50 beam splitter, together with a coincidence measurement, has been widely used in quantum optical experiments, such as teleportation, dense coding, etc., for interferometrically distinguishing, measuring, or projecting onto one of the four two-photon polarization Bell states $|{\psi }^{\left(-\right)}〉.$ In this paper, we demonstrate that the coincidence measurement at the output of a beam splitter cannot be used as an absolute identifier of the input state $|{\psi }^{\left(-\right)}〉$ nor as an indication that the input photons have been projected to the $|{\psi }^{\left(-\right)}〉$ state.

We present the results of experimental and theoretical study of the scattering of low-energy $p\mu$ atoms in solid hydrogen cooled to 3 K. Strong effects resulting from the solid state interactions have been observed in the TRIUMF experiment E742 where muons were stopped in thin frozen layers of hydrogen. The resulting emission of low-energy $p\mu$ atoms from the hydrogen layer into the adjacent vacuum was much higher than that predicted by calculations which ignored the solid nature of the hydrogen. New differential scattering cross sections have been calculated for the collisions of $p\mu$ atoms on solid hydrogen to account for its quantum crystalline nature. Analysis of the experimental data performed using such cross sections shows the important role of the coherent scattering in $p\mu$ atom diffusion. For $p\mu$ energies lower than the Bragg cutoff limit $\left(\approx 2\mathrm{meV}\right)$ the elastic Bragg scattering vanishes which makes the total scattering cross section fall by several orders of magnitude, and thus the hydrogen target becomes transparent allowing the emission of cold $p\mu$ atoms to occur.

We show that in a four-level atomic system with electromagnetically induced transparency, a coherent pump field can induce light amplification without or with population inversion. As the pump field intensity increases, the atomic system evolves from normal dispersion and amplification without population inversion into anomalous dispersion and amplification with population inversion. We report an experiment on light amplification in cold rubidium atoms and present experimental measurements that agree with theoretical calculations based on the four-level model system.

We show that the two definitions of spin squeezing extensively used in the literature [M. Kitagawa and M. Ueda, Phys. Rev. A 47, 5138 (1993) and D.J. Wineland et al., Phys. Rev. A 50, 67 (1994)] give different predictions of entanglement in the two-atom Dicke system. We analyze differences between the definitions and show that the spin squeezing parameter of Kitagawa and Ueda is a better measure of entanglement than the commonly used spectroscopic spin squeezing parameter. We illustrate this relation by examining different examples of a driven two-atom Dicke system in which spin squeezing and entanglement arise dynamically. We give an explanation of the source of the difference using the negativity criterion for entanglement.

We show here that the $\Lambda$ and V configurations of three-level atomic systems, while they have recently been shown to be equivalent for many important physical quantities when driven with classical fields [M. B. Plenio, Phys. Rev. A 62, 015802 (2000)], are no longer equivalent when coupled via a quantum field. We analyze the physical origin of such behavior and show how the equivalence between these two configurations emerges in the semiclassical limit.

Recently, entanglement concentrations have been experimentaly demonstrated by postselection [T. Yamamoto et al., Nature (London) 421, 343 (2003), and Z. Zhao et al., Phys. Rev. Lett. 90, 207901 (2003)], i.e., to each individual outcome state, one has to destroy it to know whether it has been purified. Here we give proposal for entanglement concentration without any postselection by using only practically existing linear optical devices. In particular, a sophisticated photon detector to distinguish one photon or two photons is not required.

We compute the shift of the transition temperature for a homogeneous weakly interacting Bose gas in leading order in the scattering length a for given particle density n. Using variational perturbation theory through six loops in a classical three-dimensional scalar field theory, we obtain $\Delta T_c{/T}_c=1.25\mathrm{}\pm {0.13an}^{1/3},$ in agreement with recent Monte Carlo results.

To reproduce in a local hidden variables theory correlations that violate Bell inequalities, communication must occur between the parties. We show that the amount of violation of a Bell inequality imposes a lower bound on the average communication needed to produce these correlations. Moreover, for every probability distribution there exists an optimal inequality for which the degree of violation gives the minimal average communication. As an example, to produce using classical resources the correlations that maximally violate the Clauser-Horne-Shimony-Holt inequality, $\sqrt{2}-1\simeq 0.4142$ bits of communication are necessary and sufficient. For Bell tests performed on two entangled states of dimension $d>~3$ where each party has the choice between two measurements, our results suggest that more communication is needed to simulate outcomes obtained from certain nonmaximally entangled states than maximally entangled ones.

Quantum-classical correspondence in conservative chaotic Hamiltonian systems is examined using a uniform structure measure for quantal and classical phase-space distribution functions. The similarities and differences between quantum and classical time-evolving distribution functions are exposed by both analytical and numerical means. The quantum-classical correspondence of low-order statistical moments is also studied. The results shed considerable light on quantum-classical correspondence.

We extend the concept of negativity, a good measure of entanglement for bipartite pure states, to mixed states by means of the convex-roof extension. We show that the measure does not increase under local quantum operations and classical communication, and derive explicit formulas for the entanglement measure of isotropic states and Werner states, applying the formalism presented by Vollbrecht and Werner [Phys. Rev. A 64, 062307 (2001)].