The emission spectra of a Λ-type quantum-beat three-level atomic system in a cavity is investigated. Our results suggest that the atom cannot interact with a single-mode squeezed vacuum. A variety of field inputs exhibit nonclassical effects, including the vacuum Rabi splitting and quantum beats, only for low field intensities. In the case of a coherent field input, sidebands appear whose widths are governed by the input field statistics. Off-resonant spectra exhibit transitions from predominantly spontaneous to predominantly stimulated emission.

Recently it was reported that replacing an incoherent pumping mechanism by a spectrally colored (partially coherent) pump can lead to significant gain enhancement in lasing without inversion schemes [Phys. Rev. A 48, R4055 (1993)]. We extend that study further by considering the effects of the noise parameters (strength and bandwidth) of the pump on the gain in two types of three-level atomic energy-level schemes—the ladder and the Λ models. The calculations presented in this paper show a way to continuously ‘‘tune’’ the bandwidth of the pump and make a direct comparison between the gain obtained for coherent, incoherent, and partially coherent pumping. We find that for a given set of atom-field parameters, the gain for coherent pumping is larger than for incoherent pumping, and that maximum gain is obtained for a partially coherent pump. Increasing the strength of the noise also leads to an increase in the gain. The frequency of the colored pump plays a critical role in determining the maximum gain that can be obtained.

We study the photon statistics of a micromaser with a nonzero thermal background for a large range of the pumping parameter θ. The photon statistics are examined in a two-dimensional space, parametrized by θ and k, where k is the photon number. For values of θ which are not too large, there are prominent peaks in the photon-number distribution. The locations of these peaks are determined by well-defined structures in θ-k space. These structures lie along curves in this space. As θ is increased, these structures disappear and the number distribution becomes diffuse. When θ becomes sufficiently large, however, new structures which are well localized in θ and k appear. We call these states ‘‘island states.’’ These states exhibit a strong squeezing of the photon number and are fairly insensitive to the thermal background. Their noise increases slowly due to fluctuations of the atomic beam as long as the spread in values of the pump parameter θ is smaller than the distance between the islands. Bistable behavior can be induced by fluctuations that overlap adjacent island states. We also present the photon statistics of a micromaser pumped by atoms in a mixture (incoherent superposition) of their upper and lower levels. It is shown that the noise in island states can be drastically reduced by an optimum amount of injected absorption. These features render these states experimentally feasible, so that they could be used for generating squeezed quantum states of the radiation field that are well localized in θ and k.

We introduce a theoretical framework to describe the interaction of an electromagnetic radiation field and a molecular system, such as a single molecule or a molecular crystal. By knowing in advance which electronic transitions are in resonance with the frequencies of the incident radiation, we propose a procedure to reduce the full problem to a description in terms of an effective Hamiltonian that fully takes into account the vibrational (nuclear) degrees of freedom, but that explicitly involves only those electronic states that meet the resonance condition. The influence of the rest of the electronic states appears as the polarizability of the system. We keep only those terms that give rise to Raman scattering but the scheme allows for a systematic inclusion of higher-order multiphoton processes. The resulting effective Hamiltonian is used to study the interaction of ultrashort laser pulses with a single molecule and with a molecular crystal. As applications, we study the interaction of a single ultrashort nonresonant pulse, and a train of such pulses, with a single molecule; we show that via Raman scattering the pulse impulsively transfers momentum to the molecule leaving it in a vibrational coherent state. We also study the interaction of two crossed laser pulses with a molecular crystal and show that a diffraction grating of lattice vibrations is impulsively created.

Atomic inversion is studied in the Jaynes-Cummings model with a Kerr nonlinearity when the interacting field is initially prepared in a binomial state (BS), a thermal state (TS), or a squeezed vacuum (SV). The inversion can, under suitable conditions, show a very steady beat phenomenon with a time evolution very similar to that found in classical physics for the BS, and even for the TS and SV. This means that in this system any field can reveal its ‘‘granularity.’’

Explicit expressions are derived for calculating the two-time coincidence probability density, the Mandel Q parameter of the counting statistics, and the waiting-time distribution between detector clicks for the detection of de-excited atoms leaving a micromaser with Poissonian pumping. The procedure is illustrated by applying it to the simplest trapped micromaser state for which all results can be obtained analytically. Moreover, by making use of a symmetry relation which determines the properties of the time-dependent micromaser master equation solution, it is shown that in the stationary regime for negligible thermal photon number the normalized two-time intensity correlation function of the cavity field with respect to a given time difference is equal to the normalized two-time coincidence probability density of detecting two de-excited atoms with the same time difference at the exit of the micromaser.

The twin-stripe semiconductor laser is analyzed theoretically through the nonlinear eigenmodes of the spatiotemporal distribution of the output intensity. The transverse laser modes in three spatiotemporal regimes are identified as a function of stripe separation: the regime of quasi-isolated independently operating laser stripes leading to a continuous-wave output, the intermediate regime with the laser displaying chaotically pulsating signals, and the strong-coupling regime with high-frequency more regular oscillations due to a reduced number of active spatiotemporal degrees of freedom.

A quantum analysis of the above-threshold intensity fluctuations in a nondegenerate parametric oscillator with direct-detection feedback onto the pump amplitude is presented. We derive a master equation for the signal (in-loop) and idler (out-of-loop) modes by adiabatically eliminating the pump mode and incorporating a feedback term, using the Wiseman-Milburn quantum feedback theroy [Phys. Rev. Lett. 70, 548 (1993)]. In the absence of feedback and far above threshold, we find that both beams are 50% intensity squeezed. For small negative (positive) feedback, the intensity fluctuations in the out-of-loop (in-loop) beam are reduced further. For larger values of feedback, the fluctuations grow, the fields eventually becoming unsqueezed.

We define a new representation, the hyperbolic phase representation, which enables optimal estimation of a squeeze parameter in the sense of quantum estimation theory. We compare the signal-to-noise ratio for such measurements, with conventional measurement based on photon counting and homodyne detection. The signal-to-noise ratio for hyperbolic phase measurements is shown to increase quadratically with the squeezing parameter for fixed input power.

The experimental results of the laser peak-amplitude statistics as a function of the delay time at turn-on are presented for both pump and loss switching in a ${\mathrm{CO}}_2$ laser: the data show slopes having a different sign for the two cases. A comparison between the two kinds of switching and a detailed physical interpretation of the mechanisms that cause distinct statistics is offered. We describe in detail the experimental setup and carefully discuss the conditions that must be met to obtain a true statistics of the influence of additive noise. We present an example for the statistics of multiplicative noise and summarize the characteristics of the different kinds of statistical distributions in the laser turn-on process. A detailed discussion of the meaning of the statistics obtained with swept parameters is also included.

The photon distribution function of an N-mode mixed state of light described by the Wigner function of generic Gaussian form is calculated explicitly in terms of the Hermite polynomials of 2N variables with equal pairs of indices. Simple formulas for the mean values and dispersions of photon numbers are found. The N-mode photon distribution functions for squeezed photon number states and for squeezed coherent states are expressed in terms of the Hermite polynomials of 2N and N variables, respectively.

The exposition of the formalisms of the quantum optical phase has been provided commencing from the quantum mechanics of a massive particle. The clockwise and counterclockwise components of the planar motion are shown to correspond to the signal and idler modes in the heterodyne detection scheme. The appropriate ideal phase proposal has been embodied in this scheme.

A mean-field model for light propagation in wide-aperture, lossy semiconductor lasers is derived and validated by comparison with a full counterpropagating wave code. The model includes inhomogeneities transverse to (index or gain guiding) and along the laser structure in addition to light diffraction and carrier diffusion. The model is tested on single-stripe index- and gain-guided lasers, on multistripe index- and gain-guided laser arrays, and on broad-area lasers.

Agreement with quantum theory and experiment exists for locally real models violating the apparently plausible additional assumptions of Bell inequalities subject to the use of low-efficiency detectors. A locally real optical hidden-variable model of this class is constructed here with asymmetric correlated photon pairs from the physical basis of Malus’s law. The model introduces no arbitrary constants, naturally violates factorization and no enhancement, predicts a 1/${3\mathrm{c}\mathrm{o}\mathrm{s}}^2$θ joint probability for high-efficiency detectors, and is testable with currently available low-efficiency detectors.

Some aspects of quantum tunneling of a particle in a double-well potential periodically driven by an external force are studied within the two-level approximation. A closed expression for the temporal evolution of the occupation probability is obtained in the limit of large-amplitude oscillation by the transfer-matrix formalism. The mechanism of coherent destruction of tunneling found by Grossmann et al. [Phys. Rev. Lett. 67, 516 (1991)] is made clear from a viewpoint of interference at periodic level crossings.

The first ionization potential of tantalum has been determined to be 60 891.4±0.2 ${\mathrm{cm}}^{\mathrm{-}1}$ by performing double-resonance field-ionization spectroscopy on a supersonic beam of laser-vaporized tantalum atoms.

Work on the reduction of independent variables in the Schrödinger equation for two-particle systems from six to three is extended to give a closed expression of the variational equation for states of arbitrary total angular momentum. The method consists of writing the Hamiltonian in six coordinates, by a suitable choice of transformation equations, and evaluating integrals involving real angular-momentum functions. An existing variational equation for P states follows as a special case of the present formalism.

Variational calculations are reported for the ground state of the helium isoelectronic series. An ansatz is introduced and it achieves an accuracy comparable to that hitherto achieved only with basis functions containing logarithmic terms. Energies accurate to better than one part in ${10}^{14}$ are obtained for the ground states of He through ${\mathrm{Ne}}^{8+}$ using 308-term expansions, and the ground state of ${\mathrm{H}}^{\mathrm{-}}$ using 455 terms.

New bounds to the maximum characteristics ${\mathit{u}}_{\max }$ and ${\mathit{h}}_{\max }$=h(${\mathit{u}}_{\max }$) of the spherically averaged electron-pair density h(u) and to the electron-electron coalescence h(0)=〈δ(u)〉 of a many-electron system are shown in a rigorous manner (i.e., no approximate wave functions were used). The resulting rigorous inequalities also allow one to bound a given interelectronic moment 〈${\mathit{u}}^{\mathrm{\beta }}$〉 from above and from below. In particular, an interesting inequality is obtained for the electron-electron repulsion energy ${\mathit{E}}_{\mathit{e}\mathit{e}}$ of an N-electron system: 2πh(0)${\mathit{u}}_{\max }^2$≤${\mathit{E}}_{\mathit{e}\mathit{e}}$≤3N(N-1)/4${\mathit{u}}_{\max }$. For completeness, just to have an idea of the worth of these results, some of the rigorous inequalities are numerically studied for two-electron ions with nuclear charge Z=1, 2, 3, 4, 5, and 10 using a highly accurate electron-pair density h(u) constructed from the 204-term Hylleraas wave functions. The accuracy is found to increase, generally, with increasing Z and decreasing order β of the involved moments.

A finite-basis-set variational method with the two-limit basis functions proposed to calculate the states 1${\mathit{s}}_0$ and 2${\mathit{p}}_{\mathrm{-}1}$ by Chen and Goldman [Phys. Rev. A 45, 1722 (1992)] is used to calculate the energy levels of a hydrogen atom in a magnetic field. The accurate energy eigenvalues for the eigenstates with major quantum numbers less than or equal to 3 are obtained. The finite-basis-set method with the two-limit basis functions can be used to obtain accurate results not only for the ground state but also for any excited state.