Resolvent Operator Formalism Research Articles

Resonance fluorescence in the resolvent-operator formalism

The Mollow spectrum for the light scattered by a driven two-level atom is derived in the resolvent operator formalism. The derivation is based on the construction of a master equation from the resolvent operator of the atom-field system. We show that the natural linewidth of the excited atomic level remains essentially unmodified, to a very good level of approximation, even in the strong-field regime, where Rabi flopping becomes relevant inside the self-energy loop that yields the linewidth. This ensures that the obtained master equation and the spectrum derived matches that of Mollow.

Three-photon ionization of lithium

Abstract We study three-photon ionization of neutral lithium, in the presence of a strong laser light intensity of up to 15 GW cm −2 , involving the absorption of three photons combined in such a way that first we have one-photon resonant plus two-photon non-resonant ionization transitions, then the reverse case is studied. The resolvent operator formalism and projection operators are used in the calculations. An atomic central field model potential is used to generate orbital wavefunctions. We compare our calculations with previous calculations done by Chang and Poe [Phys. Rev. A 16 (1977) 606] for non-resonant three-photon ionization rates of lithium, with which we obtained a very good agreement.

Non-adiabatic effects on resonant two-photon dissociation of HD+ in the presence of two frequency laser fields

The time-dependent dissociation probabilities, lineshapes of dissociation rates and branching ratios of photofragments between the neutral hydrogen and deuterium channels have been investigated for resonant two-photon dissociation of HD+ from the ground level in the presence of two laser fields of different intensities I1, I2 and frequencies omega 1, omega 2 using the resolvent operator formalism. The symmetry breaking due to non-adiabatic (NA) interactions causes splitting between the two asymptotic channels, unlike the Born-Oppenheimer (BO) approximation. Simultaneous dissociation to the continua of the two electronic states at two different energies occurs through the absorption of either omega 1+ omega 2 or 2 omega 1 photons. Only the field of frequency omega 1 was considered to resonantly couple the near-resonant level nu '=17, J'=1 or nu '=18, J'=1 to the ground level nu =0, J=0. Non-resonant discrete and continuum states significantly affect the dissociation process in the case of high intensity fields. The electric field gauge (E.d) form of interaction Hamiltonian has been used in the computation of various laser-dependent parameters. The results with NA coupling included are found to deviate appreciably from those obtained with the BO approximation.

Resonant two photon dissociation dynamics of HD+ in intense infrared laser field

The intensity dependent line shapes of resonant two photon dissociation process in HD+ from the 1sσg (v=6, J=0) are obtained at three different intensities (1.53×1010, 1.53×1012, and 6.12×1012 W/cm2 ) in the wavelength range 16 000–17 200 Å using the resolvent operator formalism. The discrete state v=11, J=1 (1sσg) is the intermediate resonant state. The position of the resonance on the wavelength scale depends strongly on intensity. It is shown that for sufficiently strong fields the earlier semiperturbative theory formulated in analogy with Fano’s theory of atomic autoionization breaks down near resonance due to saturation of the strongly coupled resonant transition. Also, when the dissociative transitions to both the electronic states 1sσg and 2pσu are considered simultaneously, the line shape is altered from that obtained by the superposition of the line shapes of these two transitions separately. The conditions under which a unique time independent transition rate is ill defined are discussed. For such situations the time dependent transition probabilities can be obtained from the effective Fano asymmetry parameters, and line shifts and widths of the ground and resonant states. The limiting transition rates for such cases for short and long pulse times are also shown.

Air broadening of the hydrogen halides—I. N 2-broadening and shifting in the HCl fundamental

The widths and shifts of the fundamental band vibration-rotation lines of HCl under N 2 pressure have been calculated using the resolvent operator formalism of Kolb-Griem-Baranger. Time-development operator matrix elements are evaluated in a manner that is similar to the linked-cluster techniques, except that all anisotropic terms that are bilinear and second order are accounted for, as well as isotropic effects to all orders. The calculations include the use of a parabolic trajectory model and explicit velocity averaging. It is found that the major contributions to the linewidths arise from dipole-quadrupole, quadrupole-quadrupole and vibrationally dependent isotropic dispersion forces. Due to the reduction of the dipole-quadrupole and quadrupole-quadrupole contributions with increasing ¦ m¦, the widths decrease with a leveling off at high ¦ m¦, where dispersion forces dominate. A comparison between calculated and measured widths and shifts, for a range of temperatures from T=163 to 295 K, shows good overall agreement.

Remarks on high field collision rates in polar semiconductors

Field-dependent scattering rates for the electron-LO phonon interaction are calculated using first-order perturbation theory and the displaced Maxwellian approximation. Barker's approximate result based on a general resolvent operator formalism is regained for the scattering rate but a proper evaluation of its value results in a negligible field contribution in disagreement with his conclusion, obtained by unjustifiable linearisation in the field variable. This result resolves the long-standing discrepancy in the literature on the importance of inter-collisional effects.

The linear response functions for 3He (B) and superconductors in the quasistatic London regime

The quasistatic response of the superfluid Fermi-liquid with BCS and BW pairing is considered in the London collisionless regime. By using the resolvent operator formalism the autocorrelation functions of the density and the transversal current are calculated for both the BCS and the BW systems. The dynamics of the mentioned Fermi-liquids are discussed in terms of the transversal conductivity. The presence of an anomalous skin effect for superconductors and 3He (B) is predicted from these results.

A Kinetic Approach to the Friction Constant of a Brownian Particle

The density expansion of the friction constant of a Brownian particle in a gas is inves­ tigated with the use of the resolvent operator formalism of the time correlation function for the transport coefficient. To lowest order in density, the results are identical with those derived from the Boltzmann equation. A divergence appears in the first (second) density correction in a two (three) -dimensional system and is removed by summing up the most divergent contributions to all orders in density. This gives rise to a logarithmic density dependence n'ln(n) (n'ln(n)) of the friction constant. Long time behaviour of the force-force (on the Brownian particle) correlation function is also examined. Its long time tail is derived by performing further resummation of collisional events.

Theory of the optical properties of resonant states in nitrogen-doped semiconductor alloys

The optical properties of N-doped semiconductor alloys, such as GaAs-P and In-GaP, are investigated theoretically in the range of compositions, near the direct-indirect crossover, in which the discrete electronic state associated with the nitrogen trap is degenerate with the conduction-band continuum near the center of the Brillouin zone. The resolvent-operator formalism is applied to obtain the density of states and the optical absorption and emission spectra, by approximating the short-range impurity potential by a Koster-Slater interaction and using a simple parametrized description of the density of states of the host alloy. The presence of the discrete autoionizing trap state is shown to produce a characteristic Fano resonance-antiresonance line shape, in agreement with recent experimental observations, and in contrast to earlier theoretical predicitons of a sharp and resonantly enhanced emission spectrum.

Hartree-Fock perturbation theory for systems with one-particle perturbation

The Hartree-Fock perturbation theory for theN-electron system with a one-particle perturbation is rederived using the resolvent operator formalism. It is shown that the second-order contribution to the total energy can be expressed in a compact form using a properly defined effective one-particle operator. Relations of the Hartree-Fock perturbation theory with both the many-body theory and the regular Hartree-Fock formalism are discussed.

Self-Broadening of Molecular Spectral Lines. I. General Theory

A general theoretical treatment of spectral line broadening of gas molecules is given using a resolvent operator formalism in Liouville space. The methods introduced previously by Mead for treating resonance broadening in monatomic gases are developed and generalized here for molecular spectral lines. The basic equation relating the susceptibility to resolvent operator matrix elements is derived here for the case of a molecular gas and takes into account the rotational-vibrational structure of the spectra and the presence of complicated molecular interactions.

Theory of resonance pressure broadening: Resolvent operator formalism and classical path approximation

The problem of resonance pressure broadening of spectral lines in monatomic gases is discussed using a resolvent operator formalism. A differential equation is developed to determine the resolvent, and it is shown how its solution for a limiting case yields the familiar classical path approximation for the translational motion of the atoms, and how quantum corrections may be systematically studied. Commonly used limiting cases within the classical path approximation (two-body static and impact approximations) are also exhibited as limiting cases, with methods for systematic evaluation of corrections. Closed form solutions are obtained for the two-body static and impact cases. The results are compared with available experimental data, and generally satisfactory agreement is obtained. Of some theoretical interest is the formalism, which embraces all the usual approximations and permits them to be studied together with corrections to them from a unified point of view. New results of more practical interest are the closed form solutions for the limiting cases, and the estimation of the lowest-order quantum corrections, which are appreciable under some experimental conditions.