Subpicosecond half-cycle pulses and a single-shot imaging detector have been used to monitor the evolution of electronic radial wave packets in calcium. The time-dependent momentum-space probability distribution is obtained using the impulsive momentum retrieval (IMR) method. The measured distributions are compared to the results of quantum and classical simulations allowing a comprehensive evaluation of the benefits and limitations of the IMR method.

The Schrödinger equation with minimal coupling for a nonrelativistic electron interacting with a single-mode photon field is not satisfied by the nonrelativistic limit of the exact solutions to the corresponding Dirac equation. A Schrödinger-like equation valid for arbitrary photon intensity is derived from the Dirac equation without the weak-field assumption. The “eigenvalue” in the present equation is an operator in a Cartan subalgebra. An approximation consistent with the nonrelativistic energy level derived from its relativistic value replaces the eigenvalue operator by an ordinary number, recovering the Schrödinger eigenvalue equation used in the formal scattering formalism. The Schrödinger-like equation for the multimode case is also presented.

We study, in the framework of the Boltzmann-Bloch-Nordheim equation (BBN), the kinetic properties of a boson gas above the Bose-Einstein transition temperature $T_c.$ The BBN equation is solved numerically within an algorithm that we test with exact analytical results for the collision rate of a homogeneous system in thermal equilibrium. In the classical regime $\left(T\gg T_c\right),$ the relaxation time of a quadrupolar deformation in momentum space is proportional to the mean free collision time ${\tau }_{\mathrm{relax}}\propto {\tau }_{\mathrm{coll}}\propto T^{-1/2}.$ Approaching the critical temperature, quantum statistic effects become dominant, and the collision rate increases dramatically. Nevertheless, this does not affect the relaxation properties of the gas that depend only on the spontaneous collision term in BBN. The relaxation time becomes ${\tau }_{\mathrm{relax}}\propto (T-T_c{)}^{-1/2},$ exhibiting a critical slowing down. These phenomena can be experimentally confirmed looking at the damping properties of collective motions induced on trapped atoms. The possibility to observe a transition from collisionless (zero-sound) to hydrodynamic (such as first and second-sound) is finally discussed.

We determine the diffusion rates of two quantum phases associated with a two-component dilute Bose-Einstein condensate. We show that although the phase information of each individual component is lost in the course of time, the relative phase of the two components of the field can be locked without diffusion when the interaction strength between the two components equals certain critical values.

We extend quantum kinetic theory to deal with a strongly Bose-condensed atomic vapor in a trap. The method assumes that the majority of the vapor is not condensed, and acts as a bath of heat and atoms for the condensate. The condensate is described by the particle-number-conserving Bogoliubov method developed by one of the authors. We derive equations which describe the fluctuations of particle number and phase, and the growth of the Bose-Einstein condensate. The equilibrium state of the condensate is a mixture of states with different numbers of particles and quasiparticles. It is not a quantum superposition of states with different numbers of particles—nevertheless, the stationary state exhibits the property of off-diagonal long-range order, to the extent that this concept makes sense in a tightly trapped condensate.

Using a path-integral formalism, we present a reanalysis of the Sagnac experiment with electrons of Hasselbach and Nicklaus [Phys. Rev. A 48, 143 (1993)]. Our analysis, from an inertial frame of reference, makes explicit the central role of the electrostatic biprism in generating interference fringes and recovers the Sagnac formula for the phase shift induced when rotating the interferometer. This phase shift, however, is shown to differ significantly in physical origin from the similar experiment with neutrons. In the electron Sagnac experiment, rotation displaces all classical electron paths closer to (or further from, depending upon direction) the electrostatic biprisms, thereby perturbing the electrostatic potential along these paths, and a phase shift of an electrostatic nature arises. Our analysis yields a corrected expression for the projected area of the interferometer and small numerical corrections to previous work are consequently given.

A study of fragmented condensates is presented to elucidate the interplay between excitations and the collapse of relative phases within single condensates. Implications for experimental observation of interference between weakly coupled condensates are discussed, and means for computation are suggested and applied to a one-dimensional model system.

We discuss a detection scheme that reveals the existence of vortex states in a cylindrically symmetric condensate trap. It relies on the measurement of the second-order correlation function of the Schrödinger field and yields directly the topological charge of the vortex state, as well as direct evidence of the existence of persistent currents.

Using elementary microscopic methods, we theoretically study persistent flow of an alkali-metal vapor Bose-Einstein condensate around a tight toroidal trap. The angular velocity of a persistent current must be smaller than the angular frequency of the lowest condensate excitation. A supercurrent may be excited by rotating a perturbing potential that is strong enough to cut the toroidal condensate.

We present a theoretical formulation of trapped, dilute Bose-Einstein condensates (BEC’s) at zero temperature based on ordinary Schrödinger quantum mechanics. By a judicious choice of coordinates and of a variational trial wave function we reduce the many-atom problem to a linear Schrödinger equation that is easier to handle and interpret than the usual nonlinear Schrödinger equation of BEC theory. Ordinary quantum mechanics then reproduces, semiquantitatively, many of the main features of zero-temperature BEC, including the critical number of atoms in a condensate with negative scattering length. The procedure is similar in results, but completely different in spirit, to recent variational approaches to solving the nonlinear Schrödinger equation. Moreover, the present procedure represents a step in a systematic alternative method for computing quantitatively accurate wave functions for trapped bosonic atoms.

We develop a nonperturbative approach to study the generation of nonlinear signals in a coherently prepared medium. Specifically, we study the process ${\omega }_1-{\omega }_2+({\omega }_2+\Omega )$, in a system prepared in a coherent-population-trapping state. We calculate enhancement factors of the order of $\sim {10}^2$ in the generated signal, under a variety of conditions thus supplementing the work of Jain et al. [Phys. Rev. Lett. 77, 4326 (1996)]. Our approach also enables us to study other related issues. We demonstrate the existence of pulse matching at higher probe powers.

Using the complementary wavelike and particlelike natures of photons, it is possible to make “interaction-free” measurements where the presence of an object can be determined with no photons being absorbed. We investigated several “interaction-free” imaging systems, i.e., systems that allow optical imaging of photosensitive objects with less than the classically expected amount of light being absorbed or scattered by the object. With the most promising system, we obtained high-resolution (10-μm), one-dimensional profiles of a variety of objects (human hair, glass and metal wires, and cloth fibers) by raster scanning each object through the system. We discuss possible applications and the present and future limits for interaction-free imaging.

We discuss the changes in the spectrum of monochromatic modes in a double-cavity laser showing how the characteristic frequencies change from those proper of a short cavity into those proper of a long cavity using as control parameter the reflectivity of an “external” mirror. The problem is cast into the language of bifurcations in a nonlinear eigenvalue problem. The results show that the transition is mostly dictated by the boundary conditions and occurs regardless of the laser model. Hence, the study presented can be extended to other optical cavities and boundary value problems. Limits of validity of simpler double-cavity laser models, such as the Lang-Kobayashi, are drawn.

The spontaneous emission from a thin layer of a dilute solution of fluorescent dye molecules within an optical microcavity has been studied. Strong fluctuations in fluorescence intensity are observed when the average number of molecules in the measurement volume is small. We have performed experiments that simultaneously characterize these fluctuations over nine orders of magnitude of time, from ns to s. These measurements have identified photon antibunching characteristic of single-molecule emission, along with triplet-state shelving and diffusion driven number fluctuations. The results give fundamental information on the kinetics of dye molecules and allow one to speculate about the prospect of using single molecules as sources of single photons for quantum optics.

We report a series of Young’s double-slit experiments to measure the transverse spatial coherence of prepulse-induced low-$Z$ neonlike x-ray lasers for two prepulse levels. The experiments were performed using the Asterix IV iodine laser with a prepulse 5 ns before the main pulse. The main pulse energy was 400 J, with a pulse duration of 450 ps. Two slit separations of 80 and 110 μm were used to measure coherence in the vertical direction. We also present data for the horizontal transverse coherence, obtained with only a single-slit separation of 110 μm. The equivalent incoherent source sizes of the x-ray lasers along the vertical direction, as derived by the Van Cittert-Zernike theorem, were found to be 100–120 μm for the 1.5% prepulse, and 110–170 μm for the 15% prepulse level, respectively. Compared to the near-field patterns, the equivalent source sizes obtained with the lower prepulse level (1.5%) are found to be significantly smaller, indicative of an enhancement of the spatial coherence by the gain medium. The observation of a higher degree of coherence for the 1.5% prepulse is corroborated by simulations using a two-dimensional hydrocode and a ray-tracing postprocessor.

A self-homodyne detection scheme is proposed to perform two-mode tomography on a twin-beam state at the output of a nondegenerate optical parametric amplifier. This scheme has been devised to improve the matching between the local oscillator and the signal modes, which is the main limitation to the overall quantum efficiency in conventional homodyning. The feasibility of the measurement is analyzed on the basis of Monte Carlo simulations, studying the effect of nonunit quantum efficiency on detection of the correlation and the total photon-number oscillations of the twin-beam state.

We consider the problem of amplification without inversion in a three-level atomic system. When atoms are driven by a field reservoir and a low-frequency coherent field, amplification of a high-frequency probe field may occur even when there is no population inversion on any atomic transition. We prove that, depending on the ratio of the probe and coherent drive field frequencies, which we term the frequency up-conversion factor, this process may or may not require hidden inversion in the field reservoir. In the special case of a frequency up-conversion factor less than 2, we demonstrate that amplification is possible even if the field reservoir is in complete thermal equilibrium: this represents a new kind of coherent radiation source, distinct from both conventional lasers and lasers without inversion.

We study the generation of both coherent superpositions and mixtures of field states through the interaction of an initially coherent field state with a collection of two-level atoms. The proposed scheme to build up a given superposition is based on effective dispersive interactions which arise from both the large detuning limit and the strong-field limit. The coherent superposition is obtained by interacting with a classical field after the cluster leaves the cavity followed by a measurement of the atomic population.

The decoherence of nonclassical motional states of a trapped ${}^9{\mathrm{Be}}^{+}$ ion in a recent experiment is investigated theoretically. Sources of decoherence considered here destroy the characteristic coherent quantum dynamics of the system, but do not cause energy dissipation. Here they are first introduced phenomenologically, and then described using a microscopic Hamiltonian formulation. Theoretical predictions are compared to experimental results.

A numerical study of the optical bistable response of an open linear Frenkel chain of three-level molecules is carried out, making use of the one-molecule density-matrix approach. We analyze the joint effect of the presence of boundaries and of the exciton-exciton annihilation on the bistable behavior of a chain. The former is going to destroy such behavior due to the spatial inhomogeneity of the population growing with time. The latter resists a preferable creation of the population at a certain segment of the chain stabilizing the system and, thus, provides the conditions for bistability to be realized.