Some coherence properties of the light emitted from a two-level atom which is excited by a monochromatic coherent field are investigated. It is shown that the elastically scattered light is coherent, and that this compoment of the emitted field can be separated from the total field by narrow-band filtering at the driving frequency. These results are then applied to the problem of interference between the fluorescent and the elastically scattered field. An interference experiment is analyzed in which the detection of one emitted photon signifies the beginning of a Rabi cycle and the detection of a subsequent photon fixes the instant in the Rabi cycle when the interference is detected. It is shown that the visibility of the interference is near zero at the time when the fluorescence is maximum.

The vacuum Rabi splitting may be observed with population-trapping techniques. The trapped population has a lifetime much greater than the natural lifetime of the atomic transition; as a result, vacuum Rabi splittings that are much smaller than the natural lifetime may be observed. A condition for lasing without inversion in this system without any externally injected coherent field or coherence is stated.

In this paper we show how different measurement schemes for a micromaser system may be used to investigate different aspects of the maser dynamics. The features which are investigated include a measurement of the phase diffusion in steady-state, transient states with several orders of coherence, and an interesting connection to questions of the Einstein-Podolsky-Rosen paradox. In addition, it is shown rigorously that different measurement schemes acting only on the atomic part of the system after the cavity have no influence on the ensemble properties of the cavity field.

By applying a Lie-algebra method [Phys. Rev. A 42, 4302 (1990); 47, 5213(E) (1993)], we obtain analytical solutions and energy eigenvalues for a charged harmonic oscillator interacting with a single-mode photon field. The energy shifts of bound states of the harmonic oscillator due to the radiation field is also derived. By a variational method, we show that any bound state in a central potential which satisfies a power law can be treated as a harmonic oscillator around its average radial position. With this idea, we generalize the energy-shift formula obtained for a harmonic oscillator to the hydrogen-atom case. Our result shows that the energy shifts depend on the principal quantum number according to an inverse-square law.

We present a practical method of designing laser fields for generation of spatially squeezed molecular wave packets. Our approach, based on optimal control theory, generalizes and improves previous, more intuitive suggestions for the optical generation of squeezed wave packets. Spatial-temporal evolution of the squeezing is studied and several underlying physical mechanisms of the effect are explored. Possible applications to laser femtosecond chemistry and experiments on laser modification of molecular adiabatic potentials are discussed.

Lie-algebra methods for investigating quantum optical systems are presented within the framework of the Liouville-space formulation. The generalized decomposition formulas for exponential functions of the generators of su(2) and su(1,1) Lie algebras are derived and their expectation values are calculated for typical states in quantum optics. The general procedure for using Lie algebras in the Liouville space to treat quantum optical processes is given in terms of generalized decomposition formulas and their use is demonstrated by calculating the absorption line shape and photon echo signal in a localized electron-phonon system. It is also shown that the photon-counting probability can be calculated by using the su(1,1) Lie algebra and that the electron-counting probability can be calculated by using the su(2) Lie algebra. The su(1,1) Lie algebra is also used to investigate a quantum-nondemolition measurement of photon number in the four-wave-mixing model.

We will demonstrate that four-wave mixing with linearly chirped (phase-modulated) pulses is a unique tool for obtaining information on the dynamics and level structure of a system. Especially, it will be shown that the transient-grating-scattering type of experiment with chirped pulses provides an immediate answer to the question of whether the dynamics of a system occurs on a fast and/or slow time scale. In addition, we present compelling evidence that chirped four-wave mixing in a molecular system is a viable method for measuring excited-state vibrational frequencies. Double-sided Feynman diagrams are used for a third-order perturbative calculation of two-level four-wave-mixing effects and chirped coherent Raman scattering. The diagrams provide a visual representation of the quantum-mechanical pathways that the system can take as a result of the different field interactions. The number of quantum-mechanical pathways that contribute to the signal is shown to depend on the chirp rate compared to the time scale(s) of the system dynamics. A stochastic model is used to describe the optical dynamics of the system. The resulting expressions for the third-order nonlinear polarization are so complex that numerical calculations are necessary to simulate the time dependence of the optical response. It will also be shown that our theoretical results in the appropriate limits converge to those obtained for impulsive or continuous-wave excitation.

The basic concept of squeezed spin states is established and the principles for their generation are discussed. Two proposed mechanisms, referred to as one-axis twisting and two-axis countertwisting, are shown to reduce the standard quantum noise S/2 of the coherent S-spin state down to 1/2(S/3${)}^{1/3}$ and 1/2, respectively. Implementations of spin squeezing in interferometers are also discussed.

The dynamics of stimulated Brillouin scattering in a finite-length, homogeneous medium with the effects of temporal resonance detuning but no external feedback is examined numerically. The inclusion of resonance detuning leads to nonstationary behavior of the wave amplitudes including periodicity, quasiperiodicity, and chaos. The results may have applications to experiments with optical fibers and laser plasmas.

We study squeezed flucuations of the electromagnetic field in the N-photon sectors of the photon Hilbert space. For each N sector, a truncated boson algebra of photon operators is constructed in an embedded N+1 sector. An explicit construction of quantum states of light leading to maximum noise reduction is presented. An analytic expression for the minimum variance of squeezed fluctuations and the corresponding photon statistics are derived in the arbitrary N sector. A very accurate, approximate formula for the minimum variance is also given.

We consider the momentum diffusion of atoms moving in a standing-wave laser field. We show how the correlation-function approach as originally applied to atoms at rest can be generalized to derive the velocity dependence of the momentum diffusion coefficient in standing waves, and that it gives results in agreement with the transport-equation approach to laser cooling. As an example we apply our calculations to determine the achievements of laser cooling in intense fields where cooling may occur around a nonvanishing velocity. Here we obtain temperatures which are 30% lower than the corresponding minimum obtained around zero velocity. Our explicit calculations involve usage of the optical Bloch equations, the quantum regression theorem, and the matrix continued-fraction method.

The Liouville equation for the density matrix can be recast so that the external-field terms which couple density-matrix elements are second order in the field. This approach is shown to have a profound effect on the steady-state analysis of strong-field resonant nonlinear optical problems. First, in the case where parity or appropriate field restrictions apply, there is a reduction of the number of coupled equations which must be solved by at least a factor of 2. Second, this reformulation naturally leads to radiative-renormalization terms which are directly related to saturation, Stark shifts, and Rabi splittings. We can use this simple formalism to obtain solutions to a number of resonant nonlinear problems including cases where there are two or more strong fields. The renormalization described here is equivalent to a Dyson-equation analysis.

The stochastic dynamics of the quantum state of a laser conditioned on continuous intensity and phase-sensitive measurements on its output are examined. We first develop the essential model for a Poissonian laser, and then generalize it for regularly pumped lasers. We show that the rate of phase diffusion (which gives the laser linewidth) is not affected by the regularity of the pump. In both cases, heterodyne detection causes the phase variance in the conditioned laser state to become very small, yet remain significantly above (at least three times) that of a coherent state. The phase diffusion is manifest by a random walk undertaken by the mean phase, with the stochasticity arising from the local-oscillator shot noise. In contrast, intensity measurements have no effect on a Poissonian laser. For a perfectly regularly pumped laser, coarse-grained intensity measurements (for which an approximate theory is developed here) collapse the state to one with an arbitrarily small photon-number variance-to-mean ratio.

Conditions for Bragg scattering are derived for ‘‘crystalline’’ ionic systems as found in ion traps and potentially in storage rings. The effective ‘‘Debye temperature’’ for such systems is also estimated.

An initially localized Rydberg wave packet, with Δn≪n, spreads uniformly over its entire classical orbit within a time much larger than the classical period ${\mathit{T}}_{\mathrm{cl}}$. However, it eventually reassembles, with a hierarchy of recurrence times: (n/3+1/2)${\mathit{T}}_{\mathrm{cl}}$, (${\mathit{n}}^2$/4+1/2)${\mathit{T}}_{\mathrm{cl}}$, etc. This phenomenon has no classical analog.

Some recent experiments indicate that certain rare-earth negative ions exist. Some local-density calculations indicate that attachment of f electrons is most favorable for Tm and Md. Here we investigate by means of relativistic configuration-interaction methods whether ${\mathrm{Tm}}^{\mathrm{-}}$ 4${\mathit{f}}^{14}$ and ${\mathrm{Md}}^{\mathrm{-}}$ 5${\mathit{f}}^{14}$ are bound. Our results strongly suggest that they are not, and that a different attachment process (perhaps that of a p electron, as recently proposed by Vosko and Chevary [Bull. Am. Phys. Soc. 37, 1089 (1992)]) must be contemplated.

The local electron-electron quantity 〈δ(${\mathbf{r}}_{12}$)〉 of atomic systems, which plays an important role in the realization of the so-called correlation cusp condition, as well as in the description of the relativistic and radiative corrections to the ground-state energy, is investigated by means of the interelectronic radial expectation values 〈${\mathit{r}}_{12}^{\mathrm{\alpha }}$〉, α>-3. Starting from the unimodal character of the spherically averaged electron-pair density h(${\mathit{r}}_{12}$) and the recently found inequality h(${\mathit{r}}_{12}$)>h’(${\mathit{r}}_{12}$), upper ${\mathit{U}}_{\mathit{k}}$ and lower ${\mathit{L}}_{\mathit{k}}$ bounds, k=0,1,2,..., to the electron-pair density at the origin or central electron-pair density h(0), which is equal to the quantity 〈δ(${\mathbf{r}}_{12}$)〉, are found analytically. For the two-electron atoms with Z=1, 2, 3, 5, and 10, the quality of these bounds is analyzed by means of the optimum 20-term Hylleraas-type wave functions recently obtained by two of us [T. Koga and K. Matsui, Z. Phys. D (to be published)]. It is shown that the accuracy of both types of bounds increases with k for fixed Z, being greater for the lower bounds than for the upper bounds when k is small. Both bounds are of similar quality for big values of k. Moreover, any desired accuracy may be reached by increasing the k value.

The ${\mathrm{He}}_2$ molecule is examined in the ${}_{}{}^3{}_{}{}^{}\mathrm{\Delta }_{\mathit{u}}^{}{}_{}{}^{}$ symmetry via the numerical Hartree-Fock method. A previously unreported state is found with lower energy than states reported in the literature, necessitating a reassessment of the question of the stability of corresponding ‘‘daughter’’ states of the ${\mathrm{He}}_2^{\mathrm{-}}$ ion.

We show some interesting phenomena in a one-photon micromaser. They include the ‘‘ladder’’ behavior of the average Rabi oscillation angle, the striking resemblances between the change rate of the average Rabi oscillation angle and the normalized photon-number variance of the micromaser field, and the twofold transitions around a degenerate trapping state. Away from any transition, including at trapping states at very low cavity temperatures, the average Rabi oscillation angle is approximately 1/2π short of one or more complete Rabi oscillation cycles.