Motivated by the behavior of carriers in various condensed systems, we formulate and discuss the mechanics of a particle described by a nonmonotonic dispersion law. For illustration, we consider the scattering of a particle with a @sw-shaped dispersion law by a one-dimensional potential barrier. The negative mass feature of the dispersion gives rise to a number of unusual phenomena, including barrier penetration by a classical particle, particle trapping by the barrier, and scattering resonances in both transmission and reflection.

We construct the most general SO(4,2) hydrogen-atom coherent states which are the counterpart of Schrödinger’s harmonic-oscillator coherent states. We show that these states cannot be localized and cannot follow the classical orbits. Thus, Schrödinger’s conjecture for the hydrogen-atom coherent states is unattainable.

We report measurements of the 6${\mathit{p}}^2$${\mathit{P}}_{1/2}$ and 6${\mathit{p}}^2$${\mathit{P}}_{3/2}$ state lifetimes in the ${}_{}{}^{133}{}_{}{}^{}\mathrm{Cs}$ atom with precisions of 0.23% and 0.27%, respectively. The results are important to the interpretation of the next generation of parity nonconservation experiments in atomic cesium. A diode laser was used to selectively excite a fast beam of neutral cesium atoms. The decay in flight of the fluorescence was observed with photon-counting detectors. The lifetime results are 34.934±0.094 ns for the 6${\mathit{p}}^2$${\mathit{P}}_{1/2}$ state and 30.499±0.070 ns for the 6${\mathit{p}}^2$${\mathit{P}}_{3/2}$ state. We present comparisons with previous measurements and with relativistic many-body calculations of alkali-metal-atom transition matrix elements.

The g factors for the Zeeman effect, including relativistic corrections up to order ${\mathrm{\alpha }}^2$ a.u., are calculated to high precision for the 2${\mathrm{}}^3$${\mathit{P}}_{\mathit{J}}$, 2${\mathrm{}}^1$${\mathit{P}}_1$, 2${\mathrm{}}^3$${\mathit{S}}_1$, and 3${\mathrm{}}^3$${\mathit{P}}_{\mathit{J}}$ states of helium, using variational wave functions constructed from doubled Hylleraas-type basis sets. Our results clarify the present disagreements among the existing theoretical values for the g factors. The experimental values of the fine-structure splittings for the helium 3${\mathrm{}}^3$${\mathit{P}}_{\mathit{J}}$ states, measured by Yang et al. [Phys. Rev. A 32, 2249 (1985); 33, 1725 (1986)], are reanalyzed, using our improved g factors.

Two-color photodetachment of a negative ion in the presence of a constant magnetic field is proposed as a process in which to observe the ponderomotive shift. Appropriate calculations are reported of the process under consideration based on a simple one-electron model and with the basic physical parameters well within the experimental state of the art.

Laser sideband cooling of trapped ions is studied in a standing wave for localization conditions far from the Lamb-Dicke limit. Cooling is shown to be possible even in the antinode of a standing wave, where in the Lamb-Dicke limit only heating appears. Tuning the laser to the second-sideband increases the cooling effect significantly. Moreover, second-sideband cooling is expected to yield a nonclassical, sub-Poissonian occupation statistics of the vibrational states of the ion.

We describe our use of recoil-induced resonances or stimulated optical Compton scattering to measure the velocity distribution of laser-cooled cesium atoms in one dimension. The technique works well at velocities near 1 cm/s, is insensitive to the effects of light shifts or stray fields, requires only a few ${\mathrm{mm}}^3$ of work space, and may be completed in 1 ms. It may be extended to allow the measurement of velocity distributions in three dimensions and for in situ measurements in optical molasses, traps, or lattices. Our measurements are compared with traditional ballistic measurements in the same apparatus.

I consider a lossless micromaser with cascade three-level atoms in a coherent superposition of its three levels. I find that for some values of the atomic flight time and some probability amplitudes for the intermediate atomic level, the field evolves to a pure state which is the well-known general squeezed state, and the squeeze and displacement parameters are functions of the atomic input parameters. Therefore it is possible to choose atomic parameters which produce squeezing in the phase or in the amplitude of the field inside the cavity.

We show that four-wave mixing in optically dense media is very different than in an optically thin medium. In time-resolved degenerate four-wave mixing we experimentally observe ‘‘negative’’ time delay response, fast decay rates at short delay times, and broad shoulders at long delays. The observations are explained very well in terms of pulse propagation effects, and a theoretical framework is presented for the analysis of the nonlinear interaction. We treat both the incident and generated fields self-consistently, and solve for the interaction of short pulses with a resonantly absorbing medium. The implications for the extraction of relaxation rates from four-wave-mixing experiments involving ultrashort pulses in optically dense matter are discussed.

We investigate the possibility that high-energy photons are channeled, when passing through an oriented single crystal, due to Delbrück scattering. For this purpose the exact electron propagator for the single-string model is constructed. Starting from a separation of variables, we solve the Dirac equation for a cylindrical electrostatic potential. The propagator for such external fields is constructed from solutions of the radial Dirac equation. This propagator is applied to a calculation of the S matrix for Delbrück scattering. We specify the conditions under which photon channeling takes place. Unfortunately these conditions are only matched for a very small fraction of those photons being produced by channeled electrons.

In this paper we present some calculations regarding the average number of photons produced in the dynamical Casimir effect for the ideal case of two perfectly conducting uncharged parallel plates, using the zero-point energy summation method. We show that it is possible to create intense photon radiation when the two plates are modulated periodically.

The two quantum invariant operators are found from the time-dependent Hamiltonian of the harmonic oscillator with an auxiliary condition. The solution of the Schrödinger equation for the system, such as the eigenfunctions, eigenvalues, and minimum uncertainty, is derived by utilizing these invariant operators. The coherent states of this system are not the squeezed states, and the eigenfunction of the invariant operator is not the eigenfunction of the Hamiltonian of the system unless it is in the invariant representation. The squeezing function, which is an eigenfunction of the Hamiltonian of the system in the invariant representation and which also gives the minimum uncertainty, is obtained by a set of unitary transformed operators, i.e., squeezing operators.

The model problem of atomic closed shells in a bare Coulomb field has been the subject of considerable interest following the recent demonstration by Blinder [Phys. Rev. A 29, 1674 (1984)], with subsequent generalization by March [Phys. Lett. 111A, 47 (1985)], that the electron density in an arbitrary closed shell in a bare Coulomb field is expressible solely in terms of its s-state contribution. The present paper will provide a simple derivation of this important relationship by application of the methods of supersymmetric quantum mechanics to the radial Coulomb problem. Using this relation, differential equations are derived which are satisfied by the electron density for an arbitrary closed shell and the Slater sum for an arbitrary number of closed shells in a bare Coulomb field.

Quantum cryptography cannot prevent eavesdropping, but any eavesdropping attempt can be detected by the legitimate users of the communication channel. This is because eavesdropping affects the quantum state of the information carriers and results in an abnormal error rate. In this paper, we analyze various eavesdropping techniques, which may be either translucent or opaque to the transmitted photons, and we estimate the error rate above which the key distribution is deemed unsafe and should be abandoned.

It is proposed that the contribution of vacuum fluctuations to spontaneous emission and the Casimir force can be attributed to the creation of single photons at the positions of charged particles as in relativistic quantum field theory. Thus the change from normal to symmetric order in the particle-field interaction Hamiltonian and the preservation of the equal-time commutation relations need not imply vacuum fluctuations in the absence of matter.

One difficulty with the correspondence principle is its vagueness. To what should the quantum theory correspond in the quasiclassical domain? Here we show that, whatever it is, it cannot be Hamilton’s equations. This is done using Weinberg’s generalized nonlinear quantum theory [S. Weinberg, Ann. Phys. (N.Y.) 194, 336 (1989)] by exploiting the fact that it contains an exact copy of classical dynamics [K. R. W. Jones, Phys. Rev. D 45, R2590 (1992)]. An enlarged dynamical theory incorporating mixed quantum and classical interactions is shown to have some desirable properties in relation to measurement. By studying this system, we show that the existence of observable physical domains obeying intrinsically classical laws would violate the uncertainty principle; thereby ruling out an entire class of such larger theories. We interpret this result as a demonstration that the correspondence principle is essentially approximate. Further, the given exclusion is suggestive as a guide to physical models of quasi- classical emergence in a scenario based upon environment noise and stochastic reduction.

We study the quantum effect of chaos on dynamical tunneling in the driven pendulum. We analyze the avoided level crossing between the Floquet states associated with the chaotic part of the phase space and a member of the quasidegenerate doublet. As a result of the interaction, the doublet state whose Husimi distribution was initially localized on Kolmogorov-Arnold-Moser symmmetric islands exchanges its structure with the chaotic state. We investigate the implications of this kind of avoided crossing on the quantum dynamics of a wave packet initially centered on one of the symmetric islands.

In this work we report a Doppler-free investigation of atomic nitrogen. As a laser source we used a narrow-band semiconductor diode laser emitting in the near infrared. Atomic nitrogen was produced by dissociating ${\mathrm{N}}_2$ molecules in a radio-frequency discharge sustained by helium as a buffer gas. Hyperfine structures and isotope shifts of the transitions 3p ${}_{}{}^4{}_{}{}^{}$${\mathit{P}}_{1/2\mathrm{-}5/2}$–3s ${}_{}{}^4{}_{}{}^{}$${\mathit{P}}_{1/2\mathrm{-}5/2}^{\mathit{o}}$ were investigated for the two stable isotopes ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ and ${}_{}{}^{15}{}_{}{}^{}\mathrm{N}$ by using absorption-saturated laser spectroscopy.

A deformed version of the vibron model for diatomic molecules is constructed. Both the O(4) and U(3) dynamical symmetries of the model are rewritten, using the concept of complementary subalgebras, in a more convenient form, which is subsequently deformed. The present model unifies the so far independent successful quantum-algebraic approaches to rotational and to vibrational spectra of diatomic molecules. In addition, the method can be used for the construction of deformed versions of the U(5) and O(6) limits of the interacting boson model of nuclear structure.

A systematic study of relative K x-ray intensities has been made on the elements Mn, Ni, Cu, Ga, Ge, Ag, Cd, Sn, and Sb in the form of pure elements, alloys, and compounds to look into the influence of solid-state effects. The vacancies in the K shell were created by 59.54-keV γ rays from an ${}_{}{}^{241}{}_{}{}^{}\mathrm{Am}$ radioactive source and the x rays were measured using a Si(Li) detector. Our results are in good agreement with the previously published data. Alloying was found to have a negligible effect on the Kβ-to-Kα ratio. The present experimental data agree very well with Scofield’s [At. Data Nucl. Data Tables 14, 121 (1974)], theoretical data in all cases except silver and antimony.