Two classes of analytic solutions for three-state systems involving two overlapping laser pulses of different shapes, or of similar shapes but with their centers displaced, are presented. We find a remarkable connection between the order of arrival of the two overlapping pulses and the effectiveness of transfer from the ground state to the third state, and we find remarkable results for the maximum occupation probability of the intermediate state. The approach of these analytic solutions to the adiabatic-following process is also demonstrated.

We investigate the semiclassical electric-dipole-allowed interaction of a unidirectional plane-wave electric field with a homogeneously broadened two-level medium prepared in a coherent superposition of energy eigenstates. Atomic level pumping and the effects of phase matching the new polarization contributions are discussed. The slowly varying polarization is derived and applied to the problem of the propagation of a weak field. The polarization of the medium acquires a direct (field-independent) contribution due to the injected coherence. We find that the slowly varying envelope propagation equation retains the standard single-mode absorption coefficient but develops additional driving terms. Phase matching in both time and space is crucial for the injected coherence to couple to a field. The phase-matched case of weak-field propagation proves to be a linear superposition of two processes: the usual Beer’s law exponential decay (or growth) and a constant field supported by the medium. The injected coherence enables a weak electric field to persist in an absorbing medium.

The coupling of an electric field to an atomic beam prepared in a phase-locked coherent superposition of energy eigenstates is examined for a ring-laser cavity. The active medium is assumed to be a collection of noninteracting homogeneously broadened two-level atoms whose transition is electric-dipole allowed. The atom-field interaction is treated semiclassically and the atomic coherence injected into the cavity is assumed to be phase matched to the unidirectional plane-wave cavity mode. The polarization is derived for the case in which the electric-field-mode envelope has at most linear phase variations in time and is applied to the problem of frequency locking in a cavity. The presence of the atomic coherence causes the active medium to possess an inherent polarization, i.e., a field-independent contribution. This enables an optical cavity to support laser oscillation over the entire range of relative excitations, in particular, even for strongly absorbing media. A simple linear stability analysis is performed on the electric-field envelope by describing the medium with a slowly varying polarization valid when the time scales of the atomic response are much smaller than those of the variations in the envelope. The stability of frequency-locked oscillation depends on the detuning of the cavity from line center and the strength of the injected coherence relative to that of the injected population difference.

In this paper, we report on the effect of an external force on the dynamical behavior of the ${\mathrm{CO}}_2$ laser with a saturable absorber. Different regimes have been obtained as the modulation amplitude or frequency is changed. These regimes are compared to the standard phenomenology of the circle map, i.e., the transition from quasiperiodicity to locked regimes and chaos according to the Farey hierarchy with Arnold tongues. Return maps of the trajectories reconstructed from time series are shown. These results are compared with those of numerical simulations based on a simple model of the laser with a saturable absorber.

The influence of the bandwidth of the radiation source on light-induced drift (LID) of Na is studied experimentally. Broadband radiation can be used to eliminate optical hyperfine pumping on the one hand, and to provide more efficient excitation due to an increased velocity coverage, on the other hand. These aspects are highlighted in two separate experiments. An increase of the drift velocity of Na by a factor of 4 compared to monochromatic excitation has been measured. A frequency-modulated (FM) ring dye laser is used as a broadband radiation source, having a bandwidth continuously variable from single mode to multimode with a bandwidth of 10 GHz. Contrary to passive multimode lasers, the spectrum of such a laser is well defined and stable. Various modulation frequencies are used to study the dependence of the drift velocity on the mode spacing of the multimode laser. Only small differences are found. All experimental results are compared with results of a four-level rate-equation model for LID of Na, in which the excited-state hyperfine structure of Na and the detailed shape of the FM spectrum are taken into account. Good agreement between the model and the experimental data is found. The model is also used to show that the FM spectrum yields almost the same values for the drift velocity as a rectangular spectrum, which so far has been considered optimal for LID.

This paper presents an analysis of the Rabi oscillations of two-level atoms in the scattering-state representation. A collision complex obtained from a pair of identical two-level atoms is coupled to a field mode and it is found that there can be three distinct Rabi frequencies. These reduce to a single Rabi frequency for a photon distribution that is sharply peaked around an average number n¯≫1. One then finds that, in addition to the three frequency components in the off-diagonal element of the atomic density matrix, there are two components that are symmetrically displaced around the mode frequency at intervals of twice the Rabi frequency. They represent the collisionally induced cooperative motion of the atoms. When various observable quantities are averaged over the orientation of the complex, one obtains results that apply to many-atom systems in the binary collision approximation. Collisional effects do not enter the above results as lifetimes due to the fact that scattering states have precisely defined energies and correspond to entire particle histories. The collision potential opens up new radiative coupling channels, which collectively represent spectral line broadening. The collision potential and the radiative coupling combine to produce static and quasistatic dipole moments for the complex. At the threshold for atomic population inversion, the density matrix for the complex, as well as for an atom, becomes a constant multiple of the identity matrix, demonstrating that the threshold of stimulated emission is also a critical point for collisional effects, within the approximations of this paper.

A semiadiabatic treatment of the matter-field coupling is presented that accounts for the nonlinear variations affecting the widths and positions of laser-induced resonances in photodissociation as a function of the electromagnetic-field intensity. The procedure developed here goes beyond the widely used decoupled electronic-plus-field adiabatic treatment by retaining two ‘‘semiadiabatic’’ potentials that result from partial diagonalization of several blocks in the Floquet Hamiltonian. All closed channels lead to a unique multiphoton-dressed adiabatic closed channel that crosses a unique dressed adiabatic open channel. The remaining nondiagonal interaction is treated diabatically within a two-coupled-channel frame. The relative merits of diabatic approximations and of the semiadiabatic scheme are discussed within a large range of laser intensities and wavelengths on the example of ${\mathrm{H}}_2^{+}$(1s${\mathrm{\sigma }}_{\mathit{g}}$, v=0, J=1→2p${\mathrm{\sigma }}_{\mathrm{u}}$) photodissociation. Uniformally accurate results are reached for the semiadiabatic approach. This is very promising for studying field-induced nonlinearities for very intense lasers operating at rather short wavelengths where many electronic states including rotational structures may play a role.

We calculate the response of hydrogen to the presence of both a strong dc electric field (necessary to isolate a nearly one-dimensional motion) and a strong radiation field of higher frequency than the binding energy of the system, a regime that has not previously been examined by theory or experiment. We determine the classical ionization threshold, the quantum-delocalization threshold, and the threshold of n mixing due to chaotic effects. The analysis indicates that the dc field can have a dramatic effect on the quantum localization of classically chaotic diffusion, changing the delocalization threshold by more than an order of magnitude. Moreover, this system provides a large spectral region in which quantum-mechanical localization inhibits classical chaotic diffusion. This theory is well suited to experimental testing.

We employ supersymmetry arguments to calculate the exact eigenvalue spectra of a general multimode, multiphoton Hamiltonian for a two-level atom. First, supercharges are built from both the atom and the photon fields. The exact diagonalization of the Hamiltonian is achieved by utilizing spinorial behavior of these supercharges.

The concept of photon antibunching as a manifestation of nonclassical character in single-mode radiation is extended to two-mode radiation. A simple criterion for the existence of nonclassical effects in two-mode radiation is established. It implies that the intermode photon bunching, rather than antibunching, can play a key role in rendering two-mode radiation nonclassical. The two-mode squeezed vacuum states are used as simple examples to illustrate the essential point of the criterion. The criterion is then used to study the nonclassical properties of two types of two-mode squeezed states. A state generated by applying the squeeze operator to the two-mode vacuum first, followed by the displacement operator, is called a two-mode coherent squeezed state. If the order of the two operators is reversed, a two-mode squeezed coherent state is obtained. It is found that the latter has a much stronger tendency to become a nonclassical state than the former, assuming that the parameters involved are all the same. A measure of nonclassical depth of radiation is adopted. It is found that, according to this measure, the effect of squeezing in making two-mode coherent squeezed states nonclassical is not monotonic. Such phenomena do not occur in squeezed coherent states.

A novel coherent transient spectroscopy, cw photon echo, is described. A medium is exposed to broadband cw laser radiation and then to a pulsed laser, resulting in a continuous emission signal from the medium. The temporal profile of this signal is studied using full density-matrix theory for the cases of a two-level system and a multilevel system. It is shown that such signal decays with a homogeneous dephasing time ${\mathit{T}}_2$ and can have a quantum-beat-type modulation, reproducing in a single shot the conventional two-pulse photon echo plot versus first-to-second pulse separation. Experimental demonstrations are given for the ${}_{}{}^7{}_{}{}^{}$${\mathit{F}}_0$${\mathrm{-}}^5$${\mathit{D}}_0$ transition of ${\mathrm{Eu}}^{3+}$ and the ${}_{}{}^3{}_{}{}^{}$${\mathit{H}}_4$${\mathrm{-}}^1$${\mathit{D}}_2$ transition of ${\mathrm{Pr}}^{3+}$; both ions are doped in ${\mathrm{YAlO}}_3$. The Eu ions exhibit a single exponential decay with a slight modulation due to the ground-state hyperfine splittings. The temperature dependence of the signal is also studied. The Pr ions show a very deep modulation pattern, which provides excellent agreement with the independent two pulse echo measurement. A numerical simulation based on the modulation theory also agrees with the observed decay curves and the nuclear axis configuration in this crystal is discussed.

We investigate the steady-state spontaneous emission spectrum of a three-level atom driven by two coherent fields and the absorption spectrum of a weak probe passing through a collection of such driven atoms. We find that the fluorescence spectrum is strongly affected by the decay rates of all the levels involved in the atomic evolution and not just by the decay parameters of the specific transition whose emission spectrum is being monitored. In particular, the spectral components can acquire very different widths and peak heights relative to the case of the standard resonance fluorescence in which a two-level system is driven by a single near-resonant field. An external probe signal passing through the gas of three-level atoms may be absorbed or amplified, as in the standard two-level case, but under specific operating conditions, amplification (or absorption) occurs over the entire range where the atomic response is appreciable. In this case the existence of amplification or absorption is controlled solely by the population difference between two dressed states of the system. We provide numerical results in support of our arguments for arbitrary values of the atomic and field parameters and also develop an analytic description in the limit of strong driving fields that leads to explicit line-shape and linewidth formulas.

It is shown analytically that under certain experimental conditions the steady-state photon statistics of a micromaser field are directly connected to the fluctuation in number of the atoms in transition from the upper to the lower maser level under the influence of the maser field. The analytical results are compared to the results of a computer simulation of the maser process.

We explore the similarity between dc-field ionization and low-frequency multiphoton ionization atoms. If the frequency ω of the light is below the characteristic atomic-orbital frequency ${\mathrm{\omega }}_{\mathrm{at}}$, ionization of the atom occurs by tunneling provided that the intensity I is sufficiently high that the ratio of the tunneling time to the cycle time—this is essentially the ‘‘Keldysh parameter’’ γ— is less than unity. However, if I exceeds a critical intensity ${\mathit{I}}_{\mathrm{cr}}$, the electron flows over the top of the potential barrier rather than tunneling through it. ${\mathit{I}}_{\mathrm{cr}}$ depends on the magnetic quantum number m of the initial bound state, and is proportional to, but significantly less than, the characteristic atomic intensity. We give a simple approximate expression for ${\mathit{I}}_{\mathrm{cr}}$ in terms of m, valid in the absence of an exceptional symmetry (such as exists for hydrogen). We find that ${\mathit{I}}_{\mathrm{cr}}$ increases as m does; consequently, electrons with m=0 are stripped first as the intensity rises, and the residual ion will be left in a state of alignment, in agreement with calculations of ionization rates for Xe [K. Kulander, Phys. Rev. A 38, 778 (1988)].

We present results of Floquet calculations of rates for ionization of H(1s) by circularly or linearly polarized light in the wavelength range 355 to 1064 nm, at intensities somewhat below ${\mathit{I}}_{\mathrm{cr}}$. At these wavelengths, the rates approach more or less the same value as I increases, in accord with the Keldysh tunneling theory. We show that, provided ω<${\mathrm{\omega }}_{\mathrm{at}}$, the ac shift and the ac width, respectively, tend to the dc shift and the dc width (cycle averaged over the instantaneous field) once I is sufficiently large when γ<1. On the other hand, we show that for ω>${\mathrm{\omega }}_{\mathrm{at}}$ there is no tunneling regime; rather, in the absence of strong intermediate resonances, the ionization rate reaches a peak when γ≊1, and decreases toward zero as γ does. Presumably the Floquet picture becomes inadequate when the ionization width Γ approaches the photon energy ħω, for then ionization takes place in less than a cycle. We speculate as to how the Floquet picture breaks down and, finally, we show that the statement Γ≊ħ${\mathrm{\omega }}_{\mathrm{at}}$ yields the correct Z scaling of ${\mathit{I}}_{\mathrm{cr}}$ for ionization in a Coulomb field.

Collision-induced coherence transfer between infrared molecular transitions is studied using a technique that permits the complete distribution of accompanying velocity changes to be determined in a simple way. The experiments are carried out by measuring the intensity of two pulse photon echoes as a function of applied Stark field at fixed large echo time delay. The velocity change distribution for coherence-transfer collisions is obtained directly as the shape of the echo intensity versus Stark field curve. Previously unpublished data for dipole-quadrupole and van der Waals interactions are presented, and a theory of coherence-transfer velocity-changing kernels is developed that is in good agreement with the data.

We use a recently developed model for the interaction of a two-level atom with a coherent and a chaotic field of arbitrary bandwidth to study population fluctuations induced by the chaotic pump. We report numerical results for the fluctuations in the intensity of the fluorescence and their power spectra. We also give results for the effect of field fluctuations on the macroscopic polarization produced by the atoms. We show how detuning of the laser from the resonance frequency of the atoms affects the fluctuations in the fluorescence. The fluctuation behavior is quite sensitive to the correlation time of the chaotic field.

The manifestation of coherence effects in quantum yield measurements probing nonradiative decay is considered within the framework of effective Liouvillian dynamics. Special attention is given to the theoretical treatment of the quantum yield problem for the Freed-Jortner mesoscopic model for nonradiative decay. Exploiting the mathematical apparatus of dual Lanczos transformation theory, we obtain infinite-order analytic expressions for the fluorescence quantum yield and nonradiative decay rate of the initially prepared state and the quantum yields of hot fluorescence and hot phosphorescence.

Self-induced transparency in a resonant two-level system creates a 2π-soliton pulse, which realizes large optical nonlinearities with a small absorption loss α for a short pulse duration τ. Quantum-mechanical zero-point field fluctuations introduce an ultimate dissipation loss in such a resonant and coherent process and place fundamental limits on the ${\mathrm{\chi }}^{\mathrm{}\left(3\right)\mathrm{}}$/ατ value. This value is independent of the dipole moment, atomic density, and pulse duration and is uniquely determined by an optical wavelength, e.g., ${\mathrm{\chi }}^{\mathrm{}\left(3\right)\mathrm{}}$/ατ∼1.2×${10}^{21}$${\lambda }^4$ esu cm/s. The similar limit on ${\mathrm{\chi }}^{\mathrm{}\left(3\right)\mathrm{}}$/ατ value is obtained in a usual operation mode, when the pulse duration becomes much longer than the atomic decay constants and the real excitation of the atoms occurs instead of the virtual excitation in self-induced transparency. The implication of these limits on optical squeezed-state generation, quantum nondemolition measurement, and reversible logic is discussed.

We analyze a quantum nondemolition measurement scheme similar to that advocated by Song, Caves, and Yurke [Phys. Rev. A 41, 5261 (1990)] for generating superpositions of macroscopically distinct quantum states, but with the parametric amplifier and the back-action evader interchanged. We determine the asymptotic behavior of the output and obtain the conditions under which a superposition of two coherent states is approached. By presqueezing the signal port input, we find that gain requirements of the back-action evader are much less demanding.

With use of a model set of initial data, the scattering data for stimulated Raman scattering are obtained. For a small Stokes envelope, the scattering data consist only of solitons, each of which is roughly stationary, but with a uniformly growing amplitude. When the Stokes envelope dominates, the scattering data consist of only a continuous spectrum.