A semiclassical theory of single and multimode lasing is derived for open complex or random media using a self-consistent linear response formulation. Unlike standard approaches which use closed cavity solutions to describe the lasing modes, we introduce an appropriate discrete basis of functions which describe also the intensity and angular emission pattern outside the cavity. This constant flux (CF) basis is dictated by the Green function which arises when formulating the steady state Maxwell-Bloch equations as a self-consistent linear response problem. This basis is similar to the quasibound state basis which is familiar in resonator theory and it obeys biorthogonality relations with a set of dual functions. Within a single-pole approximation for the Green function the lasing modes are proportional to these CF states and their intensities and lasing frequencies are determined by a set of nonlinear equations. When a near threshold approximation is made to these equations a generalized version of the Haken-Sauermann equations for multimode lasing is obtained, appropriate for open cavities. Illustrative results from these equations are given for single and few mode lasing states, for the case of dielectric cavity lasers. The standard near threshold approximation is found to be unreliable. Applications to wave-chaotic cavities and random lasers are discussed.

We experimentally demonstrate isotope-selective alignment in a mixture of ${}^{14}\mathrm{N}_2$, ${}^{15}\mathrm{N}_2$ isotopes. Following a strong ultrashort laser pulse rotational excitation, the angular distributions of the isotopes gradually become different due to the mismatch in their moments of inertia. At predetermined times, the desired isotope attains an aligned state while the other component is antialigned, facilitating further selective manipulations by polarized light. By a properly timed second laser pulse, the rotational excitation of the undesired isotope is almost completely removed.

Quantum cryptography shows that one can guarantee the secrecy of correlation on the sole basis of the laws of physics, that is, without limiting the computational power of the eavesdropper. The usual security proofs suppose that the authorized partners, Alice and Bob, have a perfect knowledge and control of their quantum systems and devices; for instance, they must be sure that the logical bits have been encoded in true qubits and not in higher dimensional systems. In this paper, we present an approach that circumvents this strong assumption. We define protocols, both for the case of bits and for generic $d$-dimensional outcomes, in which the security is guaranteed by the very structure of the Alice-Bob correlations, under the no-signaling condition. The idea is that if the correlations cannot be produced by shared randomness, then Eve has poor knowledge of Alice’s and Bob’s symbols. The present study assumes on the one hand that the eavesdropper Eve performs only individual attacks (this is a limitation to be removed in further work), and on the other hand that Eve can distribute any correlation compatible with the no-signaling condition (in this sense her power is greater than what quantum physics allows). Under these assumptions, we prove that the protocols defined here allow extracting secrecy from noisy correlations, when these correlations violate a Bell-type inequality by a sufficiently large amount. The region in which secrecy extraction is possible extends within the region of correlations achievable by measurements on entangled quantum states.

We introduce a constructive method to calculate the achievable secret key rate for a generic class of quantum key distribution protocols, when only a finite number $n$ of signals is given. Our approach is applicable to all scenarios in which the quantum state shared by Alice and Bob is known. In particular, we consider the six state protocol with symmetric eavesdropping attacks, and show that for a small number of signals, i.e., below $n\sim {10}^4$, the finite key rate differs significantly from the asymptotic value for $n\to \infty$. However, for larger $n$, a good approximation of the asymptotic value is found. We also study secret key rates for protocols using higher-dimensional quantum systems.

Double-charge-transfer cross sections into singly and doubly excited states for collisions of $\alpha$ particles with helium atoms have been studied in the energy range of 50 to $500\mathrm{keV}∕\mathrm{amu}$. We have also studied the double electron capture cross sections into ground states for collisions of ${}^7\mathrm{Li}^{3+}$ and ${}^{10}\mathrm{B}^{5+}$ with helium atoms. In our study we have applied the four-body boundary corrected continuum intermediate state approximation. The intermediate continuum states of each electron and static correlations of the electrons have been taken into account in this formalism. Present calculated results for total charge transfer cross sections for the reaction $\alpha +\mathrm{He}$ and ${\mathrm{Li}}^{3+}+\mathrm{He}$ compare favorably well with the existing experimental and other theoretical predictions. Due to the nonavailability of any theoretical and experimental finding for the reaction ${\mathrm{B}}^{5+}+\mathrm{He}$, the energy variation of capture cross sections into the ground state of ${\mathrm{B}}^{5+}$ ion has been shown within the same energy range. However, charge transfer cross sections into singly and doubly excited states of He are compared with the available theoretical observations only due to nonavailability of any experimental result. In this case as well, agreement is very encouraging.

The energy distributions of ions emitted from argon clusters Coulomb exploded at an intensity of $<{10}^{17}\mathrm{W}∕{\mathrm{cm}}^2$ with an intense femtosecond laser have been experimentally studied. The power $m$ of energy $E$ of the ion energy distribution $(dN∕dE\sim E^m)$ is expected to be $1∕2$ for spherical ion clusters, but it is in fact reduced smaller than $1∕2$ as the laser intensity is decreased. This reduction can be well interpreted as resulting from the instantaneous ionization of the surface of the cluster. The validity of this interpretation was confirmed by experiments with double pulse irradiation. A cluster irradiated by the first pulse survives as a skinned cluster, and the remaining core part is Coulomb exploded by the second pulse. It is shown that a cluster can be skinned by an intense short laser pulse, and the laser-intensity dependence of the skinned layer thickness can be reasonably explained by the laser-induced space charge field created in the cluster.

Free heterogeneous argon-krypton clusters have been produced by coexpansion and investigated by means of x-ray photoelectron spectroscopy. By examining cluster surface and bulk binding energy shifts, relative intensities, and peak widths, we show that in the mixed argon-krypton clusters the krypton atoms favor the bulk and argon atoms are pushed to the surface. Furthermore, we show that krypton atoms in the surface layer occupy high-coordination sites and that heterogeneous argon-krypton clusters produced by coexpansion show the same surface structure as argon host clusters doped with krypton. These observations are supported by site-dependent calculations of chemical shifts.

The time-dependent configuration interaction singles (TDCIS) method—an ab initio electronic-structure technique with predictive character—is reformulated in terms of an effective one-electron theory with coupled channels. In this form, the TDCIS equations of motion may be evaluated using standard wave-packet propagation techniques in real space. The time-dependent orbital formulation of TDCIS has computational and conceptual advantages for studying strong-field phenomena in many-electron systems. A simplified version of this theory, referred to as the determinantal single-active-electron (d-SAE) method, is derived. TDCIS and d-SAE are tested by their application to a one-dimensional two-electron model in a strong laser field. The numerically exact time-dependent dipole moment of the interacting system is found to be very well reproduced with TDCIS. The d-SAE method is less accurate, but still provides superior performance in comparison to the standard single-active-electron approach.

We investigate the presence of squeezing in the weakly repulsive uniform Bose gas, in both the condensate mode and in the nonzero opposite-momenta mode pairs, using two different variational formulations. We explore the U(1) symmetry breaking and Goldstone’s theorem in the context of a squeezed coherent variational wave function and present the associated Ward identity. We show that squeezing of the condensate mode is absent at the mean field Hartree-Fock-Bogoliubov level and emerges as a result of fluctuations about mean field as a finite volume effect, which vanishes in the thermodynamic limit. On the other hand, the squeezing of the excitations about the condensate survives the thermodynamic limit and is interpreted in terms of density-phase variables using a number-conserving formulation of the interacting Bose gas.

We present a general derivation of the electron spin noise power spectrum in alkali gases as measured by optical Faraday rotation, which applies to both classical gases at high temperatures as well as ultracold quantum gases. We show that the spin-noise power spectrum is determined by an electron spin-spin correlation function, and we find that measurements of the spin-noise power spectra for a classical gas of ${}^{41}\mathrm{K}$ atoms are in good agreement with the predicted values. Experimental and theoretical spin noise spectra are directly and quantitatively compared in both longitudinal and transverse magnetic fields up to the high magnetic-field regime (where Zeeman energies exceed the intrinsic hyperfine energy splitting of the ${}^{41}\mathrm{K}$ ground state).

Hitting times are the average time it takes a walk to reach a given final vertex from a given starting vertex. The hitting time for a classical random walk on a connected graph will always be finite. We show that, by contrast, quantum walks can have infinite hitting times for some initial states. We seek criteria to determine if a given walk on a graph will have infinite hitting times, and find a sufficient condition, which for discrete time quantum walks is that the degeneracy of the evolution operator be greater than the degree of the graph. The set of initial states which give an infinite hitting time form a subspace. The phenomenon of infinite hitting times is in general a consequence of the symmetry of the graph and its automorphism group. Using the irreducible representations of the automorphism group, we derive conditions such that quantum walks defined on this graph must have infinite hitting times for some initial states. In the case of the discrete walk, if this condition is satisfied the walk will have infinite hitting times for any choice of a coin operator, and we give a class of graphs with infinite hitting times for any choice of coin. Hitting times are not very well defined for continuous time quantum walks, but we show that the idea of infinite hitting-time walks naturally extends to the continuous time case as well.

Following the linear programming prescription of Jafarizadeh et al. [Phys. Rev. A 72, 062106 (2005)], the $d\otimes d$ Bell diagonal entanglement witnesses are provided. By using Jamiolkowski isomorphism, it is shown that the corresponding positive maps are the generalized qudit Choi maps. Also by manipulating particular $d\otimes d$ Bell diagonal separable states and constructing corresponding bound entangled states, it is shown that the obtained $d\otimes d$ Bell states diagonal entanglement witnesses (consequently qudit Choi maps) are nondecomposable in a certain range of their parameters.

We analyze different aspects of multiparty communication over quantum memoryless channels and generalize some of the key results known from bipartite channels to the multiparty scenario. In particular, we introduce multiparty versions of subspace and entanglement transmission fidelities. We also provide alternative, local, versions of fidelities and show their equivalence to the global ones in context of capacity regions defined. An equivalence of two different capacity notions with respect to two types of fidelities is proven. In analogy to the bipartite case it is shown, via sufficiency of isometric encoding theorem, that additional classical forward side channel does not increase capacity region of any quantum channel with $k$ senders and $m$ receivers which represents a compact unit of general quantum networks theory. The result proves that recently provided capacity region of a multiple access channel [M. Horodecki et al., Nature 436, 673 (2005); J. Yard et al., e-print quant-ph/0501045], is optimal also in a scenario of an additional support of forward classical communication.

The errors caused by qubit displacements from their prescribed locations in an ensemble of spin chains are estimated analytically and calculated numerically for a quantum computer based on phosphorus donors in silicon. We show that it is possible to polarize (initialize) the nuclear spins even with displaced qubits by using controlled-NOT gates between the electron and nuclear spins of the same phosphorus atom. However, a controlled-NOT gate between the displaced electron spins is implemented with large error because of the exponential dependence of exchange interaction constant on the distance between the qubits. If quantum computation is implemented on an ensemble of many spin chains, the errors can be small if the number of chains with displaced qubits is small.

We consider pure quantum states of $N$ qubits and study the genuine $N$-qubit entanglement that is shared among all the $N$ qubits. We introduce an information-theoretic measure of genuine $N$-qubit entanglement based on bipartite partitions. When $N$ is an even number, this measure is presented in a simple formula, which depends only on the purities of the partially reduced density matrices. It can be easily computed theoretically and measured experimentally. When $N$ is an odd number, the measure can also be obtained in principle.

The energies and some other bound state properties of the ten five-body bimuonic ions $pdt{\mu }_2$, $ppt{\mu }_2$, $pdd{\mu }_2$, etc. are determined numerically with the use of our variational procedure. The bound state structure and stability of these Coulomb five-body systems are also discussed. By using the computed expectation values of the binary and three-particle $\delta$ functions we make a few predictions about possible experimental observations of the three-particle nuclear reactions in some of these five-body bimuonic systems.

The one-photon absorption cross sections of molecular systems have been determined in the high-energy region from the imaginary part of the electric dipole polarizability tensor. In contrast to commonly adopted state-specific methodologies, the complex polarization propagator approach does not require explicit consideration of the excited states and it is open-ended towards multiphoton absorption. It is shown that the electronic relaxation in the core-hole state is well accounted for in the present approach with use of standard density-functional based electronic structure methods. Sample calculations are presented of the $K$-edge x-ray absorption spectra for ${\mathrm{H}}_2\mathrm{O}$, CO, ${\mathrm{C}}_4{\mathrm{H}}_4\mathrm{N}$, and ${\mathrm{C}}_6{\mathrm{H}}_6$.

X-ray emission yields from highly charged iodine ions incident on a hydrogen terminated silicon surface were measured. It was found that the $K$ shell vacancies were filled through x-ray transitions with the probability of approximately 100%, while only about 20% of $L$ shell vacancies were filled through x-ray transitions and almost all the $M$ shell vacancies were filled nonradiatively. Dissipation of the potential energy $E_p$ of an incident ion through x-ray emissions increases gradually with the number of $L$ shell vacancies and amounts to 10% of $E_p$ for the He-like ${\mathrm{I}}^{51+}$ ion. 30 to 40 % of $E_p$ for ${\mathrm{I}}^{52+}$ and ${\mathrm{I}}^{53+}$ with $K$ shell vacancies was measured to be dissipated mainly by $K$ x-ray emissions.

We present a complete analysis of the laser control of a model molecular system using both optimal control theory and adiabatic techniques. This molecule has a particular potential energy surface with a bifurcating region connecting three potential wells which allows a variety of processes such as isomerization, tunneling, or implementation of quantum gates on one or two qubits. The parameters of the model have been chosen so as to reproduce the main features of ${\mathrm{H}}_3\mathrm{C}\mathrm{O}$ which is a molecule benchmark for such dynamics. We show the feasibility of different processes and we investigate their robustness against variations of laser field. We discuss the conditions under which each method of control gives the best results. We also point out the relation between optimal control theory and local control.

By using exact path-integral Monte Carlo methods we calculate the equation of state of an interacting Bose gas as a function of temperature both below and above the superfluid transition. The universal character of the equation of state for dilute systems and low temperatures is investigated by modeling the interatomic interactions using different repulsive potentials corresponding to the same $s$-wave scattering length. The results obtained for the energy and the pressure are compared to the virial expansion for temperatures larger than the critical temperature. At very low temperatures we find agreement with the ground-state energy calculated using the diffusion Monte Carlo method.