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Journal of Physics B Atomic Molecular and Optical Physics

The modified tri-level photon echo

Igor V. Yevseyev, Yu.V. Men'shikova, V. N. Tsikunov

Published Jun 14, 1989• 3 citations
Publisher

Abstract

A theory is developed for the modified tri-level photon echo formed in gaseous media. Consideration is given to the cases when echo is generated both by atoms for molecules with zero nuclear spin and by atoms with non-zero nuclear spin. In the first case, it is shown that this particular kind of photon echo can be used to measure the relaxation characteristics of the multipole moments of the optically forbidden transition. On the basis of these considerations new experiments are suggested for the observation of the relaxation characteristics mentioned above. In the second case, formulae are obtained for the calculation of pre-exponential factors describing the dependence of the quantum beats of the intensity of the modified tri-level photon echo as a function of the time intervals between the exciting pulses. Values of the pre-exponential factors need to be known in order to correctly obtain spectroscopic information about an optically forbidden transition.

DOI
10.1088/0953-4075/22/11/018

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A theory is developed for the modified tri-level photon echo formed in gaseous media. Consideration is given to the cases when echo is generated both by atoms for molecules with zero nuclear spin and by atoms with non-zero nuclear spin. In the first case, it is shown that this particular kind of photon echo can be used to measure the relaxation characteristics of the multipole moments of the optically forbidden transition. On the basis of these considerations new experiments are suggested for the observation of the relaxation characteristics mentioned above. In the second case, formulae are obtained for the calculation of pre-exponential factors describing the dependence of the quantum beats of the intensity of the modified tri-level photon echo as a function of the time intervals between the exciting pulses. Values of the pre-exponential factors need to be known in order to correctly obtain spectroscopic information about an optically forbidden transition.
A method of determining relaxation rates of electronic and electronic nuclear multipole moments of gas atoms with non-zero nuclear spin, using the Stokes three-level echo (STE) and the photon echo (PE), has been proposed. This method utilises the polarisation properties and damping laws of the STE and PE on the inhomogeneously broadened transitions. Correct account was taken of the hyperfine structure (HFS) of the atomic levels and of the effect of the depolarising atomic collisions. The STE polarisation properties found have also been assumed to be a basis method for the identification of optically forbidden transitions in total angular momentum.
In the limit of small exciting light-pulse areas the amplitude and polarization of the tri-level photon echo in gases formed by the exciting pulses with arbitrary shapes are obtained. It is shown that the dependence of the tri-level photon echo signal on the mutual orientation of the exciting pulse polarization vectors may be used to determine the optical coherence-matrix relaxation characteristics for an optically forbidden transition. The conditions under which a tri-level photon echo pulse repeats the shape of each of the exciting pulses are defined. It is proved that the tri-level photon-echo polarization properties do not depend on the shapes of the exciting pulses, either for small light-pulse areas or for the tri-level echo formation on narrow spectral lines.
The Raman photon echo (RPE) in atomic vapour, allowing for depolarising atomic collisions and hyperfine structure of the atomic levels, has been studied theoretically. A new method of determining the electronic and electronic nuclear relaxation rates of the multipole moments of gas atoms with nonzero nuclear spin using the RPE has been proposed. The RPE method also makes it possible to measure the derivatives of these relaxation rates with respect to the impurity gas pressure. A method of determining the energy separation between the hyperfine structure sublevels has been developed. This method is based on the quantum beats of the RPE intensity and may be used when the hyperfine splitting is less than the Doppler linewidth. A possibility of identifying the forbidden transitions in both the electronic and total angular momenta has been shown.
The primary objective of this paper is to provide a formalism to predict and characterize the echoes which may be produced in a gaseous sample by an arbitrary sequence of one- or two-frequency laser excitation pulses which successively transfer atomic population between two or more atomic energy levels. The resulting echoes can occur at times which depend on the relative frequencies of the excitation pulses as well as on the times at which the pulses were applied. Using an idealized model of the excitation pulses and the atoms, the authors derive a simple transformation equation which provides the density matrix of a single atom after a general excitation sequence. Equations are derived which utilize the single-atom density matrix to predict the properties of the echoes (if any) which result. The means by which the sample of atoms "remembers" the information necessary to produce different types of echoes is discussed, and it is then shown how a study of the echo can provide information concerning the atomic relaxation processes which tend to destroy this information. It is observed that trilevel echoes can be used to determine the relaxation characteristics of superposition states between energy levels coupled by two-photon transitions. In the case of certain other echoes (such as the three-excitation-pulse stimulated echo) the authors discuss the heretofore unappreciated fact that the sample remembers the "echo information" via a nonthermal velocity distribution of the atoms in one specific atomic state. In these cases a study of the echo behavior can provide information pertaining to the relaxation processes affecting only the one atomic state. The formalism developed is used to predict the properties of several echo effects. First, to provide a connection with previous work, the well-known photon echo is briefly discussed. Then important new properties of the three-excitation-pulse-stimulated echo are described. Finally, three different types of trilevel echo are analyzed. Each of the trilevel echoes discussed has widespread applicability in the study of relaxation processes.
A method of determining the relaxation constants of the multipole moments of gas atoms with non-zero nuclear spin has been proposed by using the polarisation properties and damping law of the non-stationary Raman scattering (NRS) of light. Correct account was taken of the depolarising atomic collisions and of the effect of the hyperfine structure (HFS) of the atomic levels. The NRS polarisation properties found have been assumed to be a basis method for the identification of optically forbidden transitions in both the electronic and total angular momenta. A possible method of determining the HFS constants through analysis of the NRS quantum beats has been established.