The excitation amplitude after multiple crossings is not a mere product of Landau-Zener transition probabilities at each crossing, due to coherent evolution of the system in between crossings. In the three-level ladder system, the trapping of population by frequency modulated fields ensures coherent evolution, and inclusion of phase effects for population redistribution after multiple crossings becomes necessary. The relative phase accumulated by various adiabatic states as they evolve along different paths is tailored to show the existence of quantum interference effects. We present a method of inverting the population in a three-level system, without affecting the population in the intermediate state. We also present an all optical implementation of the three-level ladder system, where these effects can be realized.

We calculate the ionization of elliptic Rydberg states by half-cycle unipolar electromagnetic-field pulses and examine the dependence of ionization probabilities on the eccentricity and the orientation of the ellipse with respect to the field direction of the pulse. It is suggested that the predicted large geometrical dependences be tested experimentally.

We show that the coherent part of the atomic fluorescence spectrum in a dark optical superlattice can be interpreted as a new type of Bragg scattering of the trapping lasers by the periodic atomic distribution. We explicitly solve the 1D problem to demonstrate that this built-in mechanism provides a diagnostic tool to determine the atomic position and energy distribution without any extra disturbance of the system. Hence, in principle, this method allows one to gain important information on atom-atom interactions and quantum statistics in the case of several atoms confined within a single optical (super)well.

We show that zero ejection energy of the photoelectrons is classically impossible for hydrogenlike ions, even when field ionization occurs adiabatically. To prove this we transform the basic equations to those describing two two-dimensional anharmonic oscillators. The same method yields an alternative way to derive the anomalous critical field of hydrogenlike ions. The analytical results are confirmed and illustrated by numerical simulations.

It was shown recently that systems subject to a strong modulating interaction can exhibit a new property in their response to a probe field. Under certain conditions an infinite number of resonances are simultaneously forbidden [V. N. Smelyanskiy, G. W. Ford, and R. S. Conti, Phys. Rev. A 53, 2598 (1996)]. In the present paper we investigate this effect in the case of a three-state system in which a strong pump field with a periodic frequency modulation Ω couples a pair of excited levels while the complex Autler-Townes spectrum is probed via a weak field that connects one of the coupled states to the ground state. Under certain conditions a half-infinite comb of spectral lines, spaced by Ω, simultaneously disappear from the Autler-Townes spectrum. These lines are positioned above or below a unique edge frequency, which is that of the probe transition in the absence of the strong field. It is shown that the aforementioned effect results from a special factorization property of the corresponding Floquet Hamiltonian that describes the Autler-Townes spectrum. Detailed analysis of this property is presented. In particular, it is found that the subset of the parameter space of the system where the factorization occurs consists of an infinite number of quasiperiodic manifolds. These manifolds exhibit some universal features related to the degeneracy of the dressed states. The line shapes of the probe resonances near the degeneracy points are derived. The intensities of the probe resonances are investigated in the limit of Ω small compared with the modulation depth and the strength of the pump field. In the latter case, effects related to the avoided crossings of the dressed-state levels are considered. The Floquet Hamiltonian that describes the Autler-Townes spectrum in the case considered, effectively corresponds to a special model of a periodically driven system (with period 2π/Ω) in which an external perturbation has the form of an operator projecting onto a single-quantum state. We generalize this model to the case of an N-level periodically driven system where the simultaneous vanishing of a half-infinite number of the dressed-state Fourier harmonics are analyzed. Possible experimental tests of the effect are suggested.

The interaction of a hydrogen or Rydberg atom with a circularly polarized microwave field leads to the creation of global equilibrium points that may be stable or unstable depending on the particulars of the applied field. The additional application of a magnetic field, perpendicular to the plane of polarization, can be used to manipulate both the nature and the stability of these points. We show that stable three-dimensional motion can be maintained that is localized at either a maximum or a minimum in the corresponding surface of zero velocity. At these equilibria, the zero-velocity surface may be locally quadratic in coordinates and stable harmonic-oscillator-like, nondispersive, coherent states can be supported. As the fields are varied, repeated order-chaos transitions may be observed, including various passages through rigorously integrable limits. Classical simulations are presented for a range of field strengths, and the effects of deviations of the microwave field from exactly circular polarization (i.e., elliptical polarization) are examined using a pulsating zero-velocity surface.

We present the quantal dynamics of electronic wave packets in the hydrogen atom in the presence of circularly polarized microwave and magnetic fields in regions of classical stability. Whereas wave packets may disperse without the stabilizing influence of a magnetic field, in its presence stable motion can be maintained for wave packets that are localized either at global equilibria that are either a maximum or minimum in a zero-velocity surface. Because these extrema are locally harmonic their vacuum states are truly coherent states in the original sense of Schrödinger.

The manifestation of atomic and core resonances in photoelectron energy spectra of two-electron atoms is discussed in detail. An approach to the general problem of elimination of strongly coupled continua is presented and quantitative requirements for the validity of the theory are obtained. The theory is applied to calcium thus providing a theoretical interpretation of, and additional insight into, all features of an experiment by Walker et al. [Phys. Rev. Lett. 75, 633 (1995)].

The degenerate parametric oscillator above threshold is studied with phenomenological stochastic colored (nonwhite) pump noise for arbitrary pump to subharmonic relaxation rate. The current experimental limits of large intracavity threshold photon numbers (very small quantum noise) are considered, allowing for a semiclassical treatment of the system dynamics. A comparison between the effects of isotropic and squeezed pump noise on the internal transient and steady-state fluctuations is presented by simulation of the nonlinear semiclassical stochastic Langevin equations in the Wigner quadrature representation. It is found that the transient squeezing for the system starting in the unstable steady state (the vacuum) is not degraded by stochastic pump noise. A damped oscillatory behavior of the noise levels (periodic exchange of fluctuations between the squeezed quadrature of the signal and the pump) is observed for large damping of the signal in the turn on of pump depletion. Finally, it is shown that the limited squeezing above threshold in the steady state (50%) due to pump depletion can be enhanced if squeezed stochastic noise with sufficient significant spectral components (broadband squeezing) is fed to the pump. The above-threshold steady-state squeezing has been calculated analytically from the linearized stochastic equations and the effects of the time scale associated to the relaxation of the pump noise (the noise correlation time) compared to the dissipative time scale of the system and the pump to subharmonic loss ratio are presented.

We solve the spontaneous and induced emission problem for an atom coupled to a ring cavity, taking into account the center-of-mass motion. We solve analytically the non-Hermitian Schrödinger equation for the spontaneous emission. Then we use this solution to test our quantum Monte Carlo solution for the induced processes. The coherence of atomic center-of-mass wave function combined with a well-defined phase of the field produces noteworthy interference phenomena. They may be understood with the help of the semiclassical solution.

Interferometers with M paths are studied. It is shown that the accuracy of the phase-shift measurement can be improved by increasing the number of paths. For a detection scheme that uses coherent input states, phase sensitivity rescales as Δφ∝${\mathrm{M}}^{\mathrm{-}1}$, and nonunit quantum efficiency η at detectors only decreases the effective M by a factor $\sqrt{\eta }$.

In this paper we develop a three-element vector model to describe the stimulated Raman interaction in a Λ system. This model is valid over the range of interaction energies for which the excited state follows the ground states adiabatically. We use the model to present simple physical interpretations of the generation of Raman-Ramsey fringes in a separated field excitation, the ac Stark shift in the Raman clock, the ultrahigh-resolution mapping of microwave phase using Raman probes, and the coherent transfer of population by adiabatic passage for atomic beam splitters. The expressions for observables are derived by inspection and agree quantitatively with published experimental results.

A numerical method was developed to simulate the performance of vertical-cavity surface-emitting lasers. A two-dimensional code takes into account the spatial variation of both the carrier distribution and the electromagnetic field inside a cylindrical structure (dependence on the third spatial coordinate, the azimuthal angle, is trivial). The eigenmodes of the electromagnetic field inside the structure are identified. It is explained that these modes are self-oscillations of the combined system of the electromagnetic field and the dielectric and depend on the injection current. The spontaneous-emission spectrum is reproduced at threshold and slightly below it and above it. Due to simplifications in the analysis the modes obtained are restricted to those propagating in directions forming a small angle with the normal to the distributed Bragg reflector mirrors. An estimate is made for the fraction of spontaneous emission into the lasing mode, with the value of 2% in line with experimental determinations.

Atoms can nowadays be placed in increasingly exotic environments such as microscopic cavities and materials with photonic band gaps. High-Q cavities can now easily result in a strong coupling between an atom and its environment where perturbation theory should no longer be appropriate. The purpose of this paper is to describe the dynamics of a multilevel V-type atomic system (including the case of a two-level system) which interacts with a reservoir modeled by a generalized density of states. A theoretical construct, the pseudomode, is utilized to develop general methods for solution. Without using perturbation theory the equivalent master equation is developed and the relationship between the master equation, the pseudomodes, and the generalized density of states function is explored with examples. Utilizing a straightforward definition of the pseudomode, it is found that many functions for the density of states lead to problematic non-Lindblad master equations. Several examples are given, and it is shown how to convert the non-Lindblad master equations into a Lindblad form in these cases. The examples include a non-Lorentzian resonance and a simple model of a photonic band gap.

A scheme which stabilizes the trapping states in micromasers is proposed and studied. It uses an atomic beam composed of a mixture of two types of atoms. Numerical simulations based on the Monte Carlo wave-function method show that, despite collective events, it is possible to obtain a steady-state photon number distribution limited (``trapped'') to a certain domain of the photon number space. For the one-photon trapping condition this steady state approaches a Fock state in the limit of low cavity losses.

Electronic dephasing of solutions of all-trans-bis-(dimethylamino)-heptamethinium chloride, its photoisomer, and of 1,$1^{|\mathrm{I}\mathrm{H}}$,3,3,$3^{|\mathrm{I}\mathrm{H}}$,$3^{|\mathrm{I}\mathrm{H}}$-hexamethylindotricarbocyanine iodide (HITCI) is studied using forced light scattering by broad-bandwidth incoherent pump lasers in the wavelength region from 440 to 770 nm. The dephasing slows down as the pump laser wavelength is tuned over the 0-0 transition. Photoisomer and parent heptamethine molecule show comparable behavior in dephasing experiments. Absorption line-shape analysis including resonance Raman experiments indicates a considerable spectral cross relaxation in the absorption band of the parent molecule. The results for HITCI are close to those reported for two-pulse femtosecond photon echoes.

At the third order of the order parameter expansion, the system under study is variational, and for some range of parameters, a two-mode structure may occur. Both a square pattern and a 48° rhombic pattern are shown to minimize the free energy, while the numerical simulations of the full equations display only the squares. The expansion at the nontrivial fifth order removes the degeneracy between the two different patterns and predicts squares.

We investigate the quantum noise properties of lasers in which both the laser and pump form resonant cavity modes. We find that under conditions typical of solid-state lasers small signals placed on the pump beam of such systems can be found to be amplified on the laser output without incurring the usual 3 dB noise penalty associated with linear amplifiers. We also show that such systems can be very efficient producers of squeezed light.

The effects of field correlation on Raman-enhanced nondegenerate four-wave mixing (RENFWM) have been investigated by examining the RENFWM spectra as a function of time delay between two beams. We present a theory in which the underlying physics is emphasized. The field correlation has little influence on the RENFWM spectra when the laser has narrow bandwidth. In contrast, the ratio between the resonant and nonresonant RENFWM signal intensities increases as time delay is increased when the laser has broadband linewidth. Experiments with ${\mathrm{CS}}_2$ as sample have been performed to demonstrate the field-correlation effects on the RENFWM spectra.

The steady-state resonance fluorescence spectrum of a two-level atom driven by a bichromatic field in a broadband squeezed vacuum is studied. When the carrier frequency of the squeezed vacuum is tuned to the frequency of the central spectral line, anomalous spectral features, such as hole burning and dispersive profiles, can occur at the central line. We show that these features appear for wider, and experimentally more convenient, ranges of the parameters than in the case of monochromatic excitation. The absence of a coherent spectral component at the central line makes any experimental attempt to observe these features much easier. We also discuss the general features of the spectrum. When the carrier frequency of the squeezed vacuum is tuned to the first odd or even sidebands, the spectrum is asymmetric and only the sidebands are sensitive to phase. For appropriate choices of the phase the linewidths of only the odd or even sidebands can be reduced. A dressed-state interpretation is provided.