We present a theoretical treatment of the coherent three-level beat signals occurring in the transient response of a Doppler-broadened molecular system with coupled closely spaced levels resonating with an intense monochromatic cw laser field. When the degenerate levels of the molecular system are suddenly split by means of an external Stark or Zeeman field, the transmitted laser radiation exhibits decaying beats at frequencies related to the level splitting or Raman frequency. This effect has been the subject of earlier theoretical analyses, but some relevant aspects such as the velocity integration, were not taken into account. A perturbation treatment, complete to third order in laser field strength, is used to calculate the velocity-integrated induced polarization and the corresponding reradiated field. The calculation takes into account both Raman-type processes, which lead to transient oscillations at the Raman frequency ${\ensuremath{\omega}}_{21}$, and population-saturation effects. In particular, population-induced transient oscillations at half the Raman frequency, $\frac{{\ensuremath{\omega}}_{21}}{2}$, are predicted. The relative importance of the various oscillations is analyzed as a function of the laser detuning and other parameters, including velocity-changing collisions. The relationship between the three-level beat signals and the well-known quantum-beat effect studied in fluorescence is explored.We present a theoretical treatment of the coherent three-level beat signals occurring in the transient response of a Doppler-broadened molecular system with coupled closely spaced levels resonating with an intense monochromatic cw laser field. When the degenerate levels of the molecular system are suddenly split by means of an external Stark or Zeeman field, the transmitted laser radiation exhibits decaying beats at frequencies related to the level splitting or Raman frequency. This effect has been the subject of earlier theoretical analyses, but some relevant aspects such as the velocity integration, were not taken into account. A perturbation treatment, complete to third order in laser field strength, is used to calculate the velocity-integrated induced polarization and the corresponding reradiated field. The calculation takes into account both Raman-type processes, which lead to transient oscillations at the Raman frequency ${\ensuremath{\omega}}_{21}$, and population-saturation effects. In particular, population-induced transient oscillations at half the Raman frequency, $\frac{{\ensuremath{\omega}}_{21}}{2}$, are predicted. The relative importance of the various oscillations is analyzed as a function of the laser detuning and other parameters, including velocity-changing collisions. The relationship between the three-level beat signals and the well-known quantum-beat effect studied in fluorescence is explored.

Physical Review ASep 1, 197628 citations

Modulated coherent Raman beats

Eric W. Van Stryland, R. L. Shoemaker

The authors study the phenomenon of coherent Raman beats in $^{15}\mathrm{N}$ ${\mathrm{H}}_{3}$ using a C ${\mathrm{O}}_{2}$ laser and Stark switching. In particular, a three-level system in which the two upper levels always remain split by a few MHz is prepared by switching the transitions into resonance with a short Stark pulse whose bandwidth is large enough to coherently excite both transitions. When one of the coherently excited levels remains in resonance with the laser after the Stark pulse, this system exhibits a qualitatively new effect which has not been seen heretofore. For Stark shifts on the order of the upper-state splitting or smaller, the Raman beat is amplitude modulated at a frequency related to the optical nutation frequency. This is interpreted as being due to an interaction between the two-photon coherent Raman beat process and a single-photon optical nutation process which occurs simultaneously. Numerical calculations as well as a simple analytic model are presented to support this interpretation. By reducing the laser power, one can make the modulation of the Raman beat disappear. From the Raman signal in this regime the permanent electric dipole moment of $^{15}\mathrm{N}$ ${\mathrm{H}}_{3}$ in an excited vibrational state is determined and the Raman beat decay rate measured. By comparing the latter result with a delayed optical nutation measurement we show that phase-changing collisions are negligible for the transition studied.The authors study the phenomenon of coherent Raman beats in $^{15}\mathrm{N}$${\mathrm{H}}_{3}$ using a C${\mathrm{O}}_{2}$ laser and Stark switching. In particular, a three-level system in which the two upper levels always remain split by a few MHz is prepared by switching the transitions into resonance with a short Stark pulse whose bandwidth is large enough to coherently excite both transitions. When one of the coherently excited levels remains in resonance with the laser after the Stark pulse, this system exhibits a qualitatively new effect which has not been seen heretofore. For Stark shifts on the order of the upper-state splitting or smaller, the Raman beat is amplitude modulated at a frequency related to the optical nutation frequency. This is interpreted as being due to an interaction between the two-photon coherent Raman beat process and a single-photon optical nutation process which occurs simultaneously. Numerical calculations as well as a simple analytic model are presented to support this interpretation. By reducing the laser power, one can make the modulation of the Raman beat disappear. From the Raman signal in this regime the permanent electric dipole moment of $^{15}\mathrm{N}$${\mathrm{H}}_{3}$ in an excited vibrational state is determined and the Raman beat decay rate measured. By comparing the latter result with a delayed optical nutation measurement we show that phase-changing collisions are negligible for the transition studied.

Physical Review AOct 1, 19798 citations

Stimulated Raman gain in a Lambda-type three level system with transitions driven by multiple oscillating fields

Jason L. Bowie

Jan 1, 19980 citations

Excitation of coherent raman beats with a bichromatic laser field

Tilo Blasberg, Dieter Suter

European Quantum Electronics Conference (EQEC)Aug 24, 20050 citations

Coherent Raman beats from dark states

Ken-ichi Harada, Koji Motomura, 隆典越水 +2 more

We have observed coherent Raman beat signals from a Lambda-type three-level system in a sodium atomic vapor. The sample is first prepared in a coherent superposition state of the ground-state hyperfine levels, or a dark state, by resonant bichromatic radiation. A following sudden frequency shift of one of the excitation beams causes the beat signals. Detailed analytical calculations based on the three-level Liouville equations are presented and are compared with experimental results. This simple technique is particularly suited for the obtaining of information on the generated sublevel coherence, including magnitude, phase, and decay time.We have observed coherent Raman beat signals from a Lambda-type three-level system in a sodium atomic vapor. The sample is first prepared in a coherent superposition state of the ground-state hyperfine levels, or a dark state, by resonant bichromatic radiation. A following sudden frequency shift of one of the excitation beams causes the beat signals. Detailed analytical calculations based on the three-level Liouville equations are presented and are compared with experimental results. This simple technique is particularly suited for the obtaining of information on the generated sublevel coherence, including magnitude, phase, and decay time.

Journal of the Optical Society of America BMay 1, 20057 citations

Raman Coherence Beats Induced by Frequency Modulated Raman Field in a Three-level

\Lambda

System

The authors study the phenomenon of coherent Raman beats in

^{15}\mathrm{N}

{\mathrm{H}}_{3}

using a C

{\mathrm{O}}_{2}

laser and Stark switching. In particular, a three-level system in which the two upper levels always remain split by a few MHz is prepared by switching the transitions into resonance with a short Stark pulse whose bandwidth is large enough to coherently excite both transitions. When one of the coherently excited levels remains in resonance with the laser after the Stark pulse, this system exhibits a qualitatively new effect which has not been seen heretofore. For Stark shifts on the order of the upper-state splitting or smaller, the Raman beat is amplitude modulated at a frequency related to the optical nutation frequency. This is interpreted as being due to an interaction between the two-photon coherent Raman beat process and a single-photon optical nutation process which occurs simultaneously. Numerical calculations as well as a simple analytic model are presented to support this interpretation. By reducing the laser power, one can make the modulation of the Raman beat disappear. From the Raman signal in this regime the permanent electric dipole moment of

^{15}\mathrm{N}

{\mathrm{H}}_{3}

in an excited vibrational state is determined and the Raman beat decay rate measured. By comparing the latter result with a delayed optical nutation measurement we show that phase-changing collisions are negligible for the transition studied.