We report multiphoton ionization experiments on ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$ molecules at 1053- and 526.5-nm excitation wavelengths in the intensity range 5×${10}^{13}$–5×${10}^{14}$ W/${\mathrm{cm}}^2$. The intensity dependence of the total ion yield, the dissociation fraction, and the photoelectron spectrum is investigated. At 1053 nm we find a strong isotope effect in the dissociation fraction, whereas at 526.5 nm no such effect is observed. Up to 1×${10}^{14}$ W/${\mathrm{cm}}^2$ the photoelectron spectrum at 526.5 nm is dominated by resonant ionization processes via Rydberg states of the molecules. They are shifted into resonance at intensities above ∼${10}^{13}$ W/${\mathrm{cm}}^2$. The spectra show that the potential energy curves of the resonant states must have a shape very similar to the corresponding ionic ones. They are therefore mainly determined by the dipole coupling between the ion core orbitals 1s${\mathrm{\sigma }}_{\mathit{g}}$ and 2p${\mathrm{\sigma }}_{\mathit{u}}$. At 1053 nm two photoionization regimes are observed: the multiphoton regime with Keldysh parameter γ>1 showing resonance ionization structures, and the tunnel regime (γ<1) at high intensity. The isotope effect in the dissociation fraction at 1053 nm has no influence on the shape of the corresponding photoelectron spectra at this wavelength. © 1996 The American Physical Society.

We perform nonperturbative analysis of forward scattering of resonance laser light on atoms in magnetic field when the laser drives transitions between states with total angular momenta F=1,2 and study the role of the induced higher-order multipole moments in the forward-scattering signal. It is shown how the multipole moments affect these signals and why not all possible multipoles are revealed for some transitions. The analysis is performed in terms of density-matrix formalism and in terms of coupled and uncoupled (trap) states. Evolution of the trap states in a magnetic field is found to be responsible for specific dependencies of the forward-scattering signals on the multipoles of various ranks. The general theory is applied to the case of the Na ${\mathit{D}}_1$ line. We also present a pump-probe method for studying multipoles in systems with states of high angular momenta and with complex transitions overlapping within their Doppler width. © 1996 The American Physical Society.

Two-step resonant photoionization of free Ni atoms is studied by one-color and two-color processes, using pulsed lasers with photon energies around half the ground-state ionization energy. Two-color two-step resonance ionization from the ground state a${\mathrm{}}^3$${\mathit{F}}_4$ and the first metastable state a${\mathrm{}}^3$${\mathit{D}}_3$ via the triplet states z${\mathrm{}}^3$${\mathit{G}}_{3,4,5}^0$ was used to probe the autoionizing states just above the ionization limit. Several strong lines in the one-color ionization spectrum are explained as direct two-photon transitions to autoionizing states. Photoionization cross sections were deduced from saturation measurements. The large cross sections observed for specific one-color two-step transitions are due to the near double resonant excitation into autoionizing states. © 1996 The American Physical Society.

We analyze the ‘‘polarization-gradient-assisted velocity-selective coherent population-trapping’’ laser cooling scheme in the presence of a homogeneous force. In the limit of a slow rate of cooling this system may be treated using a set of rate equations after applying the secular approximation. This uses a basis of states which form a band structure resulting from the periodic optical potentials. We show that in the presence of a force the secular approximation may be retained, and derive the required modification to the rate equations. This is a density operator method of treating the action of a force on a particle in a band structure, and clearly shows reflections at the band edge. We solve for the steady-state momentum distribution, which provides information on the amount to which the presence of a force limits the achievable temperature. We solve also for the steady-state fluorescence and suggest that the fluorescence from atoms cooled with this scheme could be used as a force meter. © 1996 The American Physical Society.

We present results of numerical simulations to justify the origin of the width in ring-shaped atomic distributions of cold atoms held in a magneto-optical trap. We have considered the effects of laser fluctuations (phase and intensity) and the presence of recoil due to spontaneous emission. The results show that the occurrence of spontaneous emission accounts for the existence of a width in the atomic trajectory while laser fluctuations only change the average value of the atomic orbit. © 1996 The American Physical Society.

Xenon atoms are released from a magneto-optical trap and equilibrate in a one-dimensional, ${\mathrm{\sigma }}_{+}$-${\mathrm{\sigma }}_{\mathrm{-}}$ optical molasses, along which a uniform magnetic field is applied. In the rest frame of the ‘‘corkscrew’’ pattern of laser polarization, the magnetic field induces a nonzero average atomic velocity. Introducing a moving molasses through a relative difference in the two laser-beam frequencies allows straightforward, accurate measurements of the molasses-frame velocity distribution over a large range of magnetic fields. The measurements reveal the loss of polarization-gradient cooling in fields higher than ∼0.2 mT, in quantitative agreement with theoretical predictions. © 1996 The American Physical Society.

We study the propagation of squeezing in the resonance fluorescence from a two-atom system within the weak-field approximation. We show that squeezing occurs in the fluorescence from both atoms, although with different falloff in time. © 1996 The American Physical Society.

Canonical quantization of the electromagnetic (EM) field is carried out for the situation where the total charge and current densities are the sum of contributions from neutral dielectric atoms whose effect is to be described purely classically in terms of spatially dependent electric permittivity and magnetic permeability functions, and neutral, stationary radiative atoms whose interaction with the EM field is to be treated quantum mechanically. The coefficients for the expansion of the vector potential in terms of mode functions determined from a generalized Helmholtz equation are chosen as independent generalized coordinates for the EM field. The spatially dependent electric permittivity and magnetic permeability appear in a generalized Helmholtz’s equation and the former also occurs in the mode function orthogonality and normalization conditions. The quantum Hamiltonian is derived in a generalized multipolar form rather than the minimal coupling form obtained in other work. The radiative energy is the sum of quantum harmonic oscillator terms, one for each mode. The modes are independent in the present case of exact mode functions associated with the spatially dependent electric permittivity and magnetic permeability, there being no direct mode-mode coupling terms. In the electric dipole approximation the electric interaction energy contribution for each mode and radiative atom is proportional to the scalar product of the dipole operator with the mode function evaluated at the atom, times the annihilation operator, plus the Hermitian adjoint. This form has been widely used in studies of radiative processes for atomic systems in dielectric media, and it is justified here via the canonical quantization procedure. The results apply to the theoretical treatment of numerous quantum optical experiments involving such interactions in the presence of passive, lossless, dispersionless, linear classical optics devices such as resonator cavities, lenses, beam splitters, and so on. An illustrative application of the theory for atomic decay in a one-dimensional Fabry-Perot cavity is given. © 1996 The American Physical Society.

Taking Bessel beams (${\mathit{J}}_0$ beam) as a representation of a conical beam, and a slowly varying envelope approximation (SVEA) we obtain the results for the theory of third-harmonic generation from an atomic medium. We demonstrate how the phenomenon of self-phase-matching is contained in the transverse-phase-matching integral of the theory. A method to calculate the transverse-phase-matching integral containing four Bessel functions is described which avoids the computer calculations of the Bessel functions. In order to consolidate the SVEA result an alternate method is used to obtain the exact result for the third-harmonic generation. The conditions are identified in which the exact result goes over to the result of the SVEA. The theory for multiple Bessel beams is also discussed which has been shown to be the source of the wide width of the efficiency curve of the third-harmonic generation observed in experiments. © 1996 The American Physical Society.

The exact time dependence of the density operator and various physical quantities for the motion-quantized Jaynes-Cummings models (MQJCMs) is given using the operator transformation under which it is shown that the MQJCMs have the same dynamics as the ordinary JCMs in the Kerr medium. The quantum collapses and revivals of the atomic motion due to the quantum properties of light fields and the quantization of atomic position and momentum, are predicted. The effects of the initial atomic momentum distribution and the arbitrary intensity-dependent medium on the collapse and revival phenomena of the population inversion, atomic momentum and radiation are formulated in detail. © 1996 The American Physical Society.

Optical dark resonance in systems with arbitrary multilevels and multiphotons is studied theoretically. When the system configuration is treelike (the term of graph theory), all the coherence terms in the system can be categorized into several groups on dark resonance. It is proved for generic system configurations with arbitrary multilevels that the resonance conditions can be obtained successively by setting the determinant of the submatrix of the Hamiltonian with respect to each group to zero. We calculate, as one of the practical examples, all the conditions of dark resonance of potassium atoms with two laser fields and one rf field mixing one excited state and eight ground states in the hyperfine structure. Although the system configuration is very complicated, the condition is easily obtained in an analytic form and verified by the result of a numerical simulation. Furthermore, our theory can reveal the fine structure of dark lines with power broadening in the observed light-induced-fluorescence spectra and numerical calculations. In addition, the dark lines with the complicated splitting pattern observed in experiments can be assigned to the relevant level configuration and transitions by the present theory. © 1996 The American Physical Society.

We present a theoretical and experimental study of the line shape of resonant four-wave mixing induced by broad-bandwidth laser radiation that revises the theory of Meacher, Smith, Ewart, and Cooper (MSEC) [Phys. Rev. A 46, 2718 (1992)]. We adopt the same method as MSEC but correct for an invalid integral used to average over the distribution of atomic velocities. The revised theory predicts a Voigt line shape composed of a homogeneous, Lorentzian component, defined by the collisional rate Γ, and an inhomogeneous, Doppler component, which is a squared Gaussian. The width of the inhomogeneous component is reduced by a factor of √2 compared to the simple Doppler width predicted by MSEC. In the limit of dominant Doppler broadening, the width of the homogeneous component is predicted to be 4Γ, whereas in the limit of dominant homogeneous broadening, the predicted width is 2Γ. An experimental measurement is reported of the line shape of the four-wave-mixing signal using a broad-bandwidth, ‘‘modeless,’’ laser resonant with the ${\mathit{Q}}_1$(6) line of the A${\mathrm{}}^2$Σ-X${\mathrm{}}^2$Π(0,0) system of the hydroxyl radical. The measured widths of the Voigt components were found to be consistent with the predictions of the revised theory. © 1996 The American Physical Society.

A complete set of cavity modes in planar dielectric microcavities is presented which naturally includes guided modes. We show that most of these orthonormal fields can be derived from a coherent superposition of plane waves incoming on the stack from the air and from the substrate. Spontaneous emission of a dipole located inside the microcavity is analyzed, in terms of cavity modes. Derivation of the radiation pattern in the air and in the substrate is presented. The power emitted into the guided modes is also determined. Finally, a numerical analysis of the radiative properties of an erbium atom located in a Fabry-Pérot multilayer dielectric microcavity is investigated. We show that a large amount of light is emitted into the guided modes of the structure, in spite of the Fabry-Pérot resonance, which increases the spontaneous emission rate in a normal direction. © 1996 The American Physical Society.

The creation and annihilation of pairs of optical vortices have been studied in transitions between patterns produced in a photorefractive oscillator. Smooth metamorphosis between stable patterns occurs through pair creation or annihilation but can be modeled using superposition of modes taking into account lifting of degeneracy of helical modes by helical astigmatism of the resonator. © 1996 The American Physical Society.

The fluorescence field from one of the two allowed transitions in a three-level atom can sense squeezed fluctuations of a vacuum field coupled to the other transition. We examine the fluorescence spectra of strongly driven three-level atoms in Λ, V, and cascade configurations in which one of the two one-photon transitions is coupled to a finite-bandwidth squeezed vacuum field, when the bandwidth is much smaller than the difference in the atomic transition frequencies, though much larger than atomic decay rates and Rabi frequencies of the driving fields. The driving fields are on one-photon resonance, and the squeezed vacuum field is generated by a degenerate parameter oscillator. Details are only given for the Λ configuration. The extension to the V and cascade configurations is straightforward. We find that in all configurations the fluorescence spectra of the transition not coupled to the squeezed vacuum field are composed of five lines, one central and two pairs of sidebands, with intensities and widths strongly influenced by the squeezed vacuum field. However, only the central component and the outer sidebands exhibit a dependence on the squeezing phase. We also examine the fluorescence spectrum for the cascade configuration with a squeezed vacuum field on resonance with the two-photon transition between the ground and the most excited states and now generated by a nondegenerate parametric oscillator. In this case, where the squeezed vacuum field can be made coupled to both transitions, all spectral lines depend on the squeezing phase. The spectral features are explained in terms of the dressed-atom model of the system. We show that the coherent mixing of the atomic states by the strong driving fields modifies transition rates between the dressed states, which results in the selective phase dependence of the spectral features. © 1996 The American Physical Society.

We propose a scheme based on homodyne detection for enhancing antibunching in second-harmonic generation and multiatom optical bistability. We show that depending on the reflectivity of the beam splitter, relative field strengths, and relative phase it is possible to achieve perfect antibunching in the superposed field. We also discuss other nonclassical effects exhibited by the superposed field and present curves to illustrate the behavior. © 1996 The American Physical Society.

We propose schemes for measuring the joint quantum state of a two-mode optical field using balanced homodyne detection, thereby generalizing earlier single-mode schemes. We distinguish between two cases—the case where the two modes are spatially separable and the case where they are nonseparable. For each case we present a generalization of the direct sampling method of state reconstruction and point out that its advantages over inverse Radon methods are even greater here than in the single-mode case. In the case of two modes that cannot be separated we propose a scheme in which a single balanced homodyne detector is used for data collection. © 1996 The American Physical Society.

We experimentally study the production of laser gain (phase-insensitive optical amplification) with and without atomic population inversion in a doubly driven three-level system in atomic barium. The external fields are found to create inversionless gain and to enhance gain available in the presence of inversion. Laser oscillation based on enhanced gain is observed. In analysis of the driven system, we identify an irreversible multiphoton process that is intrinsically supportive of gain in the absence of population inversion. © 1996 The American Physical Society.

We address the experimentally important issue of coupling a Gaussian beam into an amplifier with a focused Gaussian gain profile. Commonly, in such an amplifier the input beam is adjusted such that it focuses at the same location and with the same Rayleigh range as the gain profile. However, we find that at high gains the input coupling efficiency of a Raman amplifier is increased by using an input beam with a short Rayleigh range that focuses well before the focus of the gain profile. Theoretical modeling and experimental data show that the input coupling efficiency is enhanced by as much as a factor of 2 over that measured with the input beam and gain profile focusing at the same position and with the same Rayleigh range. These effects are attributed to the spatial gain narrowing and wave-front modification that the amplified field undergoes during amplification. © 1996 The American Physical Society.

A theory is presented for multiple-harmonic generation from metal surfaces with the laser field polarized in the plane of incidence. The theory is applied to the analysis of a recent experiment on a gold surface. It is shown that the relatively slow decrease in the measured efficiency (${10}^{\mathrm{-}10}$-${10}^{\mathrm{-}13}$) for the second, third, fourth, and fifth harmonics is related to the stepwise nature of the excitation process. While for the second harmonic the intensities of the coherent and the incoherent component are comparable, for the higher harmonics the incoherent component dominates. © 1996 The American Physical Society.