We show that amplitude-squeezed states may be produced by driving a feedback-controlled cavity with a coherent input signal. The feedback controls the transmissivity of one output from the cavity and is essentially equivalent to nonlinear absorption. The cavity effectively acts as a nonlinear reflector. Hence, amplitude-squeezed states with arbitrarily strong coherent intensities can be obtained.

We investigate the effects of photon-number quantum-nondemolition measurements performed by an eavesdropper on a two-photon correlated state. The relation between this model and quantum cryptography is discussed. It is shown that violation of Bell’s inequality is very sensitive to the probe amplitude of the measurement system.

The quantum effects on a cavity mode of the electromagnetic field caused by measuring one of its quadrature components is analyzed. We consider three measurement schemes: an intracavity quantum-nondemolition coupling to another mode, simple homodyne detection, and balanced homodyne detection. It is shown that, for suitable initial conditions, the first scheme has an effect which approaches that of a projective collapse of the state vector for long measurement times. However, the two homodyne schemes (which are shown to be equivalent for large local-oscillator amplitudes) do not approximate a projective measurement in any limit. In particular, it is shown that homodyne measurement cannot produce a squeezed state from a classical initial state. All three schemes are analyzed in terms of ‘‘quantum trajectories’’ which link measurement theory with stochastic quantum-jump processes.

The near-resonant interaction of an atomic beam with an optical standing-wave field can produce a deflection of the beam that depends on the initial atomic state. We investigate the extent to which the momentum transfer may be regarded as a coherent nondestructive encoding of the internal atomic state on the center-of-mass motion. Techniques developed for analyzing quantum-nondemolition measurements are used to quantify the effectiveness of this encoding. The effects of varying the detuning and the profile of the optical beam are discussed using parameter values close to those recently realized experimentally by Sleator et al. [Phys. Rev. Lett. 68, 1996 (1992)].

It is shown that the standard calculation of the free-space spontaneous-emission rate leads to a spurious velocity dependence if the atomic motion is included nonrelativistically. The unphysical terms are of first order in v/c, akin to the nonrelativistic Doppler shift.

Taking into account the photon momentum (i.e., without making the dipole approximation) we derive some different expressions for the nonrelativistic amplitude for a one-electron system to undergo a transition in a classical monochromatic field. As an application, we use the Keldysh approximation, generalized beyond the dipole approximation, to examine the effect of the photon momentum on the angular distribution for multiphoton detachment of a model ${\mathrm{H}}^{\mathrm{-}}$ ion by a strong low-frequency field. We find that when the field is very strong the neglect of the transverse Doppler shift (but inclusion of the nonrelativistic Doppler shift) leads to a spuriously large rate for multiphoton detachment, even though the relativistic correction to the rate is very small.

Recently, the quantum mechanics on a curved low-dimensional space was studied. There is an embedded effect when the space embedded in three-dimensional Cartesian space has some curvature. In this paper, we will consider second quantization of the spinless Schrödinger field there at finite temperature and show that there is also an embedded effect even though the low-dimensional space has no curvature as a manifold. This effect appears as an effective chemical potential.

The dynamic Lie-algebra structure decomposition of the time-dependent Schrödinger equation for a quantum system is analyzed and the results are used to study the Aharonov-Anandan phase. The expression for Aharonov-Anandan phase is given, which is shown to be useful by the illustration of some examples and to be applicable to rather general systems.

The optical-potential method based on the Feshbach projection-operator formalism has been successfully applied to the computation of fine-structure splittings between highly excited levels of helium [R. J. Drachman, Phys. Rev. A 26, 1228 (1982)]. In this paper, I report additional terms in the nonrelativistic effective potential decreasing as ${\mathit{x}}^{\mathrm{-}9}$ and ${\mathit{x}}^{\mathrm{-}10}$, where x is the distance of the outer electron from the ${\mathrm{He}}^{+}$ core. They involve higher-multipole distortions of the wave function of the core electron, higher nonadiabatic corrections, and perturbation theory up to fourth order in the electrostatic potential. Energy shifts due to these terms are compared with the extremely accurate variational results of Drake [Phys. Rev. Lett. 65, 2769 (1990)].

We have made a careful comparison of all available high-precision data for the 1s2s ${}_{}{}^3{}_{}{}^{}$${\mathit{S}}_{1–}$1s2p ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_{0,1,2}$ transition energies for all nuclear charges ranging from helium (Z=2) to uranium (Z=92). Systematic discrepancies appear between theory and experiment for the J=1→0 transitions, but not for the J=1→1 and J=1→2 transitions. Analysis of laser-based high-resolution data (Z=2, 3, and 5), beam-foil spectroscopy data (Z=10–17), and hyperfine-quenched decay data (Z>27) suggests an additional contribution to the ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_0$ energy equal to 2.3 (Z/10${)}^4$ ${\mathrm{cm}}^{\mathrm{-}1}$.

The use of the optogalvanic technique to obtain the line profile of the Cu 5s’ ${}_{}{}^4{}_{}{}^{}$${\mathit{D}}_{5/2}$ autoionization level with different degrees of saturation broadening is demonstrated. The experimental results point out that the growth of the autoionization-level breadth follows the square root of the increase in the laser intensity. The measured value of the natural breadth of the Cu5s’ ${}_{}{}^4{}_{}{}^{}$${\mathit{D}}_{5/2}$ autoionization level is 7.2±0.6 ${\mathrm{cm}}^{\mathrm{-}1}$. The laser saturation intensity was measured by two different methods, and its value is about 0.39±0.09 MW/${\mathrm{cm}}^2$.

We present an alternative theoretical procedure for the positions and widths of the doubly excited resonances of a two-electron atom based on a configuration-interaction procedure for continuum by using a B-spline-based finite basis set. More specifically, by examining the energy variation of the probability density corresponding to the singly excited ionization channel, the resonant energy ${\mathit{E}}_{\mathit{r}}$ of the doubly excited autoionization state can be directly linked to the energy at the minimum probability density. The width of the resonance can be identified with the energy separation between two energies, which are located on the opposite side of the center of the resonance and each corresponds to a probability density twice the minimum value at ${\mathit{E}}_{\mathit{r}}$. The effectiveness of this procedure is demonstrated by the excellent agreement between our calculated widths of the Feshbach resonance for ${\mathrm{H}}^{\mathrm{-}}$ and He below the n=2 threshold and the ones from the most accurate existing theoretical calculations.

Double- and single-electron-capture processes have been studied theoretically in the energy range from 50 eV to 2 keV by using a molecular-orbital expansion method. Atomic-type electron-translation factors have been implemented to ensure that the scattering boundary conditions are correct. The cross sections for single- and double-electron capture were found to cross each other at 500 eV, with double-electron capture being dominant at the lower energies studied. This finding is consistent with recent experimental measurements.

We have solved exactly the Schrödinger equation in hyperspherical coordinates for some quantum-mechanical many-body systems. These systems, which interact with Coulomb, inverse-square, harmonic-oscillator, dipole, or Yukawa potentials, etc., can be solved in a similar way. Wave functions are expanded into orthonormal complete basis sets of the hyperspherical harmonics of hyperangles and generalized Laguerre polynomials of the hyperradius. The eigenvalues can be obtained explicitly by solving a simple secular equation. The results of practical calculations of Coulomb potential systems, such as H, He, and ${\mathrm{H}}^{\mathrm{-}}$, etc., agree well with the reported exact ones.

An extension of the Simons-Parr-Finlan approach to the analytical calculation of the rotational-vibrational energy of diatomic molecules is proposed. The obtained eigenvalues are applied in the calculation of molecular constants as well as in assignment of rovibrational spectra of the ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }$ state of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}_{}^{32}{}_{}{}^{}$S and of the ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{\mathit{g}}^{}{}_{}{}^{}$ state of ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ar}_2^{}{}_{}{}^{}$ molecules, giving quite satisfactory reproduction of the experimental data over a wide range of rotational states.

We consider potential scattering of electrons in a laser field. The field has frequencies ω and 2ω, which are out of phase by an angle cphi. We find considerable modifications of the laser-induced scattering cross sections as a function of the phase angle cphi, which for currently available experimental facilities should be observable effects.

We have solved numerically the time-dependent Schrödinger equation for an electron in a superstrong laser field while it undergoes a collision with a model one-dimensional hydrogen atom. We show that a certain fraction of the electron can be trapped by the atom in superstrong fields. This trapped portion has a dichotomous spatial probability distribution, corresponding to an effective excitation of Kramers-Henneberger field-dressed states, which is quite resistant against subsequent detachment. By varying the incoming electron’s kinetic energy these states can be selectively excited.

The multiphoton Jaynes-Cummings model with an initially unexcited two-level atom is considered in the context of its ability to produce a sub-Poissonian field in interaction with an initially chaotic (thermal) cavity field.

It is pointed out that quantum optics provides examples where the origin of geometrical phase factors can be investigated in two different ways. The first possibility relies on a line bundle in which the fibers over each base point in parameter space consist of Stark states, whereas fibers of Floquet states yield a second possibility. Both constructions are compared in some detail, and the Floquet bundle is found to offer distinct advantages.

The effect of laser fields of intermediately high intensity on the inelastic scattering of x-ray radiation below an absorption edge is theoretically investigated. The results obtained suggest a frequency-selective method for the measurement of the length of an ultrafast x-ray pulse by measuring the intensity of an inelastically scattered narrow-band fraction of the x-ray pulse at different delays of the probe pulse of an intense laser.