We calculate the effects of normal transmission through an amplifying dielectric slab on the properties of an incident pulse of light. The transmitted pulse shows shifts in peak position and additional lengthening or shortening with respect to the unamplified incident pulse. The magnitudes of these effects are generally larger than those of the corresponding changes that occur in transparent or attenuating slabs. They are interpreted in terms of the interference of multiply reflected contributions to the transmitted pulse. The theory is valid for pulses of nonclassical light, but the same reshaping occurs for appropriate pulses of classical light.

We study analytically the dynamical behaviors of class $A$ and $B$ lasers operating on two transverse modes. A generalization of the well-known multimode model of Lamb, taking into account the transverse hole burning effects as well as nonlinear phase couplings, is considered. Taking as a control parameter the difference between the empty cavity eigenfrequency of the modes, the main developments of this article are the following. The existence and stability of stationary patterns related to (i) single-mode stationary states and (ii) locked bimode phase-sensitive solutions are analyzed. (iii) Unlocked periodic behavior and frequency pushing or pulling effects are characterized in a fully analytical description. Our analysis puts in evidence the qualitative differences of stationary as well as periodic behaviors for class $A$ and $B$ bimodal lasers. Moreover, we show that the laser response is strongly dependent on the symmetry properties, or on the relative spatial parity, of the modes involved: The dynamical properties of opposite or equal parity modes laser are introduced and investigated here.

Using the formalism developed by Chew [Phys. Rev. A 38, 3410 (1988); J. Chem. Phys. 87, 1355 (1987)], we evaluate the modifications on radiative dipole transition rates with respect to their bulk values for a sonoluminescent gas bubble in water considering different spatial distributions of the emitters. The most relevant changes occur near the center of the bubble and near its surface both inside and outside the bubble. The modifications are also strongly dependent on the polarization of the emitted light. The possibility of using these properties to experimentally characterize the space distribution of sonoluminescent emitters is discussed.

We analyze a pure-state photon-number amplifier (PNA), i.e., a device that performs the action $|{\psi }_{\mathrm{in}}〉={\sum }_l{c}_l|l\overrightarrow{〉}|{\psi }_{\mathrm{out}}〉={\sum }_l{c}_l|\mathrm{Gl}〉,$ where $G$ is a positive integer. We derive expressions for the fidelity of a finite internal state PNA and demonstrate that the amplifier fidelity, i.e., the similarity between the obtained and the desired output state can be made to approach unity. Finally we outline a systematic procedure to find the Hamiltonian for any finite Hilbert-space PNA and compute the Hamiltonian for a simple but nontrivial PNA.

Here the probability for a nonlocality contradiction of the Hardy type is made to depend explicitly on both the quantum state describing the particles and the choice of one of the observables involved. One can then set the above probability to any prescribed value within a certain interval by varying a suitable experimental parameter, with the quantum state remaining unchanged.

By considering a laser-induced dipole layer along the surface of a metal and its action on an electron of the metal, it is shown that at moderate laser field intensities of some ${10}^{10}\hspace{0.5em}{\mathrm{W}\mathrm{}\mathrm{cm}}^{\mathrm{-}2}$ energetic electrons of a few 100 eV can be produced, which explains recent observations of Farkas et al. [Phys. Rev. A 41, 4123 (1990); Opt. Eng. 32, 2476 (1993)] without necessarily resorting to the mechanism of Coulomb explosion, taking place after the completion of the ionization process.

We consider the feasibility of controlling the energy transfer between an unexcited and an excited atom using microcavities. The excitation-transfer probability is related to the strength of the dipole-dipole interaction and thus the excitation-transfer rates could be increased by enhancing the dipole-dipole interaction. We demonstrate this enhancement with an explicit three-dimensional calculation for a metallic cavity, which we characterize with a realistic dielectric function. We also demonstrate the shifts in cavity resonances from their ideal positions $m\lambda /2\mathrm{}$ ($m$ is an integer and λ is the wavelength).

A method for reconstructing the quantum state of a system of atoms or spins is proposed. The $Q$ distribution is derived from the measured population in the ground state of a system that has interacted with an external field. Using multipole operators the $Q$ function is inverted to derive the density matrix.

A simple model for a particle in a double well is derived from discretizing its configuration space. The model contains as many free parameters as the original system and it respects all the existing symmetries. In the presence of an external periodic force both the continuous system and the discrete model are shown to possess a generalized time-reversal symmetry in addition to the known generalized parity. The impact of the driving force on the spectrum of the Floquet operator is studied. In particular, the occurrence of degenerate quasienergies causing coherent destruction of tunneling is discussed—to a large extent analytically—for arbitrary driving frequencies and barrier heights.

The problem of a two-level atom interacting with a radiation pulse is studied in the limit that the atom-field detuning times the pulse duration is much greater than unity. Owing to the large atom-field detuning, transitions result from nonadiabatic coupling of the states by the field. The transition probability for the atom to be excited following the pulse is studied as a function of field strength for five different pulse shapes: hyperbolic secant, Lorentzian, hyperbolic secant squared, Lorentzian squared, and Gaussian. It is shown that the behavior of the transition probability differs qualitatively for these pulses. An explanation of this qualitative difference is given in terms of the Massey parameter. Numerical solutions are compared with asymptotic solutions and several anomalies are noted. In the limit of large field strength, a universal expression for the transition probability is found. An interesting feature of the solutions is that, in the limit of very large field strengths, the transition probability for a Gaussian pulse can approach unity despite the fact that the pulse has an exponentially small Fourier amplitude at the atom-field detuning. This apparent violation of the energy-time uncertainty principle is explained in terms of the nonlinear atom-field interactions.

For the Dirac equation in one dimension, a method for constructing reflectionless pseudoscalar potentials is presented. This is a relativistic generalization of Kay and Moses’s classic method [J. Appl. Phys. 27, 1503 (1956)] that deals with a similar problem for the Schrödinger equation. This can also be viewed as an inverse scattering problem. For a set of assumed energy levels, the method furnishes a family of potentials, each of which reproduces the energy levels. These potentials are all reflectionless.

In the first part (Secs. I and II) of this paper, starting from the Pauli current, we obtain the decomposition of the nonrelativistic field velocity into two orthogonal parts: (i) the “classical” part, that is, the velocity $\mathbf{w}=\mathbf{p}/m$ in the center of mass (c.m.), and (ii) the “quantum” part, that is, the velocity V of the motion of the c.m. frame (namely, the internal “spin motion” or Zitterbewegung). By inserting such a complete, composite expression of the velocity into the kinetic-energy term of the nonrelativistic classical (i.e., Newtonian) Lagrangian, we straightforwardly get the appearance of the so-called quantum potential associated, as it is known, with the Madelung fluid. This result provides further evidence of the possibility that the quantum behavior of microsystems is a direct consequence of the fundamental existence of spin. In the second part (Secs. III and IV), we fix our attention on the total velocity $\mathbf{v}=\mathbf{w}+\mathbf{V},$ now necessarily considering relativistic (classical) physics. We show that the proper time entering the definition of the four-velocity $v^{\mu }$ for spinning particles has to be the proper time τ of the c.m. frame. Inserting the correct Lorentz factor into the definition of $v^{\mu }$ leads to completely different kinematical properties for $v^2.$ The important constraint $p_{\mu }{v}^{\mu }=m,$ identically true for scalar particles but just assumed a priori in all previous spinning-particle theories, is herein derived in a self-consistent way.

Limitations to the performance of a quantum computer arising from direct interaction between qubits are considered, and the basic scaling laws (with the computation time and the number of qubits) are established for the specific example of the quantum Fourier transform algorithm. These results should be relevant for several of the currently proposed quantum computer systems, where the dominant interaction is of the magnetic dipole-dipole type, in the limit of many qubits and long computation times.

A classical model of singly charged ion collisions with Rydberg atoms in linear Stark states directed toward the oncoming ion beam predicts a bimodal distribution of final states resulting from electron capture. At a reduced velocity $\tilde{v}{=v}_{\mathrm{ion}}{/v}_{\mathrm{Bohr}}=0.45,$ the calculated energy distribution of captured electrons peaks near the target binding energy $E_i,$ but has a second peak at energies roughly $E_i/4.\mathrm{}$ Analysis of the impact-parameter dependence of the capture probabilities indicates that the second peak arises from three-swap capture events. The decrease in binding energy of the captured electrons is attributed to excitation via united-atom rotational coupling.

We propose a photodetachment scheme for observing interference effects caused by the simultaneous action of a two-color low-frequency field with commensurate frequencies during the photodetachment event. By changing the relative phase of the low-frequency fields, considerable modifications are found to occur in the angular distributions of the photoelectrons as well as in their energy spectra. Some properties of the photoelectron angular distributions are discussed, and the extension of the energy spectra as a function of the low-frequency radiation parameters is evaluated.

Laser-cooled rubidium atoms have been trapped in a nondissipative optical lattice with a large lattice constant. The lattice potential is generated by the ac Stark shift in an infrared standing wave near 10.6 $\mu$m. The atoms are confined in steep potential wells with a periodicity of several micrometers. By modulating the potential depth we parametrically excite the atoms and measure their vibrational frequencies.

We abruptly subject laser-cooled ${}^{87}\mathrm{Rb}$ atoms to the one-dimensional, blue-detuned, optical standing-wave potential generated by two crossed probe laser beams and detect the phase change of the probe beam due to cold-atom dynamics. Damped oscillations of the observed phase signal are attributed to a temporal change of the root-mean-square position of the cold atoms relative to the minima of the periodic optical potential. The damping rate is in good agreement with numerical results, which take into account the potential anharmonicity but neglect spontaneous emission. The agreement indicates that the decay is mainly caused by dephasing due to trap anharmonicity. For sufficient low initial temperature, our calculations show quantum revivals of the wave-packet oscillation.

We study the Josephson effect between atomic Bose-Einstein condensates. By drawing on an electrostatic analogy, we derive a semiclassical functional expression for the three-dimensional Josephson coupling energy in terms of the condensate density. Estimates of the capacitive energy and of the Josephson plasma frequency are also given. The effect of dissipation due to the incoherent exchange of normal atoms is analyzed. We conclude that coherent Josephson dynamics may already be observable in current experimental systems.

We have applied the Popov version of the Hartree-Fock-Bogoliubov (HFB) approximation to calculate the finite-temperature excitation spectrum of a Bose-Einstein condensate (BEC) of ${}^{87}\mathrm{Rb}$ atoms. For lower values of the temperature, we find excellent agreement with recently published experimental data for the JILA time-averaged orbiting potential trap. In contrast to recent comparison of the results of HFB-Popov theory with experimental condensate fractions and specific heats, there is disagreement of the theoretical and recent experimental results near the BEC phase transition temperature.