We demonstrate a technique of photon-echo interferometry which provides extraordinary sensitivity for the measurement of the relative phase in the coherences for pairs of optical transitions. The method is applied to study collision-induced optical-coherence transfer between adjacent transitions in atomic samarium vapor.

Close-coupling calculations have been carried out for ion-atom collisions to show that electron-capture probabilities depend strongly on the magnetic quantum number of the initial target state if 2 the quantization axis is chosen to be perpendicular to the scattering plane. In the natural frame of reference, the probability for electron capture is largest for ${\mathit{m}}_{\mathit{i}}$=-l substates and decreases rapidly with increasing ${\mathit{m}}_{\mathit{i}}$, while states with positive values of ${\mathit{m}}_{\mathit{i}}$ have negligible probabilities. This propensity rule results from the rotation of the electron cloud with the internuclear axis in the collision. We have shown further that this propensity rule can be interpreted classically and have carried out classical-trajectory Monte Carlo calculations to confirm the same qualitative results.

We performed laser spectroscopy of ${\mathrm{In}}^{+}$ ions stored in a radio-frequency trap. The 5${\mathit{s}}^2$ ${}_{}{}^1{}_{}{}^{}$${\mathit{S}}_0$→5s5p ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_1$ transition at 230.6 nm was excited and its hyperfine splitting and isotope shift have been measured. The lifetime of the ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_1$ state was measured using intensity modulated laser excitation: τ${(}^3$${\mathit{P}}_1$)=0.44(4) μs. A single indium ion was laser cooled using this intercombination line and dark periods in the fluorescence were observed when the metastable ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_0$ state was populated by a magnetic dipole decay from ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_1$. The radiative lifetime of the forbidden transition ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_0$${\to }^1$${\mathit{S}}_0$ was determined from the duration of the dark periods: τ${(}^3$${\mathit{P}}_0$)=0.14(2) s. This value is compared to calculations based on perturbation theory. Prospects for an optical frequency standard using the narrow 5${\mathit{s}}^2$ ${}_{}{}^1{}_{}{}^{}$${\mathit{S}}_0$→5s5p ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_0$ resonance at 236.5 nm of a single laser-cooled indium ion are discussed.

Ramsey interference fringes are observed in the line shape of resonant Rydberg-atom–Rydberg-atom collisions occurring in the presence of a radiation field of frequency comparable to the inverse of the collision time. At low frequencies the fringes are phase dependent, but at high frequencies they are not. We present a theoretical interpretation based on a quasistatic field description which connects the low- and high-frequency regimes. In the high-frequency regime, this model gives results equivalent to those obtained using a ‘‘dressed-atom’’ approach.

The Gaussian noise model for a harmonic oscillator subjected to random linear fluctuations (e.g., thermal noise) is used to derive generalized Heisenberg and entropic uncertainty relations for the position-momentum and number-phase observables. The lower bounds are partitioned into pure quantum and pure noise terms, and the minimum-uncertainty states are determined. Formally similar results of Abe and Suzuki [Phys. Rev. A 41, 4608 (1990)] for the position-momentum case, derived using the thermofield formalism, are shown to correspond to amplification noise rather than thermal noise.

Laser cooling of a single trapped ion in a Paul trap is discussed theoretically in the Lamb-Dicke limit, with full consideration of the time dependence of the trapping potential. Resulting mean kinetic energies are defined as time averages over one period of the micromotion and are compared with final temperatures expected from the laser-cooling treatment with harmonic traps. For laser-atom detunings close to the micromotion frequency the results differ significantly from those expected for a harmonic trap potential. A physical interpretation is given and simple formulas are derived for the strong confinement case.

We study the quantized field in a one-dimensional electromagnetic resonant cavity. The cavity contains a linear and lossless dielectric medium with frequency-independent polarizability. The dielectric permittivity is an externally prescribed function of both the space and the time. We also allow one of the cavity’s mirrors to move in a given trajectory. Unlike other previous studies on the same system, we formulate an effective Hamiltonian so that the dynamics of the cavity field can be described in the Schrödinger picture. The effective Hamiltonian is quadratic in structure, therefore two-photon generation from the vacuum state can occur. We also discuss the case of resonant behavior of the system.

We have studied the effect of finite bandwidth of the driving field on the enhancement of refractive index and lasing without inversion in a three-level atomic system in which partial coherence is introduced either in upper-level or lower-level doublet via a strong microwave driving field having finite bandwidth. We find that both phenomena are adversely affected by the phase fluctuations in the driving field. Further, there is a range of driving field detuning for which the refractive index is considerably enhanced with vanishing absorption.

We have considered the steady-state resonance fluorescence spectrum for a beam of two-level atoms, interacting with a strong driving field with a finite bandwidth inside a cavity. The competitive effects of cavity losses and the finite bandwidth of the intense driving laser beam on the resonance fluorescence spectrum have been discussed. Our results show that the usual three-peaked resonance fluorescence spectrum starts merging back into the central peak as the bandwidth of the driving field increases. Moreover, the asymmetry introduced by the detuning of the driving field having a finite bandwidth is also affected by the cavity losses.

We report measurements of the absorption spectrum for two-photon absorption from a variety of randomly amplitude-modulated laser fields. The fields are generated by modulating the output of a stabilized tunable ring dye laser external to the laser cavity. As such, the field statistical properties are controllable and well characterized. The fields which we have used in this investigation include the real Gaussian field, the complex Gaussian field, and the real Gaussian field with a coherent component. For the last field, an interesting correlation effect is seen when the coherent component is in phase or 90° out of phase with the stochastic component. We have also investigated the effect of partial correlation of the two counterpropagating fields used in the measurements. In all cases we find excellent agreement between the measured absorption spectra and those calculated from the known fourth-order field-correlation functions.

The state evolution in the two-photon atom-field interaction with large initial fields is studied. It is shown that under certain conditions, for the initial coherent field, at one-quarter and three-quarters of the revival time the atom is converged into unique pure states, and at the revival time both the atom and field return to their initial states. The possibility for the field macroscopic superposition states to be generated is discussed. The effects of the cavity damping, photon statistics, and dynamic Stark shifts are investigated. Our results give some further insight into the validity of the effective two-photon Hamiltonian which neglects the Stark shifts.

In this paper the nearest-neighbor level-spacing distributions P(s) of the two-dimensional harmonic oscillator for which the energy contours are flat in the action space are calculated. It is found that P(s) for a given level group on an energy contour is not peaked about a nonzero value of s regardless of whether the oscillator frequency ratios are irrational or rational. The precise form of P(s) is a δ function independent of the arithmetic nature of the frequency ratios. We propose another method of constructing P(s) in which many sets of levels are taken as a whole. Using this method, some surprising distributions, such as Gaussian orthogonal ensemble-like, Poisson-like, and unit-step-function-like distributions, are exhibited for some sets of levels far away from the scaled energy contours of the harmonic oscillator.

We present a model for a two-photon phase-sensitive linear amplifier in which the phase sensitivity is introduced by injecting three-level atoms initially prepared in a coherent superposition of upper and lower levels. We have studied the quantum-statistical properties of noise and show that, under certain conditions, the additive noise is in a squeezed vacuum state whose squeezing parameter depends on the atomic variables.

In this paper, we present the results of an x-ray-laser gain experiment on Li-like ${\mathrm{Ca}}^{17+}$ ions, conducted recently at the LF12 Laser Facility of the Shanghai Institute of Optics and Fine Mechanics with a ${\mathrm{CaF}}_2$ slab target, and the time histories of amplified spontaneous emission in Li-like x-ray lasers at different distances from the target surface.

We study the formation of mixtures of superposition states of the coherent states ‖±α〉, also known as Schrödinger-cat states, from a competitive process involving a two-photon parametric process and two-photon absorption. Using the fact that photons are created or destroyed in pairs, we deduce the long-time steady-state form of the density operator. We numerically study the evolution at all times and show that generally the field is in a mixed state. We also examine nonclassical properties of the field such as squeezing and sub-Poissonian statistics, and also the evolution of the Q function.

Although an ideal degenerate optical parametric oscillator (DOPO) can generate perfect squeezing at the output of a one-sided optical cavity when operating just below threshold, its intracavity squeezing is limited to less than one-half (50%) of its perfect value. However, when two-level atoms are introduced into the DOPO cavity, the amount of intracavity squeezing can be enhanced, from its maximum value of 50%, to a maximum value of 75% in the good-cavity limit due to the strong interaction between the two-level atoms and the subharmonic field mode. This extra intracavity squeezing is significant in studying spectroscopy of atoms interacting with a squeezed field mode inside an optical cavity.

A multidimensional form of the unified colored-noise approximation is applied to obtain the Fokker-Planck equation for intensity distributions of dye-laser models simultaneously driven by colored pump noise and quantum noise. The stationary intensity distributions (SID’s) of these models are calculated. The first-order-like transitions (FOLT’s) of the models are studied and compared. With the help of the combination of Sturm’s theorem and Descarte’s rule of signs, the following conclusions on the FOLT are obtained. (1) In the limit of white pump noise (the correlation time of the pump noise τ=0), the FOLT disappears for the colored loss-noise model with saturation whereas it does not disappear for the colored gain-noise model. (2) The dependence of the FOLT on τ is intensely affected by the quantum noise. If quantum noise is neglected, the first critical curve which separates the regions of single extremum and double extrema of the SID does not change with τ. However, when the quantum noise is considered, the first critical curve does change with τ. (3) When τ→∞, the area of region II in which the SID varies monotonically contracts and tends to zero. Therefore the FOLT disappears in the models. (4) It is found that when the strength of the quantum noise P varies (τ is fixed), the critical curves also change.

We analyze the dynamics of sum-frequency generation (SFG) and difference-frequency generation (DFG) for broadband input fields. We demonstrate that amplitude modulation of the input fields significantly affects conversion efficiency of SFG and DFG, but frequency modulation does not affect conversion efficiency. Analytic results for SFG and DFG output-field intensities are thereby available for arbitrary fields. Self- and cross-phase modulation can affect the dynamics in the limit of very high field strengths, but these effects are of higher nonlinearity and therefore usually negligible. The quantum efficiency of DFG is shown to be generally higher than SFG, but the energy efficiency is much lower if the difference frequency is significantly less than the input frequencies. Optimal SFG quantum conversion efficiency for such systems approaches that of second-harmonic generation only if the quantum fluence (total number of photons) in the two input beams are equal. Optimal DFG quantum conversion efficiency occurs when the number of photons of frequency ${\mathrm{\omega }}_2$ is small yet sufficient for significant stimulation. A recently developed method for obtaining efficient SFG for multimode input fields is theoretically analyzed. The method involves using an arrangement with two or more nonlinear mixing crystals with a time-delay line situated between the crystals that delays one of the fundamental fields relative to the other. The efficiency in the second crystal depends on the cross-correlation function of the two fundamental fields upon leaving the first nonlinear crystal. The time-delay method is not effective for multimode DFG.

In this paper we study the properties of general linear transformations with complex coefficients, and the effect of such a transformation on a multimode state which is characterized by a Gaussian-Wigner function. We present general results on the changes in the correlation characteristics and the correlation entropy. We then specialize to the two-mode (or two-particle) situation where two-mode squeezed states, subsequently squeezed separately, form a closed set under linear transformations. We derive conditions on the statistical properties of the input fields and the linear transformations such that the state of the output fields is unentangled if the input is unentangled. We present various special cases. Finally, we also discuss the production of entangled states for particles in a harmonic potential.

Although the operational approach to the quantum-phase problem developed earlier by us [Phys. Rev. A 45, 424 (1992)] has now been confirmed experimentally for several different states of the electromagnetic field, so far no measurements have been reported with partially coherent light beams. This situation is remedied in the present work, where we report the results of measurements on light obeying thermal statistics with a variable degree of mutual coherence. Once again, we find agreement between experiment and our theoretical approach.