We consider the particle creation (the Dynamical Casimir effect) in a uniformly contracting ideal one-dimensional cavity nonperturbatively. The exact expression for the energy spectrum of created particles is obtained and its dependence on parameters of the problem is discussed. Unexpectedly, the number of created particles depends on the duration of the cavity contracting nonmonotonously. This is explained by quantum interference of the events of particle creation which are taking place only at the moments of acceleration and deceleration of a boundary, while stable particle states exist (and thus no particles are created) at the time of contracting.

The properties of the least-bound vibrational level $(v=14)$ of the ${}^5\Sigma _g^{+}$ state formed during the ultracold collision of two spin-polarized metastable $2{}^{3}S_1$ helium atoms are crucial to studies of photoassociation spectroscopy of metastable helium. We report a calculation of the autoionization lifetime ${\tau }_g$ of this state induced by spin-dipole coupling of the ${}^5\Sigma _g^{+}$ state to the ${}^1\Sigma _g^{+}$ state from which Penning and associative ionization processes are highly probable. We find ${\tau }_g\approx 150\mathrm{\mu }\mathrm{s}$, significantly larger than the recent experimental estimates of $(0.5-3)\mathrm{\mu }\mathrm{s}$.

In a recent paper [Phys. Rev. A 71, 042501 (2005)], Howard and March presented the exact ground state wave function of the spherical He-like atom, and many physical aspects of this solution were analyzed. We show that this function is not the exact solution of the model.

We propose a physically reversible quantum measurement of an arbitrary spin-$s$ system using a spin-$j$ probe via an Ising interaction. In the case of a spin-$1∕2$ system $(s=1∕2)$, we explicitly construct a reversing measurement and evaluate the degree of reversibility in terms of fidelity. The recovery of the measured state is pronounced when the probe has a high spin $(j>1∕2)$, because the fidelity changes drastically during the reversible measurement and the reversing measurement. We also show that the reversing measurement scheme for a spin-$1∕2$ system can serve as an experimentally feasible approximate reversing measurement for a high-spin system $(s>1∕2)$. If the interaction is sufficiently weak, the reversing measurement can recover a cat state almost deterministically in spite of there being a large fidelity change.

Concise information on the general features of the quantum-mechanical current density induced in the electrons of a molecule by a spatially uniform, time-independent magnetic field is obtained via a stagnation graph that shows the isolated singularities and the lines at which the current-density vector field vanishes. Stagnation graphs provide compact description of current-density vector fields and help the interpretation of molecular magnetic response, e.g., magnetic susceptibility and nuclear magnetic shielding. The stagnation graph of six cyclic, planar aromatic molecules has been obtained at the Hartree-Fock level via a procedure based on continuous transformation of the origin of the current density formally annihilating the diamagnetic contribution. Some common distinctive elements observed for cyclic aromatic rings ${\mathrm{C}}_n{\mathrm{H}}_n$, with $n=3,4,\dots ,8$, in the presence of a magnetic field normal to the molecular plane, are discussed. The results can be used for a general discussion of diatropism in aromatic systems.

A precision measurement of the lifetime of the lowest excited level of the $\mathrm{He}$-like ${\mathrm{S}}^{14+}$ ion carried out at the Livermore EBIT-II electron beam ion trap yielded a value of $(703\pm 4)\mathrm{ns}$. Our method extends the range of lifetime measurements accessible with electron beam ion traps into the nanosecond region and improves the accuracy of currently available data for this level by an order of magnitude.

Double- and triple-differential cross sections are presented for the electron-impact ionization of ground-state hydrogen at incident electron energies of 15.6 and $17.6\mathrm{eV}$. The time-dependent close-coupling method is used to calculate the differential ionization cross sections, and comparisons are made with previous theoretical calculations and with experimental measurements. Excellent agreement is obtained between our calculations and previous work.

Optical lattices with a large spacing between the minima of the optical potential can be created using the angle-tuned geometry where the one-dimensional periodic potential is generated by two propagating laser beams intersecting at an angle different from $\pi$. The present work analyzes the coherent transport for the case of this geometry. We show that the potential depth can be kept constant during the transport by choosing a magic value for the laser wavelength. This value agrees with that of the counterpropagating laser case, and the magic wavelength does not depend on the optical lattice geometry. Moreover, we find that this scheme can be used to implement controlled collision experiments under special geometric conditions. Finally we study the transport of hyperfine-Zeeman states of ${}^{87}\mathrm{Rb}$.

Using the Floquet formalism and the adiabatic approximation we develop a theory for optimal control of a multilevel quantum system interacting with an external electric field under multiphoton resonance conditions. Optimal solutions for the case of control over a time interval are presented. We derive a differential equation to determine the shape of the optimal pulse, and show how the order of the multiphoton resonance affects the solution. In particular, we demonstrate that optimal control in the case of two-photon resonance and using only adiabatically shaped control pulses represents a special degenerate case, for which the shape of the pulse cannot be optimized. Thus, for this particular case the final state of the controlled system is completely determined by the pulse energy.

This paper presents a mean-field numerical analysis, using the full three-dimensional time-dependent Gross-Pitaevskii equation (GPE), of an experiment carried out by Orzel et al. [Science 291, 2386 (2001)] intended to show number squeezing in a gaseous Bose-Einstein condensate in an optical lattice. The motivation for the present work is to elucidate the role of mean-field effects in understanding the experimental results of this work and those of related experiments. We show that the nonadiabatic loading of atoms into optical lattices reproduces many of the main results of the Orzel et al. experiment, including both loss of interference patterns as laser intensity is increased and their regeneration when intensities are lowered. The nonadiabaticity found in the GPE simulations manifests itself primarily in a coupling between the transverse and longitudinal dynamics.

An analytic expression is derived for a force on a weak point impurity arising from the scattering of quantum fluctuations in a slow-moving, weakly interacting, three-dimensional Bose-Einstein condensate at zero temperature. In an infinitely extended geometry, this force is shown to exist at any arbitrarily small flow velocity below Landau's critical velocity. Furthermore, this force is shown to be directly proportional to the flow speed.

We propose a phase diagram for a cold polarized atomic Fermi gas with zero-range interaction. We identify four main phases in the plane of density and polarization: the superfluid phase, the normal phase, the gapless superfluid phase, and the modulated phase. We argue that there exists a Lifshitz point at the junction of the normal, the gapless superfluid, and the modulated phases, and a splitting point where the superfluid, the gapless superfluid, and the modulated phases meet. We show that the physics near the splitting point is universal and derive an effective field theory describing it. We also show that subregions with one and two Fermi surfaces exist within the normal and the gapless superfluid phases.

We study the optical interaction in a coupled dielectric microdisks by investigating the splitting of resonance positions of interacting whispering-gallery modes (WGM’s) and their pattern change, depending on the distance between the microdisks. It is shown that the interaction between the WGM’s with odd parity about the $y$ axis becomes appreciable at a distance less than a wavelength and causes directional emissions of the resulting interacting WGM’s. The directionality of the interacting WGM’s can be understood in terms of an effective boundary deformation in ray dynamical analysis. We also discuss the oscillation of the splitting when the distance is greater than a wavelength.

The two-body Coulomb Hamiltonian, when calculated in Coulomb-Sturmian basis, has an infinite symmetric tridiagonal—i.e., Jacobi-matrix form. This Jacobi-matrix structure involves a continued-fraction representation for the inverse of the Green’s matrix. The continued fraction can be transformed to a ratio of two ${}_{2}F_1$ hypergeometric functions. From this result we find an exact analytic formula for the matrix elements of the Green’s operator of the Coulomb Hamiltonian.

Two-photon ionization of atomic helium has been measured by combining femtosecond extreme-ultraviolet pulses from the free-electron laser in Hamburg (FLASH at DESY) with intense light pulses from a synchronized neodymium-doped yttrium lithium fluoride laser. Sidebands appear in the photoelectron spectra when the two laser pulses overlap in both space and time. Their intensity exhibits a characteristic dependence on the relative time delay between the ionizing and the dressing pulses and provides an inherent time marker for time-resolved pump-probe experiments. The measurements of the sidebands are in good agreement with theoretical predictions and allow for a direct analysis of two-photon ionization, free from processes related to interference between multiple quantum paths.

We present an experimentally feasible protocol for the complete storage and retrieval of arbitrary light states in an atomic quantum memory using the Faraday interaction between light and matter. Our protocol relies on multiple passages of a single light pulse through the atomic ensemble without the impractical requirement of kilometer-long delay lines between the passages. A time-dependent interaction strength enables the storage and retrieval of states with arbitrary pulse shapes. The fidelity approaches unity exponentially without squeezed or entangled initial states, as illustrated by calculations for a photonic qubit.

We report a frequency metrology study on the $\mathrm{Mg}3s^2{}^{1}S\to 3s4p{}^{1}P$ transition near $202.5\mathrm{nm}$. For this purpose, the fourth harmonic of the output from an injection-seeded $\mathrm{Ti}:\mathrm{sapphire}$ pulsed laser is employed in a Mg atomic beam experiment with laser-induced fluorescence detection. Absolute frequency calibration with a frequency comb laser is performed on the cw seeding radiation, while the chirp-induced frequency shift between the pulsed output and the seed light is monitored on line. The resulting transition frequency for the main isotope ${}^{24}\mathrm{Mg}$ is determined at $49346.756809\left(35\right){\mathrm{m}}^{-1}$. This value is three orders of magnitude more precise than the best value in the literature. The line positions of the other isotopes ${}^{25}\mathrm{Mg}$ and ${}^{26}\mathrm{Mg}$ are also measured at comparable accuracy, giving rise to very exact values for the isotopic shifts. The achieved precision for the transition frequency at the $7\times {10}^{-10}$ level makes this second resonance line of $\mathrm{Mg}\mathrm{\text{I}}$ an additional candidate for inclusion in many-multiplet methods, aimed at detecting a possible temporal variation of the fine-structure constant $\alpha$ from comparison with quasar spectra. The isotopic shifts obtained are also important to correct for possible systematic shifts due to evolution of isotopic abundances, which may mimic $\alpha$-variation effects.

The Levinson theorem for the $(1+1)$-dimensional Dirac equation with a symmetric potential is proved with the Sturm-Liouville theorem. The half-bound states at the energies $E=\pm M$, whose wave function is finite but does not decay at infinity fast enough to be square integrable, are discussed. The number $n_{\pm }$ of bound states is equal to the sum of the phase shifts at the energies $E=\pm M$:${\delta }_{\pm }\left(M\right)+{\delta }_{\pm }(-M)=(n_{\pm }+a)\pi ,$ where the subscript ± denotes the parity and the constant $a$ is equal to $-1∕2$ when no half-bound state occurs, to 0 when one half-bound state occurs at $E=M$ or at $E=-M$, and to $1∕2$ when two half-bound states occur at both $E=\pm M$.

We investigate the collective excitations of a harmonically trapped superfluid Fermi gas at varying coupling strengths across a BCS-BEC crossover. Using a hydrodynamic approach, we solve analytically the eigenvalue problem of collective modes and provide explicit expressions for all eigenvalues and eigenfunctions, which are valid for both BCS and BEC limits and also for the whole crossover regime. Both spherical- and axial-symmetric traps are taken into account, and the features of these collective modes in the BCS-BEC crossover are discussed and compared with available experimental and numerical data.

We map out the detailed phase diagram of a trapped ultracold Fermi gas with population imbalance across a wide Feshbach resonance. We show that under the local density approximation, the properties of the atoms in any (anisotropic) harmonic traps are universally characterized by three dimensionless parameters: the normalized temperature, the dimensionless interaction strength, and the population imbalance. We then discuss the possible quantum phases in the trap, and quantitatively characterize their phase boundaries in various typical parameter regions.