Presence Of Detuning Research Articles

Four-wave mixing and terahertz emission from three-level systems in quantum wells: Effects of inhomogeneous broadening.

Using a perturbation theory based on the density-matrix formulation, we study the nonlinear optical responses of a noninteracting three-level model system to consecutive coherent pulsed excitations, as realized in several recent experiments involving excitonic transitions in quantum wells. The terahertz emission, which is a second order response, and the four-wave mixing signal, a third order response, are calculated within the rotating-wave approximation, in the presence of detuning, dephasing, and inhomogeneous broadening. We study the quantum beats in the photon echo from transient four-wave mixing experiments of a three-level system. We find that the temporal profile of the photon echo signal in the four-wave mixing experiments depends very strongly on the amount of inhomogeneous broadening of the energy levels involed. Both the position and the intensity of the peaks exhibit a smooth evolution from strong quantum beats to a conventional photon echo as the inhomogeneous broadening increases. These features from our noninteracting model system are compared with a recent experiment, and found to account for a number of experimental observations.

Effect of detuning on deep squeezing of coherent light in the Jaynes-Cummings model.

The effect of detuning on squeezing of coherent light is studied in the Jaynes-Cummings model and in the large-N (mean photon number) limit. Analytical formulas for quadrature variances are obtained both in the one-photon and two-photon transition cases. In the former case, small detuning only has a small (unfavorable) effect on squeezing. In the latter case, however, the effect of detuning is significant. No squeezing will occur at resonance, and by the presence of detuning, there will be a series of minima appearing in the suppressed quadrature variance during time evolution as happens in the one-photon transition case, with the limit of this series tending to zero

Stability and phase-dependent dynamics of an atom driven by a strong resonant field and a tunable moderate-strength perturber field.

We have studied the transient response of undamped two-level atoms to excitation by a classical bichromatic field consisting of a strong resonant component and a moderate-strength, tunable, ``perturber'' component. It is found that the strong field tends to stabilize the atom against the influence of the perturber field. Exceptions to this general result occur when the perturber is detuned from the strong field by the Rabi frequency of the latter or its subharmonics. We believe this stabilization phenomenon is a semiclassical analog of the effect that leads to the dynamical modification of spontaneous emission [M. Lewenstein and T. W. Mossberg, Phys. Rev. Lett. 59, 775 (1987)], and the presence of detunings at which the stabilization fails provides a simple motivation for the Rabi subharmonic resonances found in certain cw bichromatic spectra. Interestingly, when the perturber field is relatively weak, detuned from the atomic resonance by the strong-field Rabi frequency, and turned on with a specific initial phase relative to the strong field, one finds that the bichromatic field can be employed to dressed-state polarize initially ground-state atoms. In a related vein, we find that perturbations at the subharmonic detunings lead to interesting phase-dependent atomic dynamics. Results were obtained using both numerical and approximate analytical techniques entirely within the context of the rotating-wave approximation. The validity of the latter is ensured by demanding that all detunings and Rabi frequencies are vanishingly small compared to the atomic transition frequency.

Cooperative and dipole-dipole effects in the fluorescent spectra of two identical three-level atoms at high photon densities: II. Stimulated three-photon processes

We have studied stimulated three-photon processes arising from the interaction of a system of two-identical three-level atoms with a strong pump field and a weak signal field simultaneously. The atoms consist of an upper excited state and two lower states and they interact through their dipole-dipole and cooperative radiative interactions, respectively. The strong laser field, whose frequency mode ω b is initially populated, depletes the metastable state by bringing the electrons into the excited state from where the electrons emit photons and decay through the signal field into the lower ground states of the system. Using the Green function method in the limit of high photon densities of the laser field, the spectral functions for the signal field have been calculated describing stimulated three-photon processes of the symmetric and antisymmetric modes, respectively, which arise from the dipole-dipole and cooperative radiative interactions between the atoms. The stimulated three-photon excitations near the frequency ω≈ ω 21 − 2 ω b describe physical processes where one-photon of the signal field with frequency ω 21 is absorbed while simultaneously two photons of the laser field are emitted. At resonance and in the absence of the dipole-dipole interaction, the spectra consist of a doublet whose peaks are symmetrically located from frequency ω = ω 21 − 2 ω b, while the magnitude and sign of the intensity of the peaks depend on the value of the relative Rabi frequency η b. For η b = 3, the intensity of the doublet takes negative values and it becomes positive for η b⩾5. As the value of η b increases the magnitude of the intensity of the doublet decreases and it becomes nearly constant for values of η b between 50 and 100. The single atom spectra consist of a doublet having a constant negative intensity independent of η b. The difference between the single and two-atom spectra is attributed to the cooperative radiative interaction between the two atoms. In the presence of detunings, the symmetry in the positions and intensities of the two sidebands vanishes. In the presence of the dipole-dipole interaction and at resonance, the spectra consist of three sidebands whose position, line shape, and sign as well as magnitude of the intensities depend entirely on the strength of the dipole-dipole interactions between the atoms. In the presence of detunings, asymmetries arise, enhancing certain spectral peaks while diminishing the intensity of others. The computed spectra are graphically presented for different values of η b, dipole-dipole interactions, and detunings. Comparison between the single and two-atom spectra is made and discussed in detail.

Frequency dependence of a ring laser with backscattering.

The coupled third-order equations of motion of the two-mode ring laser with spontaneous emission noise are investigated in the presence of detuning and backscattering. The steady-state solution is obtained without linearizing approximations, and it is shown to depend on backscattering only through the sum R/sub 1/ + R/sub 2//sup */, where R/sub 1/ and R/sub 2/ are complex backscattering coefficients. Above threshold the effect of backscattering is found to be equivalent to incrementing the pump parameter of each laser mode by (1/2)chemically bondR/sub 1/ + R/sub 2//sup */chemically bond. The variations of the mean light intensities of the two modes with detuning are calculated for several different pump parameters, from well below to well above threshold. The results are compared with direct measurements of a He:Ne ring laser, and good agreement is obtained over a wide range, with the adjustment of just a single scale constant.

High-field approximations and collective behaviour in atomic fluorescence

An approximation scheme valid for high field strengths and arbitrary detuning is applied to the calculation of fluorescent spectra for various numbers (n) of emitting atoms. The presence of detuning is shown to prevent the possibility of solving this problem in closed form for arbitrary n. The one- and two-atom spectra are derived explicitly and compared with the known exact results.

Resonance fluorescence spectrum of a three-level atom. II. Numerical results

Numerical computations are presented for the excitation spectra arising from the interaction between a three-level atom in the cascade configuration and a strong electromagnetic field whose frequency mode is initially populated. The excitation spectra are considered when the laser field is at resonance with the equally spaced levels of the atom as well as a function of the detunings. The physical process of optical amplification occurs without population inversion and it is more pronounced when the laser field is detuned than when it is at resonance. The shapes of the spectral lines for a number of side-bands are of the absorption-amplification type rather than that of the absorption one. In the presence of detunings as well as in the cooperative two-photon cascade process, the resulting spectra are far more complicated than those occuring at resonance. Results of numerical calculations for a wide range of Rabi frequencies and detunings are presented graphically.

Superradiance and inhomogeneous broadening. I: Spontaneous emission by two slightly detuned sources

The co-operative decay of two initially excited quantum sources is studied when they do not have the same resonance frequency. The theory here presented avoids those assumptions which are inherent in the semi-classical approach and shows that, in the presence of detuning, quantum correlations between the sources and the field play a central role. In this first paper particular attention is devoted to the description of the method used as well as to the acquaintance with some physical quantities introduced, in view of their intensive use in the case of a large number of detuned sources, analysed in the following paper.

AC Stark effect and fluorescence in modulated laser beams. II. Two-photon stepwise excitations

For pt.I see ibid., vol.12, no.12, p.1939 (1979). The modulated fluorescence in an optical double resonance experiment, i.e. when an atom interacts with two intense monochromatic laser beams each of which is weakly modulated in amplitude at frequency Omega , is studied in detail. The modulation rate corresponding to the steady-state population of the highest atomic level exhibits resonant structures at the modulation frequencies Omega =0, +or- alpha 0, +or-2 alpha 0 due to the dynamical Stark splitting of the various energy levels; alpha 0 being related to the Rabi frequencies alpha 1 and alpha 2 associated with the two lasers and the two atomic transitions, by alpha 02= mod alpha 1 mod 2+ mod alpha 2 mod 2. The peak at Omega =+or- alpha 0 is the most intense and exhibits splitting when the applied fields are detuned from exact resonance with the respective atomic frequencies. Resonances are observed in the modulation rate of the intermediate-level population at the modulation frequencies Omega =0, +or-2 alpha 0. In the presence of detunings of the applied fields, additional resonant structures occur at Omega =+or- alpha 0 which increase in magnitude with higher detunings and split. Explicit expressions for the positions, widths and weights of these resonant components are obtained analytically for intense, resonant fields. Numerical results for general values of the laser field strengths and the detunings are given.