The influence of boson-boson and boson-fermion interactions on the stability of a binary mixture of bosonic and fermionic atoms is investigated. The density profiles of the trapped mixture are obtained from direct numerical solution of a modified Gross-Pitaevskii equation that is self-consistently coupled to the mean field generated by the interaction with the fermionic species, the fermions which in turn feel the mean field created by the bosons are treated in the Thomas-Fermi approximation. We study the effects of different combinations of signs of the boson-boson and the boson-fermion scattering lengths and determine explicit expressions for critical particle numbers as a function of these scattering lengths.

We report the magnetic trapping and evaporative cooling of bosonic and fermionic isotopes of atomic chromium. Using a cryogenic helium buffer gas, ${10}^{12}$ chromium atoms are trapped at an initial temperature of ∼1 K. The chromium atoms are then cooled adiabatically and evaporatively to temperatures as low as ∼10 mK. Elastic and inelastic ${}^{52}\mathrm{Cr}$ collisional cross sections are measured over this temperature range. Prospects for simultaneously creating a ${}^{52}\mathrm{Cr}$ Bose-Einstein condensate and ${}^{53}\mathrm{Cr}$ Fermi degenerate gas will be discussed.

We analyze the structure of the Coulomb and unitarity corrections to the single $e^{+}{e}^{-}$ pair production, as well as the cross section ${\sigma }_n$ for the multiple pair production in collision of ultra-relativistic nuclei. In the external field approximation, we consider the probability of one pair production at a fixed impact parameter $\rho$ between colliding nuclei. We obtain the analytical result for this probability at large $\rho$ as compared to the electron Compton wavelength. The energy dependence of this probability, as well as that of ${\sigma }_n,$ differ essentially from widely cited but incorrect results. We estimate also the unitary corrections to the total cross section of the process.

The one-time and two-time measurements are studied by employing the idea of Aharonov et al. that the strength of a measurement depends on the state of the measuring device in the context of von Neumann measurement theory. A measurement is classified as either a strong or a weak measurement depending on whether the interaction between the system and the measuring device is infinitely large or negligibly small. A single strong measurement yields one of the eigenvalues of the operator while a single weak measurement, in addition to the eigenvalues, has infinite other possible outcomes. Nevertheless, the expectation values of the strong and the weak one-time measurements are the same. However, the expectation values of the two-time measurements depend on the strength of the first measurement. For the strong case the result is consistent with the conventional result without having to introduce the state collapsing. For the weak case the result is the real part of the expectation value of the time-ordered two-time operator. The fact that this expectation value cannot be factorized indicates that the entanglement between the system and the measuring device introduced by a weak measurement cannot be neglected.

Recently, Badziag et al. [Phys. Rev. A 62, 012311 (2000)] obtained a class of noisy states whose teleportation fidelity can be enhanced by subjecting one of the qubits to dissipative interaction with the environment via an amplitude damping channel (ADC). We show that such noisy states result while sharing the states $|{\Phi }^{\pm }〉=1/\sqrt{2}(|00〉\pm |11〉)$ across the ADC. We also show that under similar dissipative interactions, different Bell states give rise to noisy entangled states that are qualitatively very different from each other in the sense that only the noisy entangled states constructed from the Bell states $|{\Phi }^{\pm }〉$ can sometimes be made better by subjecting the unaffected qubit to a dissipative interaction with the environment. Importantly, if the noisy state is nonteleporting, then it can always be made teleporting with this prescription. We derive the most general restrictions on improvement of such noisy states assuming that the damping parameters are different for both qubits. However, this curious prescription does not work for the noisy entangled states generated from $|{\Psi }^{\pm }〉=1/\sqrt{2}(|01〉\pm |10〉).\mathrm{}$ This shows that an a priori knowledge of the noisy channel might be helpful in order to decide which Bell state needs to be shared between Alice and Bob.

If an experimentalist wants to decide which one of n possible Hamiltonians acting on an n-dimensional Hilbert space is present, he can conjugate the time evolution by an appropriate sequence of known unitary transformations in such a way that the different Hamiltonians result in mutual orthogonal final states. We present a general scheme providing an approximation for such a sequence.

Dense coding or superdense coding in the case of high-dimension quantum states between two parties and multiparties is studied in this paper. We construct explicitly the measurement basis and the forms of the single-body unitary operations corresponding to the basis chosen, and the rules for selecting the one-body unitary operations in a multiparty case.

In the Bayesian approach to probability theory, probability quantifies a degree of belief for a single trial, without any a priori connection to limiting frequencies. In this paper, we show that, despite being prescribed by a fundamental law, probabilities for individual quantum systems can be understood within the Bayesian approach. We argue that the distinction between classical and quantum probabilities lies not in their definition, but in the nature of the information they encode. In the classical world, maximal information about a physical system is complete in the sense of providing definite answers for all possible questions that can be asked of the system. In the quantum world, maximal information is not complete and cannot be completed. Using this distinction, we show that any Bayesian probability assignment in quantum mechanics must have the form of the quantum probability rule, that maximal information about a quantum system leads to a unique quantum-state assignment, and that quantum theory provides a stronger connection between probability and measured frequency than can be justified classically. Finally, we give a Bayesian formulation of quantum-state tomography.

We consider a slightly modified version of the rock-scissors-paper (RSP) game from the point of view of evolutionary stability. In its classical version the game has a mixed Nash equilibrium (NE) not stable against mutants appearing in small numbers. We find a quantized version of the RSP game for which the classical mixed NE becomes stable.

We study the mutual catalysis of entanglement transformations, which refers to the fact that each of the two entanglement transformations cannot occur with certainty by local operations and classical communication independently, but both can occur jointly if collective local operations are performed on both of the initial entangled states. We surprisingly find that mutually catalyzed transformations can be realized even in the case when the standard entanglement catalyzed transformations [D. Jonathan and M. B. Plenio, Phys. Rev. Lett. 83, 3566 (1999)] are forbidden.

The quantum nature of the laser fields used in many proposed schemes for the manipulation of quantum information may have important consequences for some very large scale quantum computations. Some of these consequences are explored here, focusing especially on phase errors and their effects on error-correction schemes. Depending on the way the logical gates are performed, constraints are found on either the required number of photons per coherence time put out by the laser source, or the source’s power

A method is proposed to employ entangled and squeezed light for determining the position of a party and for synchronizing distant clocks. An accuracy gain over analogous protocols that employ classical resources is demonstrated and a quantum-cryptographic positioning application is given, which allows only trusted parties to learn the position of whatever must be localized. The presence of a lossy channel and imperfect photodetection is considered. The advantages in using partially entangled states is discussed.

The dynamic correlation model was used to calculate nuclear ground-state wave functions of ${}^{203}\mathrm{Tl},$ ${}^{205}\mathrm{Tl},$ and ${}^{207}\mathrm{Tl}.$ The ground states of these isotopes are characterized by strong mixing amplitudes of the valence ${3s}_{1/2}^{-1}$ hole with the intrinsic vacuum states (valence hole coupled to core excitations). Nuclear magnetic moments, radii, and the $1s$ hyperfine-structure splitting energy for the hydrogenlike ions were calculated. Experimental magnetic moments and radii of the nuclear ground states are well reproduced. The hyperfine-structure splitting of the hydrogenlike Tl isotopes have not been measured so far, hence, the obtained values are only compared with predictions of other theoretical calculations. The difference in the $1s$ hyperfine-structure splitting between ${}^{203}{\mathrm{Tl}}^{80+}$ and ${}^{205}{\mathrm{Tl}}^{80+}$ is found to be 0.026 eV, which corresponds to a 3.1 nm shift in the transiton wavelength.

In this paper, we present an alternative way to build the effective one-electron picture of a many-atom interacting system. By simplifying the many-body general problem we present two different options for the bond-pair model Hamiltonian. We have found that the successive approximations in order to achieve the effective description have a dramatic influence on the result. Thus, only the model that introduces the correct renormalization in the diagonal term due to the overlap is able to reproduce, even in a quantitative fashion, the main properties of simple homonuclear diatomic molecules. The success of the model resides in the accurate definitions (free of parametrization) of the Hamiltonian terms, which, therefore, could be used to describe more complex interacting systems such as polyatomic molecules, adsorbed species, or atoms scattered by a surface.

The contribution of toroidal moments to the spontaneous electric emission in a continuous homogeneous nonabsorbing condensed medium is calculated. The probability of toroidal emission of multipolarity L depends on dielectric and magnetic constants as $f_L^2\left(\epsilon \right){\epsilon }^{L+3/2\mathrm{}}{\mu }^{L+5/2\mathrm{}},$ where $f_L\left(\epsilon \right)$ is the local-field factor. The linear refractive-index dependence of the spontaneous emission probability for electric-dipole transitions in dielectrics in the real cavity model transforms to an $n^5$ dependence in the range $n\gtrsim 1/\omega a_B.$

We present measured and calculated differential cross sections, as well as calculated integral cross sections, for elastic electron collisions with ${\mathrm{CH}}_3\mathrm{F},$ ${\mathrm{CH}}_2{\mathrm{F}}_2,$ ${\mathrm{CHF}}_3,$ and ${\mathrm{CF}}_4.$ The calculated cross sections were obtained with the Schwinger multichannel method, and a Born-closure procedure was used to improve the differential cross sections for polar systems. Polarization effects were found to be relevant even for systems with moderately large permanent dipole moments, such as ${\mathrm{CH}}_3\mathrm{F}$ and ${\mathrm{CHF}}_3.$ In general, there is good agreement between theory and experiment.

An analytical expression for the classical form factor or impulsive probability $P_{\mathrm{if}}\left(\mathbf{q}\right)$ for $\mathrm{nl}\overrightarrow{m}{n}^{\prime }{l}^{\prime }m$ transitions is derived directly from the “phase-space distribution” method [Phys. Rev. A 60, 1053 (1999)] and is compared with quantal results. Exact universal scaling laws are derived for the classical probability for any $\overrightarrow{i}f$ transition. As n is increased, convergence of the quantal to classical results is obtained and it becomes even more rapid upon averaging in succession over the m and then the $\mathit{l}$ substates. The classical results reveal the basic reason for the underlying structure in the variation of $P_{\mathrm{if}}$ with momentum transfer $\mathbf{q}.$ Classical form factors can operate as an effective averaged version of the exact quantal counterpart.

The stochastic variational method is used in conjunction with stabilization ideas to compute the low-energy s-wave phase shifts and scattering lengths for Ps-Ps scattering. The scattering lengths obtained were ${8.44a}_0$ for the singlet-singlet and ${3.00a}_0$ for the triplet-triplet states (the spin state refers to the coupling of the two electrons and the coupling of the two positrons in the system). The positive scattering length in the triplet-triplet channel means a stable Bose-Einstein condensate of triplet Ps atoms is physically possible. The large value of the ${}^3{\mathrm{Ps}}^3{\overrightarrow{\mathrm{Ps}}}^1{\mathrm{Ps}}^1\mathrm{Ps}$ cross section, $7.41\pi a_0^2$ suggests the use of spin-polarized positrons as advanced by Platzmann and Mills [Phys. Rev. B 49 454 (1994)].

For ions that impinge grazing on solid surfaces, binary collisions with the free-electron gas are investigated by means of a modified specular-reflection (MSR) model. The proposed MSR theory is applied to the calculation of the energy lost by fast protons after colliding with an aluminum surface. We also employ the MSR binary theory to study the energy spectra of the emitted electrons. The contribution coming from atomic inner shells, calculated with the continuum-distorted-wake–eikonal-initial-state approximation, is added to the emission probability from the valence band. The total results obtained with the MSR model are in reasonable agreement with available experimental data for 100 keV protons and large ejection angles of the electron. In contrast instead, the usual specular-reflection binary model shows a prominent structure at low electron energies, which greatly overstimates the experimental spectrum.

The capture by polarization forces of low-energy electrons by closed-shell sodium clusters has been studied in the framework of the time-dependent local density approximation within the spherical jellium model and the classical scattering theory of Langevin. Results for ${\mathrm{Na}}_{20},{\mathrm{Na}}_{40},$ and ${\mathrm{Na}}_{58}$ are compared with the predictions of the classical image charge model and recent experimental results by Kasperovich et al. [Phys. Rev. A 60, 3071 (1999)].