A quantum-mechanical approach is proposed for the formation of antihydrogen $\left(\overline{H}\right)$ in the ground and excited states $(2s,2p)$ via the mechanism of three-body recombination (TBR) inside a trapped plasma of antiprotons $\left(\overline{p}\right)$ and positrons $\left(e^{+}\right)$ or in the collision between the two beams of them. Variations of the differential as well as the total formation cross sections are studied as a function of the incident energies of both the active and the spectator $e^{+}$’s. Significantly large cross sections are found at very low incident energies in the TBR process as compared to other processes leading to antihydrogen. The present $\left(\overline{H}\right)$ formation cross section decreases with increasing positron energy (temperature) but no simple power law could be predicted for it covering the entire energy range $(\sim 5–50\mathrm{eV})$, corroborating the experimental findings qualitatively, the latter being at a much lower energy regime $(\sim {10}^{-4}\mathrm{eV})$. The formation cross sections are found to be much higher for unequal energies of the two $e^{+}$’s than for equal energies, as expected physically.

The interactions between atoms and molecules with each other and with surfaces are typically deep potential wells with attractive tails behaving asymptotically as an inverse power of the distance. In such potential wells, bound state energies $E_n$ are determined by a quantization function $F\left(E\right)$ according to $n_{\mathrm{th}}-n=F\left(E_n\right)$, and $F\left(E\right)$ is dominantly determined by the singular potential tail for near-threshold states. In this paper we formulate a general theory for the contribution $F_{\text{tail}}\left(E\right)$ of the singular potential tail to the quantization function. The general expression for $F_{\text{tail}}\left(E\right)$ contains two terms: a difference of action integrals and a difference of outer reflection phases, taken at threshold and at energy $E$. Close to threshold, $E=0$, strongly energy dependent and nonanalytic contributions of both terms cancel, so $F_{\text{tail}}\left(E\right)$ acquires a universal form determined by a threshold length and an effective length which is related to a subthreshold effective range. For a homogeneous potential tail proportional to $-1∕r^{\alpha }$, one universal expression for $F_{\text{tail}}\left(E\right)$ caters for all potential strengths. We give an explicit analytical expression for the important case $\alpha =6$ and present applications involving the derivation of atom-atom scattering lengths from the binding energies of high-lying bound states of the associated diatomic molecule. We also demonstrate how the dissociation energy of a diatomic molecule can be determined from spectroscopic energies of high-lying states, and we make a quantitative comparison with the performance of the LeRoy-Bernstein formula, which fails near threshold, because the strongly energy dependent and nonanalytic contribution from the action integrals is not, as it should be, compensated by terms coming from the corresponding energy dependence of the outer reflection phase.

We establish a theory for making predictions of the state of a physical system during a few-cycle femtosecond pulse. We show by the example of fully converged ab initio calculations of ionization of atoms that the abruptness of the attosecond pulses implies that special care must be exercised in the modeling of the electromagnetic field and vector potential of the femtosecond pulse. In the dipole approximation we show that the correct desription of the physical state of the system is obtained directly with the length gauge Hamiltonian. In the velocity gauge the correct description is obtained by shifting the vector potential appropriately. We point out that the sub-femtosecond dynamics as revealed by the laser-driven recolliding electron or an attosecond pump beam is analogous to a time-domain Aharonov-Bohm effect.

We study in detail the appearance of the phenomenon of resonant transmission of matter waves (cold noninteracting atoms) through subwavelength apertures. We show how the emergence of this effect, first reported for electromagnetic waves, is associated with the excitation of surface matter waves, the analog of surface plasmon polaritons in the electromagnetic case. We describe the similarities and differences for the one-dimensional (array of slits) and two-dimensional (array of holes) cases. In this last structure, extraordinary transmission of matter waves is theoretically predicted. Finally, we also study the existence of the beaming effect for matter waves in single apertures flanked by periodic corrugations.

The first- and second-order correlation functions of trapped interacting Bose-Einstein condensates are investigated numerically on a many-body level from first principles. Correlations in real space and momentum space are treated. The coherence properties are analyzed. The results are obtained by solving the many-body Schrödinger equation. It is shown in an example how many-body effects can be induced by the trap geometry. A generic fragmentation scenario of a condensate is considered. The correlation functions are discussed along a pathway from a single condensate to a fragmented condensate. It is shown that strong correlations can arise from the geometry of the trap, even at weak interaction strengths. The natural orbitals and natural geminals of the system are obtained and discussed. It is shown how the fragmentation of the condensate can be understood in terms of its natural geminals. The many-body results are compared to those of mean-field theory. The best solution within mean-field theory is obtained. The limits in which mean-field theories are valid are determined. In these limits the behavior of the correlation functions is explained within an analytical model.

A transparent periodic structure consisting of metamaterial (double negative) layers and matching (single negative material) layers is presented. Through the calculation of the band structure and transmission spectrum, this kind of structure is found to be omnidirectionally transparent to some electromagnetic wave of any polarization. The working frequency and bandwidth can be adjusted by changing the thicknesses of material layers.

We develop a thorough connection between visibility, coherence, and phase statistics for $N$-dimensional quantum systems and $N$ classical waves.

We study the class of discrete Wigner functions proposed by Gibbons et al. [Phys. Rev. A 70, 062101 (2004)] to describe quantum states using a discrete phase space based on finite fields. We find the extrema of such functions for small Hilbert-space dimensions and present a quantum-information application: a construction of quantum random-access codes. These are constructed using the complete set of phase-space point operators to find encoding states and to obtain the codes’ average success rates for Hilbert-space dimensions 2, 3, 4, 5, 7, and 8.

Schumacher and Westmoreland [Phys. Rev. A 64, 42304 (2001)] have established a quantum analog of a well-known classical information theory result on a role of relative entropy as a measure of nonoptimality in (classical) data compression. In this paper, we provide an alternative simple and constructive proof of this result by constructing quantum compression codes (schemes) from classical data compression codes. Moreover, as the quantum data compression or coding task can be effectively reduced to a (quasi)classical one, we show that relevant results from classical information theory and data compression become applicable and therefore can be extended to the quantum domain.

We present a simple protocol to purify bipartite entanglement in spin-$1∕2$ particles by utilizing only natural spin-spin interactions, i.e., those that can commonly be realized in realistic physical systems and $S_z$ measurements on single spins. Even the standard isotropic Heisenberg interaction is shown to be sufficient to purify mixed state entanglement. Our protocol does not need controlled-NOT (CNOT) gates that are very hard to implement experimentally. This approach could be useful for quantum-information processing in solid-state-based systems.

We present a general and exact formalism for finding the evolution of a quantum system subject to external telegraph noise. The various qubit decoherence rates are determined by the eigenvalues of a transfer matrix. The formalism can be applied to a qubit subject to an arbitrary combination of dephasing and relaxational telegraph noise, in contrast to existing nonperturbative methods that treat only one or the other of these limits. Hence we are able to investigate the crossover from pure dephasing noise to pure relaxational noise in detail. New results at strong coupling include the full qubit dynamics on time scales short compared with the environmental correlation times, which reveals unexpected oscillations and induced magnetization components and strong violations of the widely used relation $1∕T_2=1∕2T_1+1∕T_{\varphi },$ which is a result of perturbation theory. We also discuss the effects of bang-bang and spin-echo controls of the qubit dynamics in general settings of the telegraph noises. Finally, we discuss the extension of the method to the cases of many telegraph noise sources and multiple qubits. The method still works when white noise is also present.

In many cases, density-functional theory (DFT) with current standard approximate functionals offers a relatively accurate and computationally cheap description of the short-range dynamic electron correlation effects. However, in general, standard DFT does not treat the dispersion interaction effects adequately which, on the other hand, can be described by many-body perturbation theory (MBPT). It is therefore of interest to develop a hybrid model which combines the best of both the MBPT and DFT approaches. This can be achieved by splitting the two-electron interaction into long-range and short-range parts; the long-range part is then treated by MBPT and the short-range part by DFT. This work deals with the formulation of a general MBPT-DFT model (i.e., valid for any type of zeroth-order Hamiltonian) based on such a range separation. Applying the Rayleigh-Schrödinger formalism in this context, one finds that the generalized Bloch equation becomes self-consistent at each order of perturbation. This complication arises because the short-range part of the energy is a functional of the exact electron density, which is expanded in a perturbation series. In order to address this “self-consistency problem” and provide computable orbital-based expressions for any order of perturbation, a general one-electron reduced-density-matrix-based formalism is proposed. Two applications of our general formalism are presented: The derivation of a hybrid second-order Møller-Plesset-DFT model and the formulation of a range-separated optimized effective potential method based on a hybrid Görling-Levy-type MBPT-DFT model.

Lifetimes for nine levels and Landé $g_J$ factors for eight levels of the $5p7p$ configuration of neutral tin have been measured by the time-resolved fluorescence method and by the Zeeman quantum beat technique, respectively. A two-step laser excitation technique has been used for the measurements. The results obtained are compared with relativistic Hartree-Fock lifetime and $g_J$ values taking core-polarization effects into account.

We investigate the nonlinear correction to two weakly linked Bose-Einstein condensates realized by two square wells. In the framework of the two-mode approximation, a tunneling term $\chi$ describing the nonlinear tunneling between the nonlinear effective potential is introduced. When the nonlinear interaction is weak, our mode reduces to the well-known boson Josephson-junction model [A. Smerzi et al., Phys. Rev. Lett. 79, 4950 (1997); S. Raghavan et al., Phys. Rev. A 59, 620 (1999)], while in the case of strong nonlinear interactions, our model presents one crucial correction and gives a better description of the static and dynamical properties of the system than that model.

We report on a detailed investigation of the dynamics and the saturation of a light grating stored in a sample of cold cesium atoms. We employ Bragg diffraction to retrieve the stored optical information impressed into the atomic coherence by the incident light fields. The diffracted efficiency is studied as a function of the intensities of both writing and reading laser beams. A theoretical model is developed to predict the temporal pulse shape of the retrieved signal and compares reasonably well with the observed results.

We have investigated the distribution of quality factors $P\left(Q\right)$ of three-dimensional disordered systems composed of pointlike magneto-optical scatterers under the influence of an external magnetic field, both in the diffusive and localized regimes of light transport. $P\left(Q\right)$ is shown to exhibit the same behavior of the distribution of delay times obtained in previous studies within different models to describe wave propagation in random media, such as the Anderson and the kicked rotator models. From the analysis of $P\left(Q\right)$ we conclude that exponentially localized (and prelocalized) electromagnetic quasimodes depend on time-reversal symmetry. We suggest that this dependence could be explored in the development of a magneto-optical random laser, in which the threshold could be tuned by the application of a magnetic field. We also argue that such laser could be used to experimentally test if prelocalized modes are at the controversial origin of random lasing with coherent feedback in diffusive systems.

We examine a proposal by Sherson and Mølmer to generate polarization-squeezed light in terms of quantum stochastic calculus (QSC). We investigate the statistics of the output field and confirm their results using the QSC formalism. In addition, we study the atomic dynamics of the system and find that this setup can produce up to 3 dB of atomic spin squeezing.

I discuss the robustness of pumped cavity dynamics against phase diffusion of the laser and conclude that optomechanical cooling has extreme sensitivity compared to laser cooling of atoms. Certain proposals for ground-state optomechanical cooling by a single cavity would require an unrealistically sharp laser linewidth or, equivalently, a very low level of phase noise. A systematic way to cancel classical excess phase noise is the interferometric twin-cavity pumping, initiated for optically trapped macromirrors of future gravitational-wave detectors.

We present an experimentally efficient and scalable method for the estimation of entanglement of mixed quantum states in terms of simple parity measurements.

A state in a $d$-dimensional Hilbert space can be simulated by a state defined in a different dimension with high fidelity. We assess how faithfully such an approximated state can perform quantum protocols using an example of the squeezed coherent superposition state, which was recently experimentally generated.