A novel form of laser frequency switching is devised which extends coherent optical transient studies to a 100-psec time scale. The technique incorporates a traveling-wave electro-optic element which imposes with unit efficiency a uniform time-varying phase and thus a frequency shift on a cw laser beam. In contrast to earlier optical traveling-wave modulators which are driven by a microwave oscillator, here the optical phase change is induced rapidly and easily by a dc electric field pulse that propagates in a microwave guide either parallel or antiparallel to the light wave. This advance enables optical free-induction decay (FID) studies on a subnanosecond time scale and reveals such new features as a rapid first-order FID that dephases with the inhomogeneous dephasing time ${T}_{2}^{*}$ . The well-known nonlinear FID can interfere with the first-order component at short times and decays over the much longer period $\frac{{T}_{2}}{[1+{(1+{\ensuremath{\chi}}^{2}{T}_{1}{T}_{2})}^{\frac{1}{2}}]}$, where $\ensuremath{\chi}$ is the Rabi frequency. A complete analytical expression is derived for optical FID of a transition subject to homogeneous and inhomogeneous broadening and supports detailed observations of the sodium ${D}_{1}$ line.A novel form of laser frequency switching is devised which extends coherent optical transient studies to a 100-psec time scale. The technique incorporates a traveling-wave electro-optic element which imposes with unit efficiency a uniform time-varying phase and thus a frequency shift on a cw laser beam. In contrast to earlier optical traveling-wave modulators which are driven by a microwave oscillator, here the optical phase change is induced rapidly and easily by a dc electric field pulse that propagates in a microwave guide either parallel or antiparallel to the light wave. This advance enables optical free-induction decay (FID) studies on a subnanosecond time scale and reveals such new features as a rapid first-order FID that dephases with the inhomogeneous dephasing time ${T}_{2}^{*}$. The well-known nonlinear FID can interfere with the first-order component at short times and decays over the much longer period $\frac{{T}_{2}}{[1+{(1+{\ensuremath{\chi}}^{2}{T}_{1}{T}_{2})}^{\frac{1}{2}}]}$, where $\ensuremath{\chi}$ is the Rabi frequency. A complete analytical expression is derived for optical FID of a transition subject to homogeneous and inhomogeneous broadening and supports detailed observations of the sodium ${D}_{1}$ line.

Physical Review ADec 1, 197937 citations

Strong Saturation of Inhomogeneously Broadened Lines

L. L. Buǐshvili, M. D. Zvidadze, G. R. Khutsishviǐ

Journal of Experimental and Theoretical PhysicsJan 1, 19732 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

Oscillatory free-induction decay

Axel Schenzle, N. C. Wong, Richard G. Brewer

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.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.

Physical Review AMar 1, 198057 citations

Inhomogeneously Broadened Lines

Charles P. Poole, Horácio A. Farach

Elsevier eBooksJan 1, 19712 citations

{T}_{2}^{*}

. The well-known nonlinear FID can interfere with the first-order component at short times and decays over the much longer period $\frac{{T}_{2}}{[1+{(1+{\ensuremath{\chi}}^{2}{T}_{1}{T}_{2})}^{\frac{1}{2}}]}$, where $\ensuremath{\chi}$ is the Rabi frequency. A complete analytical expression is derived for optical FID of a transition subject to homogeneous and inhomogeneous broadening and supports detailed observations of the sodium

{D}_{1}

line.

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.