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Physical Review Letters

Tri-Level Echoes

THOMAS W. MOSSBERG, Allen M. Flusberg, Ravinder Kachru, Sven R. Hartmann

Published Dec 12, 1977• 94 citations
Publisher

Abstract

We report a new Doppler-free rephasing effect, the tri-level echo, which we use to study Ar-Na collisional relaxation of several $3^{2}S_{\frac{1}{2}}\ensuremath{-}n^{2}D_{\frac{3}{2}}$ superpositions in atomic Na. Three excitation pulses are required: The first resonantly excites a selected state, while the others resonantly couple this state with a higher-lying state. This sequence produces a delayed rephasing on the resonance transition which radiates strongly; the radiated intensity monitors relaxation in the higher-lying stepwise-excited state.

DOI
10.1103/physrevlett.39.1523

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Echoes in gaseous media: A generalized theory of rephasing phenomena

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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.

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Optics and Spectroscopy•Sep 1, 2006•7 citations
We report a new Doppler-free rephasing effect, the tri-level echo, which we use to study Ar-Na collisional relaxation of several 32S12\ensuremath−n2D323^{2}S_{\frac{1}{2}}\ensuremath{-}n^{2}D_{\frac{3}{2}}32S21​​\ensuremath−n2D23​​ superpositions in atomic Na. Three excitation pulses are required: The first resonantly excites a selected state, while the others resonantly couple this state with a higher-lying state. This sequence produces a delayed rephasing on the resonance transition which radiates strongly; the radiated intensity monitors relaxation in the higher-lying stepwise-excited state.
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.
We have measured the He-, Ne-, and Ar-induced relaxation properties of the $3S\ensuremath{-}nS$ ($3S\ensuremath{-}nD$) superposition states of atomic sodium, where nnn ranges from 5 to 20 (4 to 34). The measurements were made using the trilevel echo effect. We find that the effective collisional cross section first increases (as a function of nnn) at low nnn, and then decreases to a lower asymptotic limit at high nnn. This behavior is similar to that previously observed for the $3S\ensuremath{-}nP$ series. We also find that the difference between the collisional cross sections for SSS and DDD series superpositions closely approximates the inelastic collision cross sections measured elsewhere for the ddd states. A theoretical description of the trilevel echo effect used to make the measurements is presented.
A new type of three-level photon echo has been predicted and analytically described. In contrast to the conventional three-level echo, whose formation involves three resonant ultrashort excitation pulses spaced in time, two of which are resonant to different optically allowed and adjacent transitions with different frequencies, the echo predicted arises under the conditions of formation of the conventional two-pulse echo and requires only two pump pulses of the same frequency. A theory is developed for the conditions of experiments on generation of a superradiance pulse at the 3 P 0-3 H 6 transition in impurity praseodymium ions in the LaF3 matrix upon ultrashort coherent excitation of the adjacent optically allowed 3 H 4-3 P 0 transition in praseodymium. It is shown that the superradiance pulse after its deexcitation does not polarize the medium at the 3 P 0-3 H 6 generation transition and completely eliminates polarization at the 3 H 4-3 P 0 excitation transition. However, simultaneously, the superradiance pulse transfers the optical coherence from the excitation transition to the optically forbidden 3 H 6-3 H 4 transition. Thus, the phase memory about the effect of the excitation superradiance pulse is retained in the medium within a time interval that is shorter than the irreversible relaxation time of the optically forbidden transition.