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Physical Review A

Second-harmonic free-induction decay in a two-level spin system

R. Boscaino, F. M. Gelardi, G. Messina

Published Jul 1, 1983• 25 citations
Publisher

Abstract

Two-photon free-induction decay (FID) was experimentally investigated in a two-level electron-spin system by revealing the second-harmonic wave emitted by the system. Oscillatory FID signals were detected for large-area pulses of the input power, analogously to recent observations by Kunitomo et al. for single-quantum resonances. Moreover, the measured decay time of the FID signal following a steady-state preparation was found to be larger than the theoretical value by a few orders of magnitude.

DOI
10.1103/physreva.28.495

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The free-induction decay (FID) signals emitted by a two-level spin system (${E}_{1}^{\mathcal{'}}$ centers in glassy silica), coherently prepared by a short pulse of resonant radiation, have been experimentally investigated in the frequency domain. Our results show that, under the same conditions in which FID signals are oscillatory in the time domain, the spectra are characterized by a regular series of emission zeros. A vectorial model accounts for the occurrence of the zeros and for their spectral positions.

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Large-amplitude oscillations are predicted in the free-induction decay (FID) of atomic or spin two-level quantum systems that are coherently prepared by a resonant electromagnetic field in the form of a square amplitude pulse of duration $T$. The effect should be detectable in nuclear magnetic resonance (NMR) or in optical resonance experiments when the transition line shape is inhomogeneously broadened (${T}_{2}^{*}\ensuremath{\ll}{T}_{2}$) and the applied field is intense enough that the pulse area $\ensuremath{\chi}T\ensuremath{\ge}2\ensuremath{\pi}$, where $\ensuremath{\chi}$ is the Rabi frequency. Physically, the effect is due to Rabi oscillations which are generated in the preparative stage and are then reproduced because of atomic memory in the radiative period which follows. The atomic polarization derived from the Bloch equations assumes the form of an integral over the inhomogeneous line shape, and can be evaluated numerically for arbitrary linewidth $\ensuremath{\sigma}$ or analytically when $\ensuremath{\sigma}\ensuremath{\rightarrow}\ensuremath{\infty}$. The characteristics of the oscillation are unusual since the oscillation frequency, which is of order $\ensuremath{\chi}$, increases with time while the oscillation envelope vanishes identically for times $t\ensuremath{\ge}2T$. Coherent emission is therefore confined to one pulse width $T$ immediately following the pulse. Previous NMR and infrared FID experiments with small-area pulses ($\ensuremath{\chi}T\ensuremath{\le}4\ensuremath{\pi}$), interpreted erroneously in terms of an edge echo effect, support the oscillatory FID behavior described here. For the case $\ensuremath{\chi}T>4\ensuremath{\pi}$, an experimental test would be even more decisive, as the oscillations are more pronounced.

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The after-saturation free-induction-decay (FID) rate of an electron spin transition has been measured in a dilute ruby sample, and a marked departure from the Bloch-like behavior has been found. The similarity with the results obtained recently by Szabo and Muramoto [Phys. Rev. A 39, 3992 (1989)] in the same system but for optical FID points out the close link between the non-Bloch behavior of the FID emission observed in optics and in magnetic-resonance systems. Our results are compared with the theoretical predictions of a statistical theory of the FID emission, but poor agreement is found.

Physical Review A•Jan 1, 1992•16 citations
Two-photon free-induction decay (FID) was experimentally investigated in a two-level electron-spin system by revealing the second-harmonic wave emitted by the system. Oscillatory FID signals were detected for large-area pulses of the input power, analogously to recent observations by Kunitomo et al. for single-quantum resonances. Moreover, the measured decay time of the FID signal following a steady-state preparation was found to be larger than the theoretical value by a few orders of magnitude.
The free-induction decay (FID) signals emitted by a two-level spin system (E1′{E}_{1}^{\mathcal{'}}E1′​ centers in glassy silica), coherently prepared by a short pulse of resonant radiation, have been experimentally investigated in the frequency domain. Our results show that, under the same conditions in which FID signals are oscillatory in the time domain, the spectra are characterized by a regular series of emission zeros. A vectorial model accounts for the occurrence of the zeros and for their spectral positions.
Large-amplitude oscillations are predicted in the free-induction decay (FID) of atomic or spin two-level quantum systems that are coherently prepared by a resonant electromagnetic field in the form of a square amplitude pulse of duration TTT. The effect should be detectable in nuclear magnetic resonance (NMR) or in optical resonance experiments when the transition line shape is inhomogeneously broadened (${T}_{2}^{*}\ensuremath{\ll}{T}_{2}$) and the applied field is intense enough that the pulse area $\ensuremath{\chi}T\ensuremath{\ge}2\ensuremath{\pi}$, where $\ensuremath{\chi}$ is the Rabi frequency. Physically, the effect is due to Rabi oscillations which are generated in the preparative stage and are then reproduced because of atomic memory in the radiative period which follows. The atomic polarization derived from the Bloch equations assumes the form of an integral over the inhomogeneous line shape, and can be evaluated numerically for arbitrary linewidth $\ensuremath{\sigma}$ or analytically when $\ensuremath{\sigma}\ensuremath{\rightarrow}\ensuremath{\infty}$. The characteristics of the oscillation are unusual since the oscillation frequency, which is of order $\ensuremath{\chi}$, increases with time while the oscillation envelope vanishes identically for times $t\ensuremath{\ge}2T$. Coherent emission is therefore confined to one pulse width TTT immediately following the pulse. Previous NMR and infrared FID experiments with small-area pulses ($\ensuremath{\chi}T\ensuremath{\le}4\ensuremath{\pi}$), interpreted erroneously in terms of an edge echo effect, support the oscillatory FID behavior described here. For the case $\ensuremath{\chi}T>4\ensuremath{\pi}$, an experimental test would be even more decisive, as the oscillations are more pronounced.
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.
We report the observation of coherent two-photon free-induction decay (FID) in a three-level Lambda system excited by a low-intensity square-modulated laser pulse. Using electromagnetically induced transparency in an Rb85 cold atomic cloud, for what we believe to be the first time, we observe FID signals with coherence time exceeding the relevant atomic excited-state natural lifetime. Because of the on-resonance enhancement, the two-photon FID signal can be observed at the falling edge without using heterodyne means.
The steady-state free-induction decay (FID) has been investigated in samples of crystalline and amorphous quartz containing paramagnetic two-level electron spin centers (S=1/2). We report experimental data on the dependence of the FID rate on the Rabi frequency \ensuremath{\chi} induced during the preparative stage. Our results confirm that the decay of the FID signal is much slower than expected on the basis of the conventional Bloch equations. The range of \ensuremath{\chi} investigated here is wide enough to show the whole transition from Bloch-type behavior to the high-power Redfield limit, in which the FID rate is determined only by \ensuremath{\chi}. The experimental data are compared with theoretical results recently obtained by hypothesizing Gaussian-Markovian fluctuations of the resonance frequency. Even if agreement is poor, the comparison suggests by itself the possibility that more than one source of fluctuations may be effective. Other possible origins of the failure of the Bloch equations as well as of the stochastic theories are examined.
The after-saturation free-induction-decay (FID) rate of an electron spin transition has been measured in a dilute ruby sample, and a marked departure from the Bloch-like behavior has been found. The similarity with the results obtained recently by Szabo and Muramoto [Phys. Rev. A 39, 3992 (1989)] in the same system but for optical FID points out the close link between the non-Bloch behavior of the FID emission observed in optics and in magnetic-resonance systems. Our results are compared with the theoretical predictions of a statistical theory of the FID emission, but poor agreement is found.