The possible three-pulse echoes in two-level systems of solids and gases are discussed with particular emphasis on backward-wave echoes. One example of the backward echoes was realized with the atomic sodium $D$ line. The detection of this echo requires neither optical shutters nor magnetic field. The decay rate of the echo due to Na-Ar collisions was measured. It is shown that the effect of velocity changing collisions is negligible compared with that of phase interrupting ones.The possible three-pulse echoes in two-level systems of solids and gases are discussed with particular emphasis on backward-wave echoes. One example of the backward echoes was realized with the atomic sodium $D$ line. The detection of this echo requires neither optical shutters nor magnetic field. The decay rate of the echo due to Na-Ar collisions was measured. It is shown that the effect of velocity changing collisions is negligible compared with that of phase interrupting ones.

Physical Review LettersApr 9, 197962 citations

Oscillatory free-induction decay and oscillatory spin echoes

Masakazu Kunitomo, T. Endo, Shunsuke Nakanishi +1 more

Oscillatory free-induction decay (FID) theoretically predicted by Schenzle, Wong, and Brewer was observed by using NMR in an inhomogeneously broadened proton system. Oscillatory behaviors were also observed, in the same system, in two-pulse echoes generated by large-area pulses. These phenomena appear in a highly inhomogeneous-broadened atomic or spin two-level system driven by resonant laser or rf pulses with areas equal to or larger than $2\ensuremath{\pi}$. Detailed studies were made for spin-locked and notched echoes. Behaviors of the oscillatory FID and the oscillatory echoes were theoretically examined by solving the Bloch equations and numerically integrating the solution over the inhomogeneous broadening. Excellent agreement between experiment and theory was obtained. Analytic expressions for the shapes of the locked- and notched-type echoes are obtained, which interpret the main characteristics of these echoes, when the infinite linewidth of the inhomogeneous broadening and the $\ensuremath{\delta}$-function-type excitation for one of the pulses are assumed.Oscillatory free-induction decay (FID) theoretically predicted by Schenzle, Wong, and Brewer was observed by using NMR in an inhomogeneously broadened proton system. Oscillatory behaviors were also observed, in the same system, in two-pulse echoes generated by large-area pulses. These phenomena appear in a highly inhomogeneous-broadened atomic or spin two-level system driven by resonant laser or rf pulses with areas equal to or larger than $2\ensuremath{\pi}$. Detailed studies were made for spin-locked and notched echoes. Behaviors of the oscillatory FID and the oscillatory echoes were theoretically examined by solving the Bloch equations and numerically integrating the solution over the inhomogeneous broadening. Excellent agreement between experiment and theory was obtained. Analytic expressions for the shapes of the locked- and notched-type echoes are obtained, which interpret the main characteristics of these echoes, when the infinite linewidth of the inhomogeneous broadening and the $\ensuremath{\delta}$-function-type excitation for one of the pulses are assumed.

Physical Review AApr 1, 198230 citations

Two-Level Systems

Ulrich Hohenester

Graduate texts in physicsDec 18, 20190 citations

Two-Level Systems

Brian P. Anderson

SPIE eBooksSep 12, 20190 citations

D

line. The detection of this echo requires neither optical shutters nor magnetic field. The decay rate of the echo due to Na-Ar collisions was measured. It is shown that the effect of velocity changing collisions is negligible compared with that of phase interrupting ones.