An effective interaction between fermions in a Bose-Fermi mixture is derived. It is induced by density fluctuations of the bosonic background. The contributions from states containing both one and two virtual phonons are taken into account self-consistently. The time dependence of the effective interaction has been removed by assuming that the velocity of the fermions at the Fermi surface is much larger than the sound velocity in the Bose gas. This assumption is more appropriate for the actual experimental situations than the usual approximation of neglecting retardation effects. The effective interaction turns out to be attractive and, as a consequence, can give rise to a superconducting phase in the Fermi component of the mixture. The fermions are considered in only one magnetic state, so that pairing can be effective only in odd-$l$ channels. It has been found that the onset of the superconducting phase can occur at temperatures $(>\mathrm{}100\mathrm{}\mathrm{nK})$ of the same order of magnitude as the Fermi temperature $\left(\sim 300\mathrm{nK}\right),$ and the energy gap in the excitation spectrum is a small fraction $(\sim 1\%)$ of the Fermi energy.

We develop a theoretical model of two-photon amplification in laser-driven potassium atoms and use it to analyze the recent experiments reported by Pfister et al. [Phys. Rev. A 60, R4249 (1999)]. The model takes into account most of the essential factors influencing the amplification process, including the atomic hyperfine structure (which makes multiphoton emission possible) and the simultaneous interaction with intense drive and probe beams with arbitrary detunings. We determine the origin and analyze the properties of different multiphoton gain resonances that appear in the light-matter interaction. In particular, the influence of the drive and probe field amplitudes and detunings on the strength and frequency of the two-photon amplification resonance is studied in detail, showing clearly the differences with respect to the behavior of single-photon or other multiphoton amplification processes. In addition, we investigate interferences between different quantum pathways originating from the hyperfine structure and determine the conditions under which they can enhance or suppress multiphoton resonances. The predictions of the model are in good agreement with the observations, indicating that it can be used to understand recent experiments on two-photon lasing reported by Pfister et al. [Phys. Rev. Lett. 86, 4512 (2001)].

The concept of off-diagonal geometric phases for mixed quantal states in unitary evolution is developed. We show that these phases arise from three basic ideas: (1) fulfillment of quantum parallel transport of a complete basis, (2) a concept of mixed-state orthogonality adapted to unitary evolution, and (3) a normalization condition. We provide a method for computing the off-diagonal mixed-state phases to any order for unitarities that divide the parallel transported basis of Hilbert space into two parts: one part where each basis vector undergoes cyclic evolution and one part where all basis vectors are permuted among each other. We also demonstrate a purification based experimental procedure for the two lowest-order mixed-state phases and consider a physical scenario for a full characterization of the qubit mixed-state geometric phases in terms of polarization-entangled photon pairs. An alternative second order off-diagonal mixed-state geometric phase, which can be tested in single-particle experiments, is proposed.

Quantum operations (QO’s) describe any state change allowed in quantum mechanics, such as the evolution of an open system or the state change due to a measurement. We address the problem of which unitary transformations and which observables can be used to achieve a QO with generally different input and output Hilbert spaces. We classify all unitary extensions of a QO and give explicit realizations in terms of free-evolution direct-sum dilations and interacting tensor-product dilations. In terms of Hilbert space dimensionality the free-evolution dilations minimize the physical resources needed to realize the QO, and for this case we provide bounds for the dimension of the ancilla space versus the rank of the QO. The interacting dilations on the other hand, correspond to the customary ancilla-system interaction realization, and for these we derive a majorization relation which selects the allowed unitary interactions between system and ancilla.

We examine various manipulations of photon number states which can be implemented by teleportation technique with number-sum measurement. The preparations of the Einstein-Podolsky-Rosen resources as well as the number-sum measurement resulting in projection to certain Bell state may be done conditionally with linear optical elements, i.e., beam splitters, phase shifters, and zero-one-photon detectors. Squeezed vacuum states are used as primary entanglement resource, while single-photon sources are not required.

We propose a universal scheme for the probabilistic generation of an arbitrary multimode entangled state of light with finite expansion in Fock basis. The suggested setup involves passive linear optics, single-photon sources, strong coherent laser beams, and photodetectors with single-photon resolution. The efficiency of this setup may be greatly enhanced if, in addition, a quantum memory is available.

State representations summarize our knowledge about a system. When unobservable quantities are introduced the state representation is typically no longer unique. However, this nonuniqueness does not affect subsequent inferences based on any observable data. We demonstrate that the inference-free subspace may be extracted whenever the quantity’s unobservability is guaranteed by a global conservation law. This result can generalize even without such a guarantee. In particular, we examine the coherent-state representation of a laser, where the absolute phase of the electromagnetic field is believed to be unobservable. We show that experimental coherent states may be separated from the inference-free subspaces induced by this unobservable phase. These physical states may then be approximated by coherent states in a relative-phase Hilbert space.

We address the problem of finding optimal CPTP (completely positive trace-preserving) maps between a set of binary pure states and another set of binary generic mixed state in a two-dimensional space. The necessary and sufficient conditions for the existence of such CPTP maps can be discussed within a simple geometrical picture. We exploit this analysis to show the existence of an optimal quantum repeater which is superior to the known repeating strategies for a set of coherent states sent through a lossy quantum channel. We also show that the geometrical formulation of the CPTP mapping conditions can be a simpler method to derive a state-dependent quantum (anti) cloning machine than the study so far based on the explicit solution of several constraints imposed by unitarity in an extended Hilbert space.

In collisions of heavy few-electron projectile ions with light targets, an electron can be transferred from the target with the simultaneous excitation of a projectile electron. We study the angular distribution of deexcitation x rays following the resonant capture process. Our results are compared to experimental values of Ma et al. [Phys. Rev. A 68, 042712 (2003)] for collisions of ${\mathrm{U}}^{91+}$ ions with a hydrogen gas target.

Electron-electron interaction is studied in the strongest possible atomic fields $\left(Z\alpha \Rightarrow 1\right)$ in the presence of only two electrons. A quasifree electron from a hydrogen gas target is resonantly captured into an $L_j$ subshell of a fast H-like ${\mathrm{U}}^{91+}$ ion by simultaneous excitation of the strongly bound $K$ electron also into an $L_{j^{\prime }}$ subshell of the projectile, with $j$ and $j^{\prime }$ the total angular momenta of 1/2 or 3/2 for the electron of concern. This resonant transfer and excitation process (RTE) ${\mathrm{KL}}_j{L}_{j^{\prime }}$ is mediated by electron-electron interaction. It is equivalent to dielectronic recombination in ion-electron collisions and leads to a doubly excited He-like ${\mathrm{U}}^{90+**}$ ion, which stabilizes—almost exclusively—via the emission of two successive $K$ x rays, first a $K$ hypersatellite $(K{\alpha }_i-H)$ and then a $K$ satellite $(K{\alpha }_{i^{\prime }}-S)$ transition. The $K$ x-ray emission characteristics associated with one-electron capture in collisions of ${\mathrm{U}}^{91+}$ ions with a hydrogen target are studied for the three resonance groups of the ${\mathrm{KL}}_j{L}_{j^{\prime }}$ RTE and one off-resonance energy, i.e., in the energy range between 100 and 135 MeV/u. The total cross section for the first resonance group ${\mathrm{KL}}_{1/2}{L}_{1/2}$ confirms the importance of the Breit contribution to the interaction. The angular distribution for the $K{\alpha }_2-H$ transition $\mathrm{}(j=1/2\mathrm{})\mathrm{}$ is isotropic in the projectile system, whereas the $K{\alpha }_1-H$ transition $\mathrm{}(j=3/2\mathrm{})\mathrm{}$ indicates a strong alignment for the 3/2 electrons in the doubly excited states for the second resonance group ${\mathrm{KL}}_{1/2}{L}_{3/2}.$ The experimental results are in agreement with fully relativistic calculations including the generalized Breit interaction.

Photodetachment cross sections have been calculated for the $5p,$ $4d,$ and $4p$ subshells of the negative iodide ion, ${\mathrm{I}}^{-},$ in the relativistic random-phase approximation (RRPA) and modifications of the RRPA that allow for the inclusion of relaxation and core-polarization effects. Total and partial photodetachment cross sections are compared with experimental measurements to gauge the effectiveness of the various approximations. Branching ratios and photoelectron angular-distribution asymmetry parameters are also presented. Core-polarization effects are found to partially cancel relaxation effects.

Absolute cross sections for electron-impact dissociation of ${\mathrm{CH}}^{+}$ producing ${\mathrm{C}}^{+}$ fragment ions were measured in the 3–100 eV range using a crossed electron-ion beams technique with total uncertainties of about 10% near the cross-section peak. Although the measured energy dependence agrees well with two sets of storage ring measurements, the magnitude of the present results lies about 15–25 % below the other results at the cross-section peak near 40 eV. Below 10 eV, the present data tend to exceed the storage ring data, consistent with the presence of excited states in the ${\mathrm{CH}}^{+}$ ion beam. For energies above 29 eV, the cross sections should also include contributions from dissociative ionization, though no clear onset of this channel is evident in any of the three sets of measured data.

Experimental results for manganese $3\overrightarrow{s}2p$ photon emission in ${\mathrm{MnF}}_2$ that occurs after resonant and nonresonant production of a $2p$ hole are presented. Transitions that involve a change in the spin of the ${3d}^5$ subshell are observed and identified. Results of a free-ion calculation that includes the effect of the interaction between the configurations with a single $3s$ hole and two $3p$ holes in the final state is also given. Good overall agreement is found between the experiment and the calculation. This comparison allows a direct interpretation of the absorption spectrum, the Raman emission spectra, and the normal or nondispersive fluorescence spectrum in terms of well-defined ionic states. Spin-changing transitions in both absorption and emission are identified, and their intensities relative to the spin-conserving transitions are found to be well predicted by theory.

Pair annihilation in the elementary process of positron ${(e}^{+})$ collisions with atoms is discussed in terms of an imaginary, absorption potential. This potential represents the QED effect of both direct annihilation during the collision and the indirect one via positronium (Ps) formation in a unified manner. These two mechanisms are inseparable from each other near the threshold for positronium formation, where the collision time becomes comparable to or even longer than the lifetime of the positronium. The theory is applied to the $e^{+}$-H collisions. The dominant s-wave annihilation cross section follows the Baz’ threshold law near the thresholds $E_{\mathrm{th}}\left(1s{}^{1,3}S\right)$ for the formation of $\mathrm{Ps}\left(1s{}^{1,3}S\right).\mathrm{}$ Simple relations between the singlet and triplet cross sections are derived. The spin-averaged annihilation cross section rises sharply but continuously, first across $E_{\mathrm{th}}\left(1s{}^{1}S\right),$ and then across $E_{\mathrm{th}}\left(1s{}^{3}S\right),$ which lies at 0.841 meV above $E_{\mathrm{th}}\left(1s{}^{1}S\right).\mathrm{}$ The cross section would diverge at $E_{\mathrm{th}}\left(1s{}^{1}S\right)$ and $E_{\mathrm{th}}\left(1s{}^{3}S\right)$ in the conventional theory where Ps is assumed to have an infinite lifetime. The change of the annihilation probability as the Ps leaves ${\mathrm{H}}^{+},$ is studied by decomposing it into the contributions from direct and indirect annihilation and from the interference between them.

The effect of nonadiabatic couplings on low-energy s-wave scattering of two hydrogen atoms is investigated. Coupling matrix elements are computed in a wide range of internuclear distances. The resulting scattering equations are numerically unstable and therefore are integrated only approximately. Computations are performed for H, D, and T atoms. The phase shifts in the zero velocity limit are inversely proportional to the nuclear reduced mass ${\delta }_0\approx 0.392/\mu .$ This leads to infinite scattering lengths.

Recently, Porter observed [L.E. Porter, Int. J. Quantum Chem. 90, 684 (2002)] that the mean excitation energy and stopping cross section of a target, obtained from fitting experimental data at given projectile charge to a modified Bethe-Block theory, gives projectile dependent results. The main result of his work is that there is a trend for the inferred target mean excitation energy, to decrease as the projectile atomic number increases. However, this result is inconsistent with the usual definition of the mean excitation energy as a function of target excitation properties only. Here we present an explanation of Porter’s results based on the Bethe theory extended to take projectile electronic structure explicitly into account.

The energy straggling of proton beams in ${\mathrm{SiO}}_2$ has been measured in the energy range from 30 to 1500 keV using the transmission, nuclear reaction analysis and Rutherford backscattering techniques. The experimental results are compared with theoretical models. We observe that at energies around 200 keV the values obtained are larger than theoretical estimations. The straggling effect produced by the electron bunching in molecular media was calculated and it was found to be a possible cause of these differences at intermediate energies.

Bosonic atoms trapped in an optical lattice at very low temperatures can be modeled by the Bose-Hubbard model. In this paper, we propose a slave-boson approach for dealing with the Bose-Hubbard model, which enables us to analytically describe the physics of this model at nonzero temperatures. With our approach the phase diagram for this model at nonzero temperatures can be quantified.

Here we analyze the practical implications of using Bell states produced through optical down-conversion in a quantum-data-hiding protocol. We show that the uncertainty in the production of Bell states through spontaneous parametric down-conversion should be taken into account, because it will cause difficulties for the encoding procedure. A set of extended Bell states and a generalized Bell-state analyzer are proposed to describe and analyze the possible states of two photons distributed in two paths. Then we present a method to integrate the above uncertainty of Bell-state preparation into the data-hiding procedure, when we encode the secret with the set of extended Bell states. These modifications greatly simplify the hider’s encoding operations, and thus pave the way for the implementation of quantum data hiding with present-day quantum optics.