We present a dressed-atom theory of a four-level, double-Λ atomic configruation interacting with a strong laser light which induces a superposition of two lower states. The presence of the cavity and of damping is fully taken into account and the conditions and characteristics of a possible lasing without inversion between the unperturbed states are determined analytically. The special case of the Zeeman-degenerate J=1 lower state is found to be particularly attractive for a possible practical realization.

We examine the problem of determining the phase difference between two optical fields, first for classical and later for quantum fields, by reference to two simple measurement schemes that yield the sine and/or cosine of the phase difference between classical fields. We show that certain difficulties exist even within the framework of semiclassical radiation theory when the field is very weak, and particularly when amplitude and phase fluctuations are correlated. We find that a clear distinction has to be made between the measured values of the sine or cosine and the values that can be inferred from a series of repeated measurements. A corresponding distinction can be made also for a quantum field, although the interpretation is not the same. The dynamical variables chosen to represent the cosine and sine that emerge from the discussion of the measurement schemes commute when the sine and cosine are obtained together, but not when the measurement yields one or the other. These sine and cosine operators have well-defined values only when there is a large dispersion of the photon number. We arrive at expressions for the moments of the measured and of the inferred sines and cosines that differ from most previous treatments. The expressions are applied to optical fields in several different quantum states. Only for the Fock state and for the so-called phase state, which was treated recently at some length by Pegg and Barnett [Phys. Rev. A 39, 1665 (1989)], do the measured and the inferred moments coincide. Our analysis of the problem of phase measurement leads to the conclusion that the appropriate dynamical variables for the measured sine and cosine depend on the measurement scheme, and that different schemes correspond to different operators.

A perturbation series is derived for the Schrödinger equation where the perturbation is permitted to go to ∞. Such an asymptotic series can be obtained in a representation where the time evolution of the states is due to the unperturbed part of the Hamiltonian of the problem and the time evolution of the observables is determined by the perturbation, contrary to the interaction picture. The equivalence between the series given by such a picture, and an asymptotic perturbation scheme is given. The method is applied to a spin-1/2 particle in a two-component magnetic field, one component of which, considered as a perturbation, can be time varying. Choosing a constant perturbation we show the equivalence between the exact solution and the approximate one when a component of the magnetic field is much larger than the other. In this case the limit t→∞ cannot be taken, as mixed-secular terms appear in the asymptotic series. Taking a linear time-varying dependence for a component of the magnetic field, we get a nonanalytic asymptotic series.

The theoretical model presented here is motivated by experimental works demonstrating the suppression of spontaneous emission by atoms placed inside a cavity with a fundamental frequency above that for the atomic transition. In my model, two distinguishable two-level atoms, one of them initially excited, the other in the ground state, are coupled to a nonresonant radiation mode, with no direct interaction between the atoms. The exchange of energy between the atoms is investigated, and it is found that it oscillates from one atom to the other with angular frequency Ω related to the radiative lifetime τ by Ωτ=(3/2${\mathrm{\pi }}^2$)(${\mathrm{\omega }}_0$/${\mathrm{\omega }}_0$-ω)(${\mathrm{\omega }}_0$/ω${)}^3$, with ${\mathrm{\omega }}_0$ and ω, the frequencies for the radiation mode and the atomic transition, respectively.

A one-to-one correspondence between spectroscopies of reduced inhomogeneous broadening and photon-echo processes is established. Photon-echo phenomena like those related to coherent Stokes Raman scattering and difference-frequency generation are predicted.

Recent studies of soliton formation in a Raman amplifier by a π phase shift have shown that the soliton will decay if the input Stokes beam is off resonance. Initial experiments indicated that this soliton decay is related to frequency shifts of the input Stokes beam that result from quantum fluctuations. In this paper we use the quantum statistics of the Raman spectral fluctuations to compare the predicted decay statistics of the soliton decay with the experimentally measured distribution. We find that, as conjectured, the soliton decay is directly related to the statistics of the initiating quantum fluctuations.

Measurements of quantum-noise reduction have been performed over a broad frequency range up to 0.5 GHz using pulses of squeezed light generated by parametric amplification in ${\mathrm{KTiOPO}}_4$ crystals. Both balanced-homodyne and direct-difference photodetection schemes were employed, and 0.5 dB of noise reduction was routinely obtained. A continuous-mode traveling-wave theory including the effects of dispersion and loss has been employed to model the experimental results.

The nonlinear dynamics of a sample of two-level systems exposed to noisy laser light is investigated. As stochastic models we treat the chaotic field and the real Gaussian field. Based on the method of marginal characteristic functions, we deduce analytical solutions for the mean values and variances of the atomic populations in terms of matrix continued fractions. We find significantly enhanced on-resonance fluctuations for a real Gaussian field compared to a chaotic field of the same bandwidth and intensity. Furthermore, in contrast to phase-noise models, the fluctuations in the fluorescence intensity do not decrease to zero in the limit of slow fluctuations.

Several quantum open-system models have been examined recently that dynamically reduce the off-diagonal terms of the density operator in the position representation by incorporating the effects of interaction with external degrees of freedom. A recent model [M. R. Gallis and G. N. Fleming, Phys. Rev. A 42, 38 (1990)] includes explicit dependence on the spatial correlations of the decoherence rate of the off-diagonal elements (in the position representation) of the density operator. In this paper, we use influence-functional techniques to examine the effect of an external potential that randomly varies as function of position and time, which leads to a natural characterization of the decay rate of the coherence between spatially separated states in terms of the spatial correlations of the potential, and the corresponding fluctuating forces. We obtain the effective master equations for short environment relaxation time scales, and discuss the similarities and differences between the effects of random external potentials versus the effects of interactions with external degrees of freedom, such as that recently investigated by Stern, Aharonov, and Imry [Phys. Rev. A 41, 3436 (1990)].

We show that the spontaneous emission of a moving atom inside a cavity is modified by two different mechanisms. The first one is a Doppler-induced detuning of the cavity line that leads to observable changes in the spontaneous emission rate for atomic velocities in excess of a characteristic velocity ${\mathit{v}}_{\mathrm{cav}}$=c/Q, Q being the quality factor of the cavity. In addition, spatial mode effects can lead to a temporal modulation of the exponential decay rate. This modulation is observable for velocities that do not exceed another characteristic velocity ${\mathit{v}}_{\mathrm{mod}}$ which is typically several orders of magnitude smaller than ${\mathit{v}}_{\mathrm{cav}}$.

We consider a composite system consisting of a degenerate optical parametric oscillator (DOPO) and a set of N homogeneously broadened two-level atoms. When the atoms are on or near resonance with the subharmonic-frequency field generated through the frequency down-conversion process, bistability appears in the intracavity field near the DOPO threshold. The bistability region will decrease as the detuning between the atomic transition frequency and the frequency of the subharmonic field increases. When the detuning becomes large enough, the atoms decouple from the cavity field and the system behaves like a normal DOPO. There are several features distinguishing this bistable behavior from the usual atomic optical bistability occurring with atoms in an optical cavity driven by an external field.

We present a theoretical study of the influence of laser-induced continuum structure on the third-harmonic generation in atomic gases. We employ the density-matrix formalism including the spatiotemporal structure of laser pulses. The theoretical model is then applied to third-harmonic generation in sodium experiments. Extensive numerical calculations using realistic atomic parameters in combination with the parameters in actual experimental situations demonstrate the subtle interplay of various effects and pinpoint causes of possible complications. We obtain good agreement with the few existing experimental data.

In laser systems, regular pumping always reduces the photon noise. In micromaser systems, however, regular pumping may lead to photon noise reduction as well as photon noise increase depending on the operation conditions. The effect of higher-order terms in the expansion of ln(1+pu) with respect to the pumping regularity parameter p is discussed. These terms have a significant effect on the photon statistics in micromaser systems. Their effect in laser systems is quite small compared with the second order and can be neglected.

The Green’s-function method is used to study the properties of the spectrum of a three-level system driven by two resonant monochromatic fields. In the case of strong fields, we find that the correlation between two transitions is too small to consider. The Green’s functions describing the two transitions consist of five Lorentzian lines rather than seven lines; furthermore, the positions at which sidebands are peaked depend on both Rabi frequencies, and only when two Rabi frequencies reach certain values can five Lorentzian lines appear. The heights of the sidebands become larger with increasing Rabi frequencies. The decay rates also affect the spectrum strongly.

A formalism for calculating Berry phases for nonadiabatic systems containing an additional adiabatic time dependence is developed. This is then applied to a two-level atom in a strong resonant polarized laser, where the laser polarization provides the adiabatic parameter. It is found that, when the laser polarization is kept constant, judicious polarization choices allow one to eliminate either the rotating-wave or non-rotating-wave part of the interaction. Furthermore, the adiabatic Berry phasor obtained when the laser polarization is varied is found to be complex. This can be compared to the case of purely adiabatic time-reversal even systems, which can only have real Berry phasors.

We construct the Wigner distribution function for a coupled boson-fermion system. This function is regarded as a certain ‘‘superfield’’ defined on the extended phase space, the points of which are labeled by the anticommuting canonical c variables together with the ordinary ones. In this approach, the variables of a fermion and a boson are treated on a completely equal footing, and the phase-space representation is fully realized. We apply the formalism to the kinetic theory of the optical Dicke model with a two-level atom, and show how systematically a set of the generalized Fokker-Planck equations, which describes the effective dynamics of the radiation field, is derived from a single superfieldlike equation.

We have measured the optical shifts for all stable isotopes of ${\mathrm{Ca}}^{+}$, with respect to isotope mass 40, in the resonance transitions 4s ${}_{}{}^2{}_{}{}^{}$${\mathit{S}}_{1/2}$–4p ${}_{}{}^2{}_{}{}^{}$${\mathit{P}}_{1/2,3/2}$. The value of our measured shift for the even isotope mass 46 falls below the King plot. From the fit to a second King plot, omitting the shift for mass 46, we obtain a value of -312 MHz ${\mathrm{fm}}^{\mathrm{-}2}$ for the field-shift constant F. A comparison of this value with ab initio calculations [G. Torbohm, B. Fricke, and A. Rosen, Phys. Rev. A 31, 2038 (1985)] and our semiempirical estimate shows better agreement when correlation effects have been included in the calculations [A.-M. Martensson-Pendrill, A. Ynnerman, and H. Warston (private communication)] and suggests that inclusion of the screening factor β in semiempirical methods results in an overestimate of F.

Photoabsorption cross sections for the ns’ and nd’ autoionizing Rydberg series of Xe have been measured with a resolution of 7.4 mÅ using a high-resolution spectrometer and synchrotron radiation. The cross sections are parametrized with the aid of a line-shape formula that is based on the multichannel-quantum-defect theory and has a form analogous to Fano’s resonance formula and are compared in detail with theoretical predictions available in the literature.

Exact formulation of the impulse approach, also known as the quantum-mechanical spectator model, is used to investigate the rapid deactivation of highly internally excited KBr, written as ${\mathrm{KBr}}^{\mathrm{*}\mathrm{*}}$, by Ar phenomenon not previously understood. The model of inelastic scattering at the repulsive wall, approximated here by a hard-core potential, using the impulse formalism is compared with the experimentally observed results obtained by scattering ${\mathrm{KBr}}^{\mathrm{*}\mathrm{*}}$ with Ar. The calculation is in excellent agreement with the measured results for the 75° center-of-mass (c.m.) scattering angle, while the calculated results for the 45° c.m. scattering near the peak (nearly elastic scattering) are a factor of about 1.5 smaller than the measured results. This is an impulse calculation where the collision energy is supplied by the internal motion of the target and not by the translational motion of the projectile.

Theoretical elastic cross sections of electron scattering with Zn and Cd atoms are provided with a static-exchange plus correlation-polarization potential formalism. A p-wave shape resonance state is predicted for Zn as well as Cd atom. Elastic total cross sections and differential cross sections at an angle of 90° are given at the energies between 0.01 and 4 eV.