The neutron-interferometry (NI) technique provides a precise and direct way to measure the bound, coherent scattering lengths $b$ of low-energy neutrons in solids, liquids, or gases. The potential accuracy of NI to measure $b$ has not been fully realized in past experiments, due to systematic sources of error. We have used a method which eliminates two of the main sources of error to measure the scattering length of silicon with a relative standard uncertainty of 0.005%. The resulting value, $b=4.1507\mathrm{}\left(2\right)\mathrm{}\mathrm{fm},$ is in agreement with the current accepted value, but has an uncertainty five times smaller.

We investigate theoretically the properties of a Bose-Einstein condensate located in a spatially periodic potential. The excitations of the condensate are obtained from linear equations involving the periodic potential and the periodic condensate density. The Bloch ansatz therefore applies and the excitation spectrum exhibits band structure. If the periodic potential is accelerated, the condensate may undergo Bloch oscillations in the accelerated frame, corresponding to an acceleration without spreading of the entire condensate.

Bose-Einstein condensation is known to occur in one-dimensional power-law potentials $V\left(x\right)\mathrm{}\propto |x{|}^{\eta }$ as a true phase transition for η<2, but only if there are no interactions between the particles. We show, via a path-integral quantum Monte Carlo scheme, that for both η<2 and η=2 the spatial distribution of finite numbers of hard-core bosons suddenly becomes bimodal below a certain temperature, with a central condensate of particles distributed according to the lowest single-particle eigenstate. At still lower temperatures, the hard-core interactions cause the single-particle ground state to become a poor description for the interacting gas. If η<2, the energy per particle undergoes a sudden decrease near the same temperature at which the bimodal distribution appears. It is found that this drop in energy disappears if the range of the interaction potential is sufficiently large.

The onset of Bose-Einstein condensation in a sample of N atoms confined to harmonic traps is critically examined. The monotonic growth of the condensate fraction f and the nonmonotic variation of the specific heat C of the sample are studied in fine detail. While no temperature is truly critical, our analysis does provide a strong theoretical basis for recognizing a temperature $T^{*},$ that has been identified and advocated by previous authors, as the transition temperature of the system. The specific-heat maximum $T_m$ (which happens to be another important “marker” in this transition), the value of the specific heat at ${T=T}_m,$ and the “jump” in the specific heat of the system when the number N becomes very large are all explicitly evaluated. Wherever comparison is possible, our analytical results are found to be in perfect agreement with the ones obtained numerically by Kirsten and Toms [Phys. Rev. A 54, 4188 (1996)] and by Haugerud, Haugest, and Ravndal [Phys. Lett. A 225, 18 (1997)].

The problem is examined whether a bistable behavior of optical response of a dimer really exists. We carry out an exact treatment of this problem based on the two-molecule density matrix, without its representation in the form of a product of the one-molecule density matrices of each molecule composing the dimer. Our conclusion is that the bistability discussed is an artifact originating from the splitting procedure. A condition for getting the bistable optical response from a linear chain of a large number of monomers is also formulated.

The collision of solitons in optical fibers is a promising scheme for the quantum-nondemolition measurement of the photon number using the cross Kerr effect. In a realistic experimental situation, the sensitivity of the measurement is limited not only by self-phase-modulation noise of the probe but also by the phase noise added due to the vibrational excitations of the fiber. Former schemes proposed to overcome either of these problems are not compatible with each other. In this paper the sensitivity of different type of detection is carefully studied. We propose a solution based on the use of a phase-shifting cavity. We show that this provides a conceptually and practically simple solution eliminating simultaneously both sources of excess noise.

We have performed systematic measurements and numerical modeling of the divergence and exit beam size of a 46.9 nm Ne-like Ar capillary discharge pumped soft-x-ray amplifier. Two-dimensional near-field and far-field measurements were obtained over a wide range of discharge parameters. The spot size and divergence of the laser beam were observed to increase significantly with decreasing discharge pressure. Simultaneously, the beam intensity distribution changed from a single peak pattern to an annular profile. These effects are shown to be the result of increased refraction of the soft-x-ray beam, caused by larger density gradients in the plasma columns of the lower pressure discharges. The spatial images are nearly cylindrically symmetric, and have less structure than those reported in the literature for laser-driven soft-x-ray lasers. Beam profiles synthesized by model calculations are found to be in good agreement with the recorded images. The obtained images in combination with the model computations clarify the origin of the different beam patterns that are observed in capillary discharge soft-x-ray laser experiments.

A cavity-modified master equation is derived for a coherently driven two-level atom coupled to a single-mode cavity in the bad cavity limit, in which the cavity frequency is tuned to either the center or one of the sidebands of the Mollow triplet. The atomic populations in both the bare- and dressed-state representations are analyzed in terms of the cavity-modified transition rates. In the bare-state basis, the role of the cavity may be interpreted as enhancing the stimulated absorption of the atom while suppressing the stimulated emission. The bare-state population may thus be inverted under appropriate conditions. The dressed-state inversion, however, originates from the enhancement of the atom-cavity interaction when the cavity is resonant with the atomic dressed-state transition. We show that two-phase quadratures of the atomic polarization decay at different rates. The decay of the in-phase (or out-of-phase) quadrature may be greatly inhibited as the driving intensity increases, depending on the cavity resonant frequency. The spectrum of the atomic fluorescence emitted out the side of the cavity is also studied. The spectral profiles are sensitive to the cavity frequency. When the cavity frequency is tuned to the center of the Mollow resonances, the fluorescence spectrum is symmetrical with three peaks whose linewidths and heights are intensity dependent. When the cavity frequency is tuned to one of the Mollow sidebands, however, it is asymmetric, and the central peak and the sideband on resonance with the cavity can be significantly suppressed for strong driving fields. All three spectral lines can be narrowed by increasing the Rabi frequency. The physics of these striking spectral features is explored in the dressed-state basis. We also investigate the probe absorption spectrum. When the cavity frequency is tuned to the center of the Mollow fluorescence triplet, the central component exhibits a Lorentzian line shape, while the side bands show the Rayleigh-wing line shape. Probe gain may occur at line center due to cavity-induced, bare-state population inversion. When the cavity is tuned to resonance with one sideband, only two sidebands, with Lorentzian profiles, dominate. Gain can occur at the sideband far off resonant with the cavity. The sideband gain is a consequence of an unbalanced dressed-state population distribution.

We study the dynamic behavior of an electron in a two-level system driven by dc-ac electric fields. Analytical solutions for the dipole moment and its emission spectrum are obtained under the approximation of the high-frequency driving case, from which the physical property of the system is found to be controlled by the field parameters. A number of time-periodic and quasiperiodic phenomena as well as their signature in the emission spectrum are revealed. By making the proper choice of the field parameters, it is possible to selectively eliminate some components in the spectrum. The analytical findings are confirmed numerically.

Recent numerical work has demonstrated how one of the bistable states of a driven, damped, anharmonic classical oscillator is metastable in the corresponding quantum oscillator [D. Enzer and G. Gabrielse, Phys. Rev. Lett. 78, 1211 (1997)]. Based on an analysis of the classical oscillator, we present a simple analytical treatment of the quantum oscillator. Calculated fluctuations in the quantum observables and the estimated decay rate of the metastable state are in an excellent agreement with the numerical results of Enzer and Gabrielse.

Observation of transient effects in electromagnetically induced transparency (EIT) is reported in ${\mathrm{Rb}}^{85}$ cooled in a magneto-optical trap. The transmission of a weak probe beam in resonance with the ${5S}_{1/2}\mathrm{}(F=3\mathrm{})\mathrm{}$ to ${5P}_{3/2}\mathrm{}(F=3\mathrm{})\mathrm{}$ hyperfine transition increased transiently when a relatively strong coupling field in resonance with the ${5S}_{1/2}\mathrm{}(F=2\mathrm{})\mathrm{}$ to ${5P}_{3/2}\mathrm{}(F=3\mathrm{})\mathrm{}$ hyperfine transition was switched on rapidly using a Pockels cell. The probe transient showed an initial Rabi half-cycle overshoot before settling down to steady-state EIT. The results agreed well with computations using a three-state model of the Λ system. The computations also suggest that transient gain should be observed with coupling field power only four times larger than that presently available to us.

An ansatz is proposed for the analytic solution of the Heisenberg equations of a two-level atom in a classical, linearly polarized and intense low-frequency field. According to this ansatz, the motion of the vector representing the state of the atom on the Bloch sphere consists of a fast precession around a direction, which in turn basculates slowly around an axis perpendicular to the field. The time evolution of the atomic state, which is obtained analytically by this vectorial model, is shown to compare quite satisfactorily with the exact numerical solution of the Heisenberg equations. The limits of validity of the ansatz are discussed. The spectrum of the light scattered by the two-level atom is evaluated analytically using the ansatz and it is shown to reproduce very precisely the exact spectrum evaluated numerically. It is shown that the slow component of the motion of the atomic Bloch vector yields the high-order harmonic part of the spectrum, whereas the fast precession gives rise to the hyper-Raman part. The appearance of the overall spectrum is discussed as a function of the various physical parameters of the model. The insight provided by the vectorial model is exploited to investigate the manifest universality of the main features of the overall spectrum and to suggest experiments to test the validity of the vectorial model.

Dynamic properties of closed three-level laser systems are investigated. Two schemes of pumping—$\Lambda$ and V—are considered. It is shown that the nonlinear behavior of the photon number as a function of pump both near and far above threshold is crucially different for these two configurations. In particular, it is found that in the high pump regime laser can turn off in a phase-transition-like manner in both $\Lambda$ and V schemes.

We show that under rather general conditions the propagation of sound pulses along the long axis of a Bose-Einstein condensed cloud in a very anisotropic trap is essentially one dimensional. In the linear regime, we demonstrate that the square of the velocity of propagation is given by the square of the local sound velocity $c^2{=nU}_0/m$ averaged over the cross section of the cloud. We also carry out calculations in the nonlinear regime and determine how the speed of the pulse depends on its amplitude.

Two-wavelength two-wave mixing in photochromic photoreversible azo and stilbenelike media is discussed for the special case in which the refractive index grating is written by two beams of angular frequency 2ω while the two-wave mixing is examined at the frequency ω. For the specific conditions stated in the paper, the analysis leads to a rigorously derived phase angle φ, followed by the expected energy exchange between the beams. Then, the influence of the experimental constraints on the gain is considered.

Using canonical and unitary transformations and the Lewis-Risenfeld invariant method, the exact Schrödinger wave function for a harmonic plus inverse harmonic potential with time-dependent mass and frequency is obtained analytically.

A systematic spectroscopy of the inner shells in superheavy quasimolecule systems with energy eigenvalues in the vicinity of the negative continuum has still not been realized. The investigation of quasimolecular x rays in collisions with bare projectiles represents a unique tool to study the transiently formed molecular orbitals. For heavy-ion collision systems it seems to be a promising approach to get information about the inner orbitals at small internuclear distances. We present calculations of quasimolecular x rays from the heavy-ion collision system U${}^{92+}$-Pb and study the dependence on the impact energy and the impact parameter. We find that up to an impact energy of 50 MeV/u the interference structure is visible in the spectrum.

We rederive the Kohn-Sham formulation of density-functional theory by considering it as a special case of the mapping of the physical density to that of a Slater determinant with an arbitrarily chosen density. It follows that the application of the variational principle requires an additional constraint, with a Lagrange multiplier function that modifies the effective local potential. The Kohn-Sham theory is then regained in the limit of the vanishing Lagrange multiplier. We then study the possibility of applying a similar idea to a formulation, proposed recently by the authors, in terms of the density matrix rather than the density; it follows from well-known relations that this cannot be done.

We report precision measurements of the energies of the Na $10{}^{2}P,$ $11{}^{2}P,$ and $10{}^{2}D$ states and their fine-structure intervals. The $P$-state results bridge the gap between earlier high- and low-$n$ measurements from other laboratories, thus facilitating calculation of quantum-defect parameters. Quantum-defect theory fits to all available data on Na are critically examined. Using the most reliable values at low, intermediate, and high $n$ leads to a single set of four quantum-defect parameters that is useful over the entire range of $n.\mathrm{}$ Also, using the present $P$-state measurements, we extract a value of the ionization potential that is in exact agreement with our earlier determination.

Using narrowband tunable linearly or circularly polarized VUV radiation an examination of the dynamical parameters describing the autoionization process of atomic xenon was performed. With a resolving power of $\sim {10}^5$ in the excitation step a fully resolved determination of the position, magnitude and shape of the angular distribution and integral spin-polarization resonances was possible for the low Rydberg orders $n=7\mathrm{}$ and $n=9\mathrm{}$ of the $d$ and $s$ series, respectively. Comparisons are drawn between the experimental data and some theoretical calculations published in recent years.