The Yudin-Ivanov formula [Phys. Rev. A 64, 013409 (2001)] is generalized such that the most general analytical expression for single-electron spectra, which includes the dependence on the instantaneous laser phase, is obtained within the strong field approximation. No assumptions on the momentum of the electron are made. Previously known formulas for single-electron spectra can be obtained as approximations to the general formula.

In a recent paper A. Akbari, N. H. March, and A. Rubio [Phys. Rev. A 76, 032510 (2007)] investigated the one-electron reduced density matrix and the momentum density of several two-electron model atoms, including Hooke’s atom. The method used by the authors for deriving an integral form of the momentum density is in fact the most suited for deriving a closed-form expression of the exact reciprocal form factor, in a special case. This function is important inasmuch as it reflects the off-diagonal side of the exact reduced density matrix.

The attractive Fermi-Hubbard Hamiltonian is solved via the Bogoliubov-de Gennes formalism to analyze the ground state phases of population imbalanced fermion mixtures in harmonically trapped two-dimensional optical lattices. In the low density limit the superfluid order parameter modulates in the radial direction towards the trap edges to accommodate the unpaired fermions that are pushed away from the trap center with a single peak in their density. However, in the high density limit while the order parameter modulates in the radial direction towards the trap center for low imbalance, it also modulates towards the trap edges with increasing imbalance until the superfluid to normal phase transition occurs beyond a critical imbalance. This leads to a single peak in the density of unpaired fermions for low and high imbalance, but leads to double peaks for intermediate imbalance.

The study of optical parametric amplifiers (OPAs) has been successful in describing and creating nonclassical light for use in fields such as quantum metrology and quantum lithography [Agarwal et al., J. Opt. Soc. Am. B 24, 2 (2007)]. In this paper we present the theory of an OPA scheme utilizing an entangled state input. The scheme involves two identical OPAs seeded with the maximally path-entangled $\mid N00N⟩$ state $(\mid 2,0⟩+\mid 0,2⟩)∕\sqrt{2}$. The stimulated amplification results in output state probability amplitudes that have a dependence on the number of photons in each mode, which differs greatly from two-mode squeezed vacuum. A large family of entangled output states are found. Specific output states allow for the heralded creation of $N=4$ $N00N$ states, which may be used for quantum lithography, to write sub-Rayleigh fringe patterns, and for quantum interferometry, to achieve Heisenberg-limited phase measurement sensitivity.

Certain classes of integrable quantum billiards provide a versatile arena for time-domain atom optics experiments. In order to learn how to fully exploit the fractional revival behavior that governs these kinds of systems, we here develop a convenient theoretical framework for their description. As an illustrative example, we present a billiard-internal realization of Grover’s quantum search algorithm. The considered devices are scalable and could be used for the construction of quantum computers using trapped neutral atoms.

We present a general formalism for quantum-error-correcting codes that encode both classical and quantum information (the EACQ formalism). This formalism unifies the entanglement-assisted coding theory and the classical coding theory in the sense that, after the encoding, error-correcting, and decoding steps, the encoded quantum and classical information can be correctly recovered by the receiver. We formally define this kind of quantum codes using stabilizer language, and derive the appropriate error-correcting conditions. We give several examples to demonstrate the construction of such codes.

The $6s\text{−}n{p}_j$ $(n=6–9)$ electric-dipole matrix elements and $6s\text{−}n{d}_j$ $(n=5–7)$ electric-quadrupole matrix elements in ${\mathrm{Ba}}^{+}$ are calculated using the relativistic all-order method. The resulting values are used to evaluate ground-state dipole and quadrupole polarizabilities. In addition, the electric-dipole $6p_j\text{−}5d_{j^{\prime }}$ matrix elements and magnetic-dipole $5d_{5∕2}\text{−}5d_{3∕2}$ matrix element are calculated using the same method in order to determine the lifetimes of the $6p_{1∕2}$, $6p_{3∕2}$, $5d_{3∕2}$, and $5d_{5∕2}$ levels. The accuracy of the $6s\text{−}5d_j$ matrix elements is investigated in detail in order to estimate the uncertainties in the quadrupole polarizability and $5d_j$ lifetime values. The lifetimes of the $5d$ states in ${\mathrm{Ba}}^{+}$ are extremely long, making precise experiments very difficult. Our final results for dipole and quadrupole ground-state polarizabilities are ${\alpha }_{E1}=124.15a_0^3$ and ${\alpha }_{E2}=4182\left(34\right)a_0^5$, respectively. The resulting lifetime values are ${\tau }_{6p_{1∕2}}=7.83\mathrm{ns}$, ${\tau }_{6p_{3∕2}}=6.27\mathrm{ns}$, ${\tau }_{5d_{3∕2}}=81.5\left(1.2\right)\mathrm{s}$, and ${\tau }_{5d_{5∕2}}=30.3\left(4\right)\mathrm{s}$. An extensive comparison with other theoretical and experimental values is carried out for both lifetimes and polarizabilities.

Angular differential cross sections are calculated for antiprotons elastically and inelastically scattered by the helium atom. The elastic cross sections are calculated quantum mechanically using both the adiabatic potential and a phenomenological optical potential. The absorptive effects, taken into account by the optical potential, are found to significantly suppress large-angle elastic scattering. Inelastic scattering (excitation and ionization) is treated by the quasiclassical fermion molecular dynamics method. The inelastic scattering is largely in the backward direction at laboratory collision energies within $\sim 30\mathrm{eV}$ of threshold, but moves to smaller angles as the energy increases.

Ab initio calculations of 0.01–10 eV collisions of positrons with fullerene ${\text{C}}_{20}$ are performed using a single-center expansion of the total wave function and a model potential to represent the positron-molecule interaction. Total elastic cross sections and eigenphase sums are generated and analyzed, while bound states and possible long-lifetime scattering resonances are explored, particularly those which are found to reside within the cage structure defined by the carbon atoms of the cluster.

Results of a theoretical study of photoionization cross sections and photoelectron angular distribution asymmetry parameters of an atom $A$ confined in spherical multiwalled fullerenes are presented and compared with those obtained for the free atom $A$ as well as for $A$ confined in giant spherical single-walled fullerenes ${\mathrm{C}}_{n⩾240}$. Each individual nested fullerene cage is represented by a spherical, short-range, attractive potential characterized by the inner radius, width, and potential depth. Trends in the strength and location of confinement resonances in the photoionization spectra, as a function of the number of nested fullerenes, are delineated. As examples, calculations of the $1s$ photoionization of Ar confined in ${\mathrm{C}}_{60}$, ${\mathrm{C}}_{240}$, ${\mathrm{C}}_{540}$, ${\mathrm{C}}_{60}@{\mathrm{C}}_{240}$, and ${\mathrm{C}}_{60}@{\mathrm{C}}_{240}@{\mathrm{C}}_{540}$ are presented. The calculations are performed within the framework of a Hartree-Fock approximation which is appropriate for a deep inner-shell photoionization. The trends seen should be a general occurrence for an inner-shell photoionization of virtually any atom confined in spherical fullerenes not only Ar.

We determine the phase diagram and the momentum distribution for a one-dimensional Bose gas with repulsive short-range interactions in the presence of a two-color lattice potential, with an incommensurate ratio among the respective wavelengths, by using a combined numerical (density matrix renormalization group) and analytical (bosonization) analysis. The system displays a delocalized (superfluid) phase at small values of the intensity of the secondary lattice ${\mathit{V}}_2$ and a localized (Bose-glasslike) phase at larger intensity ${\mathit{V}}_2$. We analyze the localization transition as a function of the height ${\mathit{V}}_2$ beyond the known limits of free and hard-core bosons. We find that weak repulsive interactions disfavor the localized phase, i.e., they increase the critical value of ${\mathit{V}}_2$ at which localization occurs. In the case of integer filling of the primary lattice, the phase diagram at fixed density displays, in addition to a transition from a superfluid to a Bose glass phase, a transition to a Mott-insulating state for not too large ${\mathit{V}}_2$ and large repulsion. We also analyze the emergence of a Bose-glass phase by looking at the evolution of the Mott-insulator lobes when increasing ${\mathit{V}}_2$. The Mott lobes shrink and disappear above a critical value of ${\mathit{V}}_2$. Finally, we characterize the superfluid phase by the momentum distribution, and show that it displays a power-law decay at small momenta typical of Luttinger liquids, with an exponent depending on the combined effect of the interactions and of the secondary lattice. In addition, we observe two side peaks that are due to the diffraction of the Bose gas by the second lattice. This latter feature could be observed in current experiments as characteristics of pseudo-random Bose systems.

The theory of nonlinear diffraction of intensive light beams propagating through photorefractive media is developed. Diffraction occurs on a reflecting wire embedded in the nonlinear medium at a relatively small angle with respect to the direction of the beam propagation. It is shown that this process is analogous to the generation of waves by a flow of a superfluid past an obstacle. The “equation of state” of such a superfluid is determined by the nonlinear properties of the medium. On the basis of this hydrodynamic analogy, the notion of the “Mach number” is introduced where the transverse component of the wave vector plays the role of the fluid velocity. It is found that the Mach cone separates two regions of the diffraction pattern: inside the Mach cone oblique dark solitons are generated and outside the Mach cone the region of “optical ship waves” (the wave pattern formed by a two-dimensional packet of linear waves) is situated. Analytical theory of the “optical ship waves” is developed and two-dimensional dark soliton solutions of the generalized two-dimensional nonlinear Schrödinger equation describing the light beam propagation are found. Stability of dark solitons with respect to their decay into vortices is studied and it is shown that they are stable for large enough values of the Mach number.

Electromagnetically induced transparency (EIT) is an important tool for controlling light propagation and nonlinear wave mixing in atomic gases with potential applications ranging from quantum computing to table top tests of general relativity. Here we consider EIT in an atomic Bose-Einstein condensate (BEC) trapped in a double-well potential. A weak probe laser propagates through one of the wells and interacts with atoms in a three-level $\Lambda$ configuration. The well through which the probe propagates is dressed by a strong control laser with Rabi frequency ${\Omega }_{\mu }$, as in standard EIT systems. Tunneling between the wells at the frequency $g$ provides a coherent coupling between identical electronic states in the two wells, which leads to the formation of interwell dressed states. The macroscopic interwell coherence of the BEC wave function results in the formation of two ultranarrow absorption resonances for the probe field that are inside of the ordinary EIT transparency window. We show that these new resonances can be interpreted in terms of the interwell dressed states and the formation of a type of dark state involving the control laser and the interwell tunneling. To either side of these ultranarrow resonances there is normal dispersion with very large slope controlled by $g$. We discuss prospects for observing these ultranarrow resonances and the corresponding regions of high dispersion experimentally.

We investigate the local implementation of nonlocal operations with the block matrix form, and propose a protocol for any diagonal or offdiagonal block operation. We generalize this method to the two-party multiqubit case and the multiparty case. We also compare the local implementation of nonlocal block operations with the remote implementation of local operations [Huelga et al., Phys. Rev. A 63, 042303 (2001)], and point out a relation between them.

We present an analytic calculation of the population of each magnetic sublevel of the ${}^{87}\mathrm{Rb}$ atom. Under the influence of a weak circularly polarized laser beam, the rate equations governing the internal dynamics of this atom were solved analytically and the results were compared with numerical calculations. As far as the condition of low intensity is satisfied, it is possible to obtain exact analytic populations regardless of the magnitude of energy spacings, transition lines, and laser polarization (circular or linear).

We have measured the intensity of Raman scattering light, which is due to optical phonons, as a function of excitation laser wavelength for the guide-mode band of ${\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$-based photonic-crystal-slab line-defect waveguide. As a result, we find that the Raman scattering efficiency is pronouncedly enhanced as the signal wavelength approaches the band edge. Comparison of the result with theoretical prediction reveals that the enhancement should reflect increase of the photon density of states in a divergent manner, which is characteristic of a one-dimensional system.

The quantum mechanics of closed systems such as the universe is formulated using an extension of familiar probability theory that incorporates negative probabilities. Probabilities must be positive for sets of alternative histories that are the basis of fair settleable bets. However, in quantum mechanics there are sets of alternative histories that can be described but which cannot be the basis for fair settleable bets. Members of such sets can be assigned extended probabilities that are sometimes negative. A prescription for extended probabilities is introduced that assigns extended probabilities to all histories that can be described, fine grained or coarse grained, members of decoherent sets or not. All probability sum rules are satisfied exactly. Sets of histories that are recorded to sufficient precision are the basis of settleable bets. This formulation is compared with the decoherent (consistent) histories formulation of quantum theory. Prospects are discussed for using this formulation to provide testable alternatives to quantum theory or further generalizations of it.

We propose a measure for the “size” of a quantum superposition of two many-body states with (supposedly) macroscopically distinct properties by counting how many single-particle operations are needed to map one state onto the other. This definition gives sensible results for simple, analytically tractable cases and is consistent with a previous definition restricted to Greenberger-Horne-Zeilinger-like states. We apply our measure to the experimentally relevant, nontrivial example of a superconducting three-junction flux qubit put into a superposition of left- and right-circulating supercurrent states, and we find the size of this superposition to be surprisingly small.

We consider the achievability problem of the Cramér-Rao bound for multiparameter estimations. In general, it is not achievable due to the noncommutativity of optimal measurements for the corresponding parameters. However, we show that, under certain conditions, it can always be attained up to the leading order in the parameters as long as $D⩽N-1$, where $D$ and $N$ denote the number of parameters and the dimension of the system, respectively. After proving that, we discuss the achievability in the context of channel estimation for a general channel called a low-noise channel, which is very useful for investigating parameter estimation in the leading order. This allows us to find an ancilla-assisted enhancement effect: if entangled input states with an ancilla system are utilized for the channel estimation together with collective measurements on those output states, the bound becomes achievable for $D⩽N^2-1$.