Motivated by the prediction of the appearance of atomic multiply charged negative ions (AMCNI) of hydrogen, induced by a linearly polarized laser field, we present an analytical quantum mechanical treatment of the appearance and structure of AMCNI in a linearly polarized field, based on high-frequency Floquet theory (HFFT). For the simplest AMCNI of hydrogen, ${\mathrm{H}}^{2\mathrm{-}}$ and ${\mathrm{H}}^{3\mathrm{-}},$ the values of ${\alpha }_0$ at which the first bound state appears are ${\alpha }_0=1.62\mathrm{}\times {10}^2$ and ${\alpha }_0=1.02\mathrm{}\times {10}^4,$ where ${\alpha }_0{=I}^{1/2}/{\omega }^2$ is the amplitude of the oscillation of a free electron in the field with frequency ω and intensity $I$ (unless stated otherwise, we use atomic units throughout this paper). Whereas in vacuum at least one of the electrons of an AMCNI autodetaches, an intense high-frequency field can change the character of the ion dramatically, such that bound states of AMCNI can appear. Due to the interaction with the field, the electrons of the AMCNI oscillate in phase along the polarization axis. This “quiver” motion enables the electrons to be spatially separated over distances of order ${\alpha }_0,$ reducing the repulsive $e-e$ interaction as ${\alpha }_0$ increases. In other words, for ${\alpha }_0$ large enough, the field enables a configuration in which the electrons, while widely separated, are bound to one proton. For the prediction of bound states of ${\mathrm{H}}^{N-}$ with $N>\mathrm{}3,$ however, a relativistic description or low-frequency theory is required.

The use of cesium Rydberg atoms as a test system for quantum ladder climbing with chirped laser pulses is described. Quantum ladders can be used in the coherent control of chemical reactions; for instance, by exciting a specific molecular bond by climbing its vibrational ladder. A Rydberg atom is an easy test system because of the large transition dipole moments between Rydberg states. The Rydberg states are easy to access and to analyze. Picosecond far-infrared laser pulses around a wavelength of 50 μm, with peak intensities of ${10}^9{\mathrm{W}/\mathrm{c}\mathrm{m}}^2,$ from the free-electron laser for infrared experiments (FELIX) at Nieuwegein, The Netherlands, were used. It is found that the complexity of the system puts severe limits on the allowed intensities that are used to drive the ladder. At high intensity the ladder is distorted due to coupling with states outside the ladder. This distortion frustrates efficient climbing.

We calculate the atomic energy-level shift and the modified dipolar radiation rate inside a hollow dielectric cylinder and outside a solid cylinder using a quantum-mechanical linear-response formalism in the dipole approximation. We first derive the electromagnetic fields scattered by the cylindrical surface for an oscillating dipole inside and outside the cylinder. When an atom is located on the axis of the cylindrical hollow, we obtain analytic expressions of the atomic level shifts in two limiting cases: when $b$ (radius of hollow) is very small, the level shift is proportional to $b^{-2}$ which is associated with the kinetic-energy change of the atomic electron, whereas when $b$ is very large, the shift is proportional to $b^{-4}$ which is identified as the retarded (Casimir-Polder) interaction energy. Moreover, we calculate the atomic potentials as a function of the position of atoms in the hollow region, which is important for the atom-guiding experiment. We also calculate the decay rates and find enhanced rates inside and outside the cylinder. In particular, we compare the radiative properties of an atom inside the hollow cylinder with those between two plates, and those near a cylinder with near a single surface.

The resonance absorption line shape from cold $(T<\mathrm{}100\mathrm{}$ $\mu$K) atomic cesium vapor has been investigated with a probe laser after switching off the magneto-optical trapping fields. An additional nonabsorbed laser field has been used to produce quantum interference in a three-level ladder scheme. Predicted but counterintuitive modifications of the natural absorption line shape have been directly observed including inhibition of resonance absorption. The validity of a nonlinear sum rule deduced from the causality principle has been satisfactorily tested.

In this paper the effects of the transverse profile of the probe and driving fields on the gain in a Raman-driven four-level system are discussed. The results show that when transverse effects are included, the probe gain spectrum has a different structure compared with that in the plane-wave approximation, the optimum focal position of a focus lens for the maximum gain is not at the center of the sample cell, and the gain is very sensitive to the changes of focal position when the waist of the driving field is small.

Two-photon correlation of the light pulse emitted from a sonoluminescence bubble is discussed. It is shown that several important features of the mechanism of light emission, such as the time scale and the shape of the emission region, could be obtained from Hanbury-Brown-Twiss interferometry. We also argue that such a measurement may serve to reject one of the two currently suggested emission mechanisms, i.e., the thermal process versus the dynamical Casimir effect.

A high Fresnel number laser close to threshold can be set at a detuning value where it displays only the first transverse pattern with zero intensity in its center. However, the availability of a large phase space gives rise to a new type of dynamics. Precisely, for this highly symmetric situation, the intensity pattern undergoes a transition between stable and oscillating superpositions of traveling and standing waves. Such a transition corresponds to the so-called Takens-Bogdanov bifurcation. We report experimental evidence of such a behavior.

Complete density-matrix equations and a one-photon counting probability are used to examine the photon statistics of fluorescence light of a single three-level atom, weakly coupled to an external cavity of low $Q$ value. The internal structure of the atom is supposed to be characterized by a weak and a strong transition. The strong transition is coherently driven by an external laser field, whereas no external field is acting on the weak transition. In free space the system exhibits quantum jumps. By placing the atom within the mirrors of an external cavity, tuned close to the transition frequency of the two upper levels, modifications in the quantum jump behavior of the atom are shown due to a modified spontaneous decay rate between the two states. In particular, it is demonstrated that the effect of the cavity is to modify the repetition rate of quantum jumps into the metastable dark state and the average duration of bright periods of fluorescence, whereas the average duration of dark periods is not changed in first order of the spontaneous decay rates involved. In view of current experiments in our laboratory a quantitative analysis is presented for the special case of a single indium ion located between the mirrors of a high-order symmetric confocal cavity.

We consider a physical process that leads to the generation of atomic Schrödinger cat states for a system of two level atoms. The effective interaction between atoms in a dispersive cavity leads to the superposition of atomic coherent states. We study in detail the quasidistributions for these states and demonstrate how the Schrödinger cat states can lead to interesting interferences over the surface of a sphere.

The theory of small-signal laser amplification is developed for homogeneously broadened systems in which the three main decay rates, for the collective atomic dipole moment, the population inversion, and the field in the laser cavity, have arbitrary relative magnitudes. The calculations extend previous work on class-$A$ and -$B$ lasers, where the dipole decay rate greatly exceeds the other two rates, to class-$C$ lasers, where the dipole decay rate is comparable to the others. The free-running laser is assumed to excite a single longitudinal mode of the cavity, whose frequency generally differs from that of the coupled atomic transition. The linear gains of the laser are derived for input signals whose frequencies are close to that of the lasing mode or to one of its adjacent nonlasing longitudinal modes. Divergences in the gain that occur for these two arrangements are associated with the previously studied single-mode and multimode instabilities of the free-running laser, respectively.

The spectral line shape of the four-wave mixing (FWM) signal, induced by broad bandwidth laser fields, is derived in the case of a nonresonant interaction. The laser fields are assumed to have a Lorentzian spectrum arising from Markovian stochastic fluctuations described by the phase-diffusion, chaotic field, and Gaussian-amplitude models. The usual “phase conjugating” geometry for FWM is considered where the nonresonant interaction is determined only by the statistics of, and the correlations between, the pump and probe fields. For each one of the four possible correlation states between the three input fields and for each of the three fluctuating field models, the line shape of the FWM signal is calculated and shown to be particularly sensitive to the field statistics.

This paper deals with electromagnetically induced transparency (EIT), i.e., a significant suppression of absorption at a material transition (in the form of a dip in an absorption spectrum), due to a strong laser field, coupling the excited level with an auxiliary excited (unpopulated) level. A comprehensive theory of EIT is developed for the cases of coherent and Markovian phase- and amplitude-phase-fluctuating coupling fields. For a coherent coupling field, a shift of the absorption minimum from the two-photon resonance is revealed in the off-resonance case. Two models of amplitude-phase fluctuating fields are considered: the chaotic field and the uncorrelated-jump field. Closed analytical expressions for EIT line shape are derived and exact limits of different regimes of EIT are obtained, the emphasis being on the near-resonance case. The main conclusion is that an amplitude-phase-fluctuating field can induce significant transparency, though reduced in comparison to a phase-fluctuating field of the same average intensity and bandwidth. EIT decreases with the increase of the bandwidth for all stochastic models considered. EIT with a chaotic field is generally less pronounced than EIT with an uncorrelated-jump field of the same intensity and bandwidth, the difference increasing with the field intensity. The possibility of experimental verification of the results obtained is discussed.

Exact analytic results are presented that represent a pair of solitary waves that can propagate through an atomic medium with their shapes invariant while producing transfer of atoms or molecules from one bound state to another via a continuum. The speed of the waves and the amount of population transfer are given in terms of the wave amplitudes. A general (not solitary wave) solution for the case of a single wave is presented, together with a nonlinear Beer’s law of absorption.

Spontaneous emission in a one-dimensional Fabry-Pérot-type optical cavity is analyzed quantum mechanically. Via a monolayer dielectric cavity model, expressions describing the atomic-location dependence of the emission intensities and the spectra observed on both sides of the cavity are obtained. The probability amplitude for the upper atomic state is analyzed and its time-evolution equation is given. The probability amplitude is shown to be proportional to “the electric field amplitude for a single emission event” introduced classically by Huang et al. [Appl. Phys. Lett. 61, 2961 (1992)]. An expression for the emission spectrum applicable to a general one-dimensional cavity structure is obtained.

The effective dipolar Hamiltonian and the vacuum Rabi frequency for a system with a dielectric microsphere and a two-level atom with arbitrary orientation of dipole momentum are found. The energy levels of such a system are determined within the rotating-wave approximation as well as by numerical methods. The solution found is close to that within the pure classical approach.

A wave-packet interference technique is proposed to measure exotic atomic Rydberg wave functions. For example, the subject wave packet is excited by an arbitrary pulse or pulse sequence. The resulting wave function is probed by a well-characterized pulse that shares a phase relationship with the excitation pulse(s). The observable is the population in each eigenstate after the probe pulse. By making a series of such measurements, varying the phase between excitation and probe pulses, the wave function created by the excitation pulse can be inferred. The method is experimentally feasible for atomic systems, and the extension of the method to molecular systems also appears possible.

It is demonstrated experimentally and theoretically that a light-shift-induced level crossing in an oblique magnetic field results in a nonmonotonous dependency of the transmission of a sodium vapor cell on the input power. If feedback by a single plane mirror is added, bistability of the transmission and of the beam profile (resonatorless transverse optical bistability) is observed. The origin of the bistable behavior and the parameter dependencies is explained by the properties of the homogeneous solution. Numerical simulations with a Gaussian incident beam reproduce well the switching behavior of the beam profile found in the experiment.

We show that, in an optically pumped resonant $J=1\mathrm{}\to J^{\prime }=0\mathrm{}$ laser, a gain anisotropy is induced by a linearly polarized coherent pump beam that can be balanced or countered by $x$-$y$ cavity-loss anisotropies, leading to switching between the $x$ and $y$ linearly polarized states of the generated laser field as the laser intensity is increased. This switching is not brought about by selection of the mode with the maximum emission intensity. A domain of bistability between the two linearly polarized states is found, whose width depends on the value of the decay rate of the two photon coherence induced among the sublevels of the $J=1\mathrm{}$ level manifold. Differently from the incoherently pumped $J=1\mathrm{}\to J^{\prime }=0\mathrm{}$ laser, the decay rate for the magnetic dipole in that manifold has no influence on the polarization of the emission.

Within the framework of probability distributions on projective Hilbert space, a scheme for the calculation of multitime correlation functions is developed. The starting point is the Markovian stochastic wave-function description of an open quantum system coupled to an environment consisting of an ensemble of harmonic oscillators in arbitrary pure or mixed states. It is shown that matrix elements of reduced Heisenberg picture operators and general time-ordered correlation functions can be expressed by time-symmetric expectation values of extended operators in a doubled Hilbert space. This representation allows the construction of a stochastic process in the doubled Hilbert space which enables a determination of arbitrary matrix elements and correlation functions. The numerical efficiency of the resulting stochastic simulation algorithm is investigated and compared with an alternative Monte Carlo wave function method proposed first by Dalibard, Castin, and Mølmer [Phys. Rev. Lett. 68, 580 (1992)]. By means of a standard example the suggested algorithm is shown to be more efficient numerically and to converge faster. Finally, some specific examples from quantum optics are presented in order to illustrate the proposed method, such as the coupling of a system to a vacuum, a squeezed vacuum within a finite solid angle, and a thermal mixture of coherent states.

We analyze the quantum motion of a cold, trapped two-level ion interacting with a quantized light field in a single-mode cavity. We show that in the nonclassical Lamb-Dicke limit the time evolution of the vibrational mode representing the quantized motion of the center of mass of the trapped ion is very sensitive to the quantum statistics of the light field. We also show that the system under consideration may evolve into the maximally entangled three-particle Greenberger-Horne-Zeilinger state. We briefly discuss the dynamics of a cluster of two-level ions trapped in a cavity and interacting with a quantized light field.