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Physical Review A

Effects of interference between one- and two-photon processes

Noriaki Tsukada, Ryoko Tsujinishi, Munehiko Nagano, Kazunaru Tomishima

Published Apr 1, 1980• 9 citations
Publisher

Abstract

Solutions are given for interaction between a three-level system and three arbitrarily intense fields, one of which has the sum frequency of the other two field frequencies. The results of a nonperturbative analytic treatment of the three-level Schr\"odinger equation are described. We find that the time dependence of the occupation probabilities of the three levels is strongly modified by the effects of interference between one- and two-photon processes.

DOI
10.1103/physreva.21.1281

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Solutions are given for interaction between a three-level system and three arbitrarily intense fields, one of which has the sum frequency of the other two field frequencies. The results of a nonperturbative analytic treatment of the three-level Schr"odinger equation are described. We find that the time dependence of the occupation probabilities of the three levels is strongly modified by the effects of interference between one- and two-photon processes.
The Schr\"odinger equation in the rotating-wave approximation has been solved nonperturbatively to study the temporal behavior of the occupation probabilities of different levels of a four-level atom interacting with four arbitrarily intense laser fields, such that the frequency of one of them equals the sum of the other three. The three-photon-excitation population dynamics, which is already complex, is strongly modified by one-photon excitation and detunings. Under certain conditions the three-photon excitation traps the population in the state initially populated; the population starts flowing into other states when one-photon excitation is also operative.
The transition probabilities and the shifts of the crossing and anticrossing points of a two-level system (spin-1/2 atom) under the simultaneous influence of a static magnetic field and three orthogonal oscillating rf fields are calculated by using the resolvent formalism in which the rf fields are quantized. A new interference effect, which can be called "crossing of the third kind" in the rf transition, is predicted, and can be interpreted as the interference between different-order transition processes such as single- and two-photon processes, single- and three-photon processes, and so on. Furthermore, for coexistence of the single- and two-photon processes and of the single- and three-photon processes, we can obtain expressions of the transition probabilities (or effective dipole-coupling coefficients) similar to the results obtained in our previous paper, where the interference between single- and two-photon processes were treated by using the time-dependent Schr\"odinger equation.
We have calculated the interference spectra of a single electron in the excited state of a four-level atom interacting with three laser fields, where two of them are on two-photon resonance with the three levels forming a `Λ' scheme while the third laser operates between the second ground and the second excited states of the atom. It is shown that in the low-intensity limit of all three laser fields, the third laser field destroys the destructive interference that occurs between the spontaneous radiative decay and the process arising from the combined field of all the three laser fields. The result is that the overall intensity of the peak at the centre of the line depends on the strength of the third laser field and it takes negative values indicating that light amplification without population inversion (LAWI) is likely to occur at the one-photon frequency. The antisymmetric two-photon state of the two lower levels as well as the two-photon process, where one laser photon is absorbed and another laser photon is emitted simultaneously by the second excited state of the atom, is found to exhibit LAWI at the one-photon frequency. The derived results are graphically presented and discussed.
In a four-level -system interacting with three coherent laser pulses, interference between population inversions in coupled three-level ladders is examined. The interference effect, which affects the process and the completeness of the inversion, is represented by the two-photon coherence. It is shown that, in the adiabatic passage method, the phase and the scaling factor of the two-photon coherence are zero and a constant, respectively, resulting in no interference effect, but, in the optimal detuning method, they are strongly time dependent enough to represent the interference effect to change the process and the amount of inversion significantly. In the latter method, the ratio of Rabi frequencies for the four-level inversion to be completed, which is changed by the interference effect, is obtained.
The rate of absorption and emission of radiation is calculated for two laser fields interacting with a homogeneously broadened, three-level molecular system. The time-dependent Schrödinger equation is used in the density matrix formalism and the laser fields are treated classically. The laser fields, at frequencies ωpand ωs, are off resonance by δpand δs, respectively, such that|\delta_{p}|, |\delta_{s}| \ll \omega_{p}, \omega_{s}. Analytic expressions are derived for the imaginary part of the electric susceptibility,\chi"(\omega_{p})and\chi"(\omega_{s}). The present work differs from previous calculations in that the laser fields may have arbitrary values of field strength and each field may be on or off resonance. A discussion is presented of the properties of the solutions for\chi"(\omega_{p})and\chi"(\omega_{s}), for both strong and weak laser fields, based on computer evaluation of the general analytic expressions. It is shown that the solutions may be divided into single-photon and two-photon, or Raman, contributions. Conditions for optimizingdI(\omega_{s})/dzand the photon conversion efficiency are derived. These results may be applied to analyzing the pulsed, optically pumped submillimeter laser and to studying two-photon absorption in a gas.