We propose and analyze a scheme by which a many-particle system can be prepared in highly entangled wave-packet states. One of the particles is prepared initially in a quantum superposition of multiple coherent states and then coupled via a quadratic interaction Hamiltonian to a number of other particles. The system evolves into a highly entangled wave-packet state. An appropriate measure of this time-dependent entanglement is given. This scheme is applicable to a number of systems of interest in quantum-information science.

Weak measurements allow a probe system to encode the transitionary weak value of a desired observable on a signal system that is both pre- and post-selected. Such interactions alter the state and measurement statistics of the probe system. We establish that by encoding the imaginary part of a weak value onto an initially entangled probe, we can modify its entanglement content, provided the probe observable can distinguish between system states of different von Neumann entropies. Apart from fundamental interest, this result illustrates the utility of the imaginary weak value as a calculational tool in certain entanglement concentration protocols.

Any $n$-qubit state with $n$ independent perfect correlations is equivalent to a graph state. We present the optimal Bell inequalities for perfect correlations and maximal violation for all classes of graph states with $n\le 6$ qubits. Twelve of them were previously unknown and four give the same violation as the Greenberger-Horne-Zeilinger state, although the corresponding states are more resistant to decoherence.

The fidelity approach to the Gaussian transitions in spin-one $\mathit{XXZ}$ spin chains with three different values of Ising-type anisotropy $\lambda$ is analyzed by means of the density matrix renormalization group technique for systems of large sizes. We find that, despite the success in the cases of $\lambda =2.59$ and 1, the fidelity susceptibility fails to detect the Gaussian transition for $\lambda =0.5$. Thus our results demonstrate the limitation of the fidelity susceptibility in characterizing quantum phase transitions, which was proposed recently in general frameworks.

We investigate the dynamics of global entanglement, the Meyer-Wallach measure, under decoherence, analytically. We study two important classes of multipartite entangled states, the Greenberger-Horne-Zeilinger and the $\mathit{W}$ state. We obtain exact results for various models of system-environment interactions (decoherence). Our results shows distinctly different scaling behavior for these initially entangled states indicating a relative robustness of the $\mathit{W}$ state, consistent with previous studies.

We propose generalized quantum key distribution schemes using spatially encoded $d$-dimensional qudits based on fractional Fourier transform operations. We determine the necessary conditions on the orders of the transforms which ensure a shared secret random key string and briefly discuss the transmission rate and a possible encoding procedure. We also show that the fractional Fourier transform can be used to analyze more general eavesdropping strategies, including an intermediate-basis attack. The error rate and information gain for the intercept-resend and intermediate-basis attacks are briefly analyzed for a particular example. Effects of atmospheric turbulence in a free-space transmission are considered.

We calculate the entanglement entropy of blocks of size $x$ embedded in a larger system of size $L$, by means of a combination of analytical and numerical techniques. The complete entanglement entropy in this case is a sum of three terms. One is a universal $x$- and $L$-dependent term, first predicted by Calabrese and Cardy, the second is a nonuniversal term arising from the thermodynamic limit, and the third is a finite size correction. We give an explicit expression for the second, nonuniversal, term for the one-dimensional Hubbard model, and numerically assess the importance of all three contributions by comparing to the entropy obtained from fully numerical diagonalization of the many-body Hamiltonian. We find that finite-size corrections are very small. The universal Calabrese-Cardy term is equally small for small blocks, but becomes larger for $x>1$. In all investigated situations, however, the by far dominating contribution is the nonuniversal term stemming from the thermodynamic limit.

We report a calculation of all two-loop quantum electrodynamics corrections with closed fermion loops for the $n=1$ and $n=2$ states of H-like ions and for a wide range of the nuclear charge numbers $Z=1–100$. The calculation is performed to all orders in the binding-strength parameter $Z\alpha$, with the exception that in a few cases the free-loop approximation is employed in the treatment of the fermion loops. Detailed comparison is made with previous $Z\alpha$-expansion calculations and the higher-order remainder term to order ${\alpha }^2{\left(Z\alpha \right)}^6$ is identified.

I show that the so-called causality paradox of time-dependent density-functional theory arises from an incorrect formulation of the variational principle for the time evolution of the density. The correct formulation not only resolves the paradox in real time, but also leads to an expression for the causal exchange-correlation kernel in terms of Berry curvature. Furthermore, I show that all the results that were previously derived from symmetries of the action functional remain valid in the present formulation. Finally, I develop a model functional theory which explicitly demonstrates the workings of the formulation.

We report absolute triple differential cross sections in coplanar ${\theta }_{12}=\pi$ geometry for the ionization of atomic hydrogen by electron impact at low energies. We used our recently extended multiconfiguration Hartree-Fock method successfully to calculate triple differential cross sections of H for incident energies $E_0$ of 14.6, 15.6, 17.6, 20, and 25 eV for equal energy sharing of excess energies by the two final state continuum electrons. It has been shown that there is very little difference between the results obtained in the Hartree-Fock and the screening potential approximations implying that in the case of H and ${\theta }_{12}=\pi$ configuration distortion effects between the two outgoing electrons are small even at low energies. Our results are compared with available absolute and relative experimental data and other existing theoretical calculations and are found to be in very good agreement.

We have performed experimental and theoretical studies of double ionization of helium by 6 MeV proton impact using a recently developed tool, four-particle Dalitz plots [Schulz et al., J. Phys. B 22, 3091 (2007)] which enable the representation of multiple differential cross sections as a function of all four fragments in a single spectrum without loss of any part of the total cross section. As a result, the relative importance of the various interactions between the fragments can be studied in great detail. Comparisons of experimental data with theoretical first-order calculations and simulations for the higher-order (TS-2) process show that elastic scattering between the heavy particles is surprisingly strong. For a large fraction of collision events, the final-state electron momenta are small compared to the momenta of the heavy particles. Our results suggest that an uncorrelated double ionization mechanism, involving two independent interactions of the projectile with both electrons, is significantly more important than previously expected for such fast collisions.

We analyze nonlinear radiation imprisonment (RI) effects in an optically thick vapor in different temperature regimes. An analytical approach is proposed to treat nonlinear decay problems. Special attention is paid to vapor samples having curvilinear geometries (cylinder, sphere) and being excited by a strong laser pulse. We derive a number of new formulas for different radiative trapping factors as functions of opacity and propose a general approach for RI evaluation allowing us to deal with samples both at room and low, or very low, temperatures, such as those customarily achieved in magneto-optical trap (MOT) experiments. As a result, we predict a “subnatural” decay of radiation escaping from cold vapors, which can be envisioned as the basis for a sensitive and reliable MOT diagnostic tool.

We study the enhanced excitation and ionization of $\text{H}_2{}^{+}$ by a single- and a two-color intense laser pulse. Our results show that the enhanced ionization in a single-color laser field is closely related to the dominant population of the $1{\sigma }_g$ or $1{\sigma }_u$ state and the corresponding width of their Floquet complex quasienergies. The overall trend of the population in higher excited states, once populated, remains flat as a function of time. Therefore, in the single-color case, the excited states do not contribute directly to the ionization. However, when the $\text{H}_2{}^{+}$ is exposed to a two-color laser field, an enhanced excitation effect to higher excited states for $\text{H}_2{}^{+}$ at some critical internuclear distance $R_c$ is observed, which contributes greatly to the enhanced ionization of $\text{H}_2{}^{+}$ because of their much higher ionization rates compared to those of $1{\sigma }_g$ or $1{\sigma }_u$ states. We also find that the enhanced ionization is sensitive to the relative phase of the two-color laser field. By adjusting the relative phase, one can manipulate the enhanced ionization to occur at some critical internuclear distances. This can help the molecule to survive the enhanced ionization peaks at smaller internuclear distances, which is very useful for those circumstances where the preparation of expanded molecules is needed, e.g., for a more efficient generation of high-order harmonic generation. Our method is based on a numerical solution of the full-dimensional time-dependent Schrödinger equation accurately using a method we recently developed.

We study the dipole collective oscillations in Bose-Fermi mixtures in a dynamical time-dependent approach, which is formulated with the time-dependent Gross-Pitaevskii equation and the Vlasov equation. While the Bose gas oscillates monotonously, the fermion oscillation shows a beat and damping. We find big differences in behaviors of fermion oscillation between the time-dependent approach and usual approaches such as the sum-rule approach. When the amplitude is not minimal, the dipole oscillation of the Fermi gas cannot be described with a simple center-of-mass motion.

Atom-molecule equilibrium for molecular formation processes is discussed for boson-fermion, fermion-fermion, and boson-boson mixtures of ultracold atomic gases in the framework of quasichemical equilibrium theory. After presentation of the general formulation, zero-temperature phase diagrams of the atom-molecule equilibrium states are calculated analytically; molecular, mixed, and dissociated phases are shown to appear for the change of the binding energy of the molecules. The temperature dependences of the atom or molecule densities are calculated numerically, and finite-temperature phase structures are obtained of the atom-molecule equilibrium in the mixtures. The transition temperatures of the atom or molecule Bose-Einstein condensations are also evaluated from these results. Quantum-statistical deviations of the law of mass action in atom-molecule equilibrium, which should be satisfied in mixtures of classical Maxwell-Boltzmann gases, are calculated, and the difference in the different types of quantum-statistical effects is clarified. Mean-field calculations with interparticle interactions (atom-atom, atom-molecule, and molecule-molecule) are formulated, where interaction effects are found to give the linear density-dependent term in the effective molecular binding energies. This method is applied to calculations of zero-temperature phase diagrams, where new phases with coexisting local-equilibrium states are shown to appear in the case of strongly repulsive interactions.

We study the crossover of a quasi-two-dimensional Fermi gas trapped in the radial plane from the Bardeen-Cooper-Schrieffer (BCS) regime to the Bose-Einstein condensation (BEC) regime by crossing a wide Feshbach resonance. We consider two effective two-dimensional Hamiltonians within the mean-field level, and calculate the zero-temperature cloud size and number density distribution. For a model 1 Hamiltonian with renormalized atom-atom interaction, we observe a constant cloud size for arbitrary detunings. For a model 2 Hamiltonian with renormalized interactions between atoms and dressed molecules, the cloud size deceases from the BCS to BEC side, which is consistent with the picture of BCS-BEC crossover. This qualitative discrepancy between the two models indicates that the inclusion of dressed molecules is essential for a mean-field description of quasi-two-dimensional Fermi systems, especially on the BEC side of the Feshbach resonance.

We investigate photon statistics emerging from the interaction of a two-level system with two laser pulses separated by a delay interval. It is shown that $P_n\left(t\right)$, the probability of emitting $n$ photons up to time $t$, may be represented as a summation over quantum trajectories, which allows simple identification of the coherent effect arising from the existence of the delay. We obtain a relation between photon statistics emerging from the interaction with a single pulse and photon statistics emerging from the interaction with two separated pulses with finite delay. In addition, the probabilities of emitting zero, one, and two photons, the expectation number of emissions, $⟨N⟩$, and Mandel’s $Q$ parameter are calculated explicitly. The case of two short and strong pulses, the so-called pump and probe setup, yielding up to two photons at most, is considered in detail. We examine different limiting behaviors of the photon statistics and obtain the upper and lower bounds for $P_0$, $P_1$, and $P_2$ in the limit of strong fields. Implications for single-molecule nonlinear spectroscopy and the theory of obtaining pairs of photons on demand are discussed briefly.

In this paper, we investigate the dynamics of the Bloch vector of a single two-level atom which interacts with a single quantized electromagnetic field mode according to the Jaynes-Cummings model, where the field is initially prepared in a thermal state. The time evolution of the Bloch vector $\mathit{S}\left(t\right)$ seems to be in complete disorder because of the thermal distribution of the initial state of the field. Both the norm and the direction of $\mathit{S}\left(t\right)$ oscillate hard and their periods seem infinite. We observe that the trajectory of the time evolution of $\mathit{S}\left(t\right)$ in the two- or three-dimensional space does not form a closed path. To remove the fast frequency oscillation from the trajectory, we take the time average of the Bloch vector $\mathit{S}\left(t\right)$. We examine the histogram of $\left\{\phantom{|}{S}_z\left(n\Delta t\right)|n=0,1,\dots ,N\right\}$ for small $\Delta t$ and large $N$. It represents an absolute value of a derivative of the inverse function of $S_z\left(t\right)$. [When the inverse function of $y=S_z\left(t\right)$ is a multivalued function, the histogram represents a summation of the absolute values of its derivatives at points whose real parts are equal to $y$ on the Riemann surface.] We examine the dependence of the variance of the histogram on the temperature of the field. We estimate the lower bound of the entanglement between the atom and the field.

Propagation of short optical pulses in a one-dimensional nonlinear medium is considered without the use of the slow envelope and unidirectional propagation approximations. The existence of uniformly moving solitary solutions is predicted for a Sellmeier-type dispersion function in the anomalous dispersion domain. A four-parametric family of such solutions is found that contains the classical envelope soliton in the limit of large pulse durations. In the opposite limit we get another family member, which, in contrast to the envelope soliton, strongly depends on the nonlinearity model and represents the shortest and the most intense pulse that can propagate in a stationary manner.

A scheme is presented for realizing a two-qubit quantum SWAP gate for intracavity fields. In the scheme, a $\mathit{V}$-type atomic ensemble prepared in its ground state mediates the interaction between the two-cavity modes. Under certain conditions, the cavity-field degree of freedom is decoupled from the atomic degrees of freedom, and the effective coupling strength between the two-cavity modes scales up with $\sqrt{N}$ ($\mathit{N}$ is the number of effective atoms). The numerical simulation shows that the quantum SWAP gate may have a high fidelity under the influence of the atomic spontaneous emission and the decay of the cavity modes.