We consider the infinite-order set of coupled, integral equations for the states of an atom in a very-narrow-bandwidth classical radiation field. In the vicinity of a one-photon resonance for two-photon ionization, this set is reduced to a pair of coupled equations describing the response of the atom to the radiation field. This set is derived by dropping terms of the original set whose lowest-order contributions to the radiation-induced shift and width of the resonance are quadratic in the intensity. In the absence of simultaneous absorption and emission, impossible except for two-photon processes from excited states, this pair can be decoupled. The remaining uncoupled integral equation describes the ac Stark effect based on contributions to the shift and width linear in the intensity. These contributions derive from radiative corrections to the intermediate atomic state and depend on the virtual processes of ionization from and recombination into, as well as emission from and reabsorption into, this state. A method for obtaining the exact numerical solution is discussed. An approximate solution is obtained by use of the single-eigenfunction approximation to the Green's function belonging to the response function. This Green's function has a pole at the static (unshifted) position of the resonance; thus, this approximation is quite accurate very near the pole. The order of nonlinearity is calculated as a function of the static detuning through the resonance and is shown to undergo rapid fluctuations about the nonresonance value of 2. The error inherent in the single-eigenfunction approximation to the Green's function is estimated and found to range from about 1% to 27% corresponding to static detunings ranging from about 1 to 25 \AA{}, respectively.We consider the infinite-order set of coupled, integral equations for the states of an atom in a very-narrow-bandwidth classical radiation field. In the vicinity of a one-photon resonance for two-photon ionization, this set is reduced to a pair of coupled equations describing the response of the atom to the radiation field. This set is derived by dropping terms of the original set whose lowest-order contributions to the radiation-induced shift and width of the resonance are quadratic in the intensity. In the absence of simultaneous absorption and emission, impossible except for two-photon processes from excited states, this pair can be decoupled. The remaining uncoupled integral equation describes the ac Stark effect based on contributions to the shift and width linear in the intensity. These contributions derive from radiative corrections to the intermediate atomic state and depend on the virtual processes of ionization from and recombination into, as well as emission from and reabsorption into, this state. A method for obtaining the exact numerical solution is discussed. An approximate solution is obtained by use of the single-eigenfunction approximation to the Green's function belonging to the response function. This Green's function has a pole at the static (unshifted) position of the resonance; thus, this approximation is quite accurate very near the pole. The order of nonlinearity is calculated as a function of the static detuning through the resonance and is shown to undergo rapid fluctuations about the nonresonance value of 2. The error inherent in the single-eigenfunction approximation to the Green's function is estimated and found to range from about 1% to 27% corresponding to static detunings ranging from about 1 to 25 \AA{}, respectively.

Physical Review AFeb 1, 19787 citations

Atomic Radiative Processes

Elsevier eBooksJan 1, 198221 citations

Atomic and Molecular Radiative Processes

В. П. Крайнов, Boris Michailovich Smirnov

Springer series on atomic, optical, and plasma physicsJan 1, 201913 citations

Polariton-Type Dispersion Laws for Three-Level Atoms Interacting with Two Laser Radiation Pulses

P. I. Khadzhi, О. В. Коровай, L. Yu. Nad’kin

Behavioral features of polariton dispersion laws are studied for three-level atoms interacting with two coherent laser radiation pulses with frequencies ω1 and ω2 that are in resonance with optically resolved one-photon transitions between levels $1 \leftrightarrows 2$ and $2 \leftrightarrows 3$ , respectively, and with regard to the direct two-photon transition between levels 1 and 3. The approximation of given photon densities of both pulses compared with the densities of atoms is used. It is shown that the dispersion law consists of three branches whose position and shape are determined by the Rabi frequencies of the above three optical transitions and the photon densities in both pulses. The direct consideration of all three optical transitions leads to the dependence of the dispersion law of atomic polaritons on a new quantum parameter—the phase difference between the three Rabi frequencies. The values of the system parameters are found for which the branches of the dispersion law may intersect. The concept of the surface of the dispersion law is introduced in the dependence of the eigenfrequencies of atomic polaritons on the photon wave vectors in both pulses.Behavioral features of polariton dispersion laws are studied for three-level atoms interacting with two coherent laser radiation pulses with frequencies ω1 and ω2 that are in resonance with optically resolved one-photon transitions between levels $$1 \leftrightarrows 2$$ and $$2 \leftrightarrows 3$$ , respectively, and with regard to the direct two-photon transition between levels 1 and 3. The approximation of given photon densities of both pulses compared with the densities of atoms is used. It is shown that the dispersion law consists of three branches whose position and shape are determined by the Rabi frequencies of the above three optical transitions and the photon densities in both pulses. The direct consideration of all three optical transitions leads to the dependence of the dispersion law of atomic polaritons on a new quantum parameter—the phase difference between the three Rabi frequencies. The values of the system parameters are found for which the branches of the dispersion law may intersect. The concept of the surface of the dispersion law is introduced in the dependence of the eigenfrequencies of atomic polaritons on the photon wave vectors in both pulses.

Journal of Experimental and Theoretical PhysicsApr 1, 20193 citations

Optical Forces from Periodic Adiabatic Rapid Passage Sequences on Metastable Helium Atoms

Daniel T. Stack

Over the past 30 years, optical manipulation of neutral atoms has been primarily performed with a monochromatic laser beam. The simplest tool for the control of atomic motion is the radiative force exerted by a monochromatic laser on a twolevel atom. The radiative force arises from absorption followed by spontaneous emission, and its magnitude is limited by the atom's excited state lifetime. The coherent momentum exchanges between light elds and atoms can be exploited to produce long-range optical forces much greater than the radiative force through the use of absorption-stimulated emission processes. Adiabatic Rapid Passage (ARP) is a long-existing method to invert the population of a two-level nuclear spin system. Its extension to the optical domain necessitates a frequency chirped light pulse to interact with a two-level atom via the dipole interaction. I will first present a numerical study of the properties of optical forces on moving atoms derived from purely stimulated processes produced by multiple ARP sequences. This will be followed by experimental observations of long-range ARP forces much larger than the radiative force in metastable helium. Sequences of properly timed laser pulses may be used for rapid deceleration of neutral atomic (or molecular) beams. | 171 pagesOver the past 30 years, optical manipulation of neutral atoms has been primarily performed with a monochromatic laser beam. The simplest tool for the control of atomic motion is the radiative force exerted by a monochromatic laser on a twolevel atom. The radiative force arises from absorption followed by spontaneous emission, and its magnitude is limited by the atom's excited state lifetime. The coherent momentum exchanges between light elds and atoms can be exploited to produce long-range optical forces much greater than the radiative force through the use of absorption-stimulated emission processes. Adiabatic Rapid Passage (ARP) is a long-existing method to invert the population of a two-level nuclear spin system. Its extension to the optical domain necessitates a frequency chirped light pulse to interact with a two-level atom via the dipole interaction. I will first present a numerical study of the properties of optical forces on moving atoms derived from purely stimulated processes produced by multiple ARP sequences. This will be followed by experimental observations of long-range ARP forces much larger than the radiative force in metastable helium. Sequences of properly timed laser pulses may be used for rapid deceleration of neutral atomic (or molecular) beams. | 171 pages

Aug 1, 20120 citations

1 \leftrightarrows 2

and

2 \leftrightarrows 3

, respectively, and with regard to the direct two-photon transition between levels 1 and 3. The approximation of given photon densities of both pulses compared with the densities of atoms is used. It is shown that the dispersion law consists of three branches whose position and shape are determined by the Rabi frequencies of the above three optical transitions and the photon densities in both pulses. The direct consideration of all three optical transitions leads to the dependence of the dispersion law of atomic polaritons on a new quantum parameter—the phase difference between the three Rabi frequencies. The values of the system parameters are found for which the branches of the dispersion law may intersect. The concept of the surface of the dispersion law is introduced in the dependence of the eigenfrequencies of atomic polaritons on the photon wave vectors in both pulses.