A novel coherent transient spectroscopy, cw photon echo, is described. A medium is exposed to broadband cw laser radiation and then to a pulsed laser, resulting in a continuous emission signal from the medium. The temporal profile of this signal is studied using full density-matrix theory for the cases of a two-level system and a multilevel system. It is shown that such signal decays with a homogeneous dephasing time ${\mathit{T}}_{2}$ and can have a quantum-beat-type modulation, reproducing in a single shot the conventional two-pulse photon echo plot versus first-to-second pulse separation. Experimental demonstrations are given for the $^{7}$${\mathit{F}}_{0}$${\mathrm{\ensuremath{-}}}^{5}$${\mathit{D}}_{0}$ transition of ${\mathrm{Eu}}^{3+}$ and the $^{3}$${\mathit{H}}_{4}$${\mathrm{\ensuremath{-}}}^{1}$${\mathit{D}}_{2}$ transition of ${\mathrm{Pr}}^{3+}$; both ions are doped in ${\mathrm{YAlO}}_{3}$. The Eu ions exhibit a single exponential decay with a slight modulation due to the ground-state hyperfine splittings. The temperature dependence of the signal is also studied. The Pr ions show a very deep modulation pattern, which provides excellent agreement with the independent two pulse echo measurement. A numerical simulation based on the modulation theory also agrees with the observed decay curves and the nuclear axis configuration in this crystal is discussed.
A novel coherent transient spectroscopy, cw photon echo, is described. A medium is exposed to broadband cw laser radiation and then to a pulsed laser, resulting in a continuous emission signal from the medium. The temporal profile of this signal is studied using full density-matrix theory for the cases of a two-level system and a multilevel system. It is shown that such signal decays with a homogeneous dephasing time T2 and can have a quantum-beat-type modulation, reproducing in a single shot the conventional two-pulse photon echo plot versus first-to-second pulse separation. Experimental demonstrations are given for the ^{7}$${\mathit{F}}_{0}$${\mathrm{\ensuremath{-}}}^{5}$${\mathit{D}}_{0} transition of Eu3+ and the ^{3}$${\mathit{H}}_{4}$${\mathrm{\ensuremath{-}}}^{1}$${\mathit{D}}_{2} transition of Pr3+; both ions are doped in YAlO3. The Eu ions exhibit a single exponential decay with a slight modulation due to the ground-state hyperfine splittings. The temperature dependence of the signal is also studied. The Pr ions show a very deep modulation pattern, which provides excellent agreement with the independent two pulse echo measurement. A numerical simulation based on the modulation theory also agrees with the observed decay curves and the nuclear axis configuration in this crystal is discussed.
We apply for the first time a novel coherent transient, the cw photon echo. The propagation direction of the optical coherence prepared in a medium by a broadband cw laser beam is reversed by a pair of counterpropagating laser pulses, resulting in a continuous emission of the signal. The signal decays with a phase relaxation time T2 and can have a quantum-beat-type modulation, giving the same wave form in one single shot as the plot of echo intensity versus pulse separation in a standard two-pulse echo experiment. Experimental demonstration is given in a Eu3+:YAlO3 crystal.
Stimulated-photon-echo measurements as a function of both the first-to-second (\ensuremath{\tau}) and the second-to-third (T) pulse separations were conducted to study the echo-modulation behavior for the 3H4${\mathrm{\ensuremath{-}}}^{1}$D2 transition of a cryogenic Pr3+:YAlO3 sample. When T is shorter than the excited-state lifetime T1, deep echo modulations along both the \ensuremath{\tau} and T axes are observed, the frequencies of which correspond to the excited-state sublevel splittings. When T exceeds T1, the modulation is still observed, although only along the \ensuremath{\tau} axis. A density-matrix theory is developed in a perturbative manner to explain these coherent dynamical properties. The numerically simulated three-dimensional plots of the echo intensity versus \ensuremath{\tau} and T are presented, predicting quite satisfactorily the seemingly complicated experimental modulation patterns.
Recently we have reported[1] on the measurements of electronic dephasing (T_2) and radiationless decay (T_1) in molecules using emission spectroscopy as a probe for the detection of the photon echo. This right-angle photon echo utilizes a single mode of a narrow-band (~MHz) cw dye laser and an intracavity electro-optical (EO) element that modulates the frequency of the laser.[2] Applying voltage pulses into the EO crystal switches the laser frequency from ω_0 (the peak frequency of the transition resonance) into another frequency ω. This switching procedure introduced by Brewer et al. for the observation of transients in the forward direction of the laser allows one to observe coherent transients in gases,[1,2] solids[3-5] and molecular beams.[6] Typically, the dispersion of the nonlinear EO crystal (e.g., AD*P) gives a 60 MHz frequency shift within the inhomogeneous resonance of the optical transition (width ~GHz or larger). Therefore, to switch the laser frequency further, one must use high-voltage signals that are usually hard to obtain especially for multiple-pulse experiments. Secondly, there is a limit on the frequency shift which is conditioned by the mode spacing of the cavity. Thirdly, because the laser is switched into a new group of molecules some complications may arise in interpreting the transient spectra especially in large molecules. This is because in large molecules the density of excited states is high and thus the buildup of transients of w molecules (which could be complex) will be superimposed on the decay of ω_0 molecules. Finally, off-resonance effects (e.g., beats) between the molecules at frequency ω and ω_0 cannot be avoided.
When the intensity of photon echo in a two-level system is measured as a function of delay time of the two input pulses, one obtains a simple exponential decay with the characteristic phase relaxation time. When the two levels contain hyperfine structures, the interference among the hyperfine levels gives rise to modulation of the decay envelope. The Fourier transform of the modulation pattern reveals the hyperfine structure of the rare-earth ions. The hyperfine structure, and therefore the modulation pattern, are both sensitively affected by the crystal environment of the ionic site. We extend photon-echo modulation spectroscopy to three-pulse, stimulated photon-echo modulation, and we find that the stimulated echo modulation patterns are quite distinct from the two-pulse, photon-echo case and are affected by a different set of atomic and crystal interaction parameters. The modulation is measured, in several photon-echo transitions of praseodymium ions in lanthanum trifluoride and yttrium aluminum garnet crystals, as functions of delay times between first and second pulses and between first and third pulses. Comparison of the experimental results with density-matrix calculations allows us to determine hyperfine parameters that are not easily observed with two-pulse echo modulation.
A new method of picosecond and femtosecond transient spectroscopy yielding information about ultrafast relaxation processes without requiring ultrashort light pulses is presented. It is based on the present theoretical analysis of the resonant degenerate four-wave-mixing process excited by two temporally incoherent light beams with wave vectors ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}}_{1}$ and ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}}_{2}$ which are originated from a single beam at frequency $\ensuremath{\omega}$ but have mutual time delay $\ensuremath{\tau}$. Under the assumption that the incoherent light field has Gaussian random complex amplitude and that the resonant material consists of the usual two-level atoms, the statistically averaged intensity of the output light field with ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}}_{3}=2{\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}}_{2}\ensuremath{-}{\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}}_{1}$ at $\ensuremath{\omega}$ is calculated as a function of $\ensuremath{\tau}$. Even with the light having a much longer duration than both T1 (the longitudinal relaxation time) and T2 (the transverse relaxation time), the correlation trace, i.e., output intensity versus $\ensuremath{\tau}$, represents a decay profile determined mainly by T2 for both homogeneously and inhomogeneously broadened transitions, as long as the light correlation time ${\ensuremath{\tau}}_{c}$ is much shorter than the relaxation times. The correlation trace does not always represent a single-exponential decay but is sometimes slightly deformed by the T1 effect. However, it does not cause a significant error in the determination of T2. Moreover, as $\frac{{T}_{2}}{{T}_{1}}\ensuremath{\rightarrow}0$, the trace becomes a single-exponential decay curve determined only by T2. The feature of the results obtained by the present method is similar to that obtained by the conventional coherent transient spectroscopy with short pulses, such as the photon echo. The time resolution in the present method, however, is limited only by ${\ensuremath{\tau}}_{c}$ much shorter than the light duration. By regarding the incoherent light as a series of random ultrashort pulses, the present four-wave-mixing process is also interpreted as the ensemble of numerous transient four-wave-mixing processes caused by various combinations of these pulses.
A class of molecular two-photon processes, occurring under transient or steady-state conditions, is analyzed exactly for certain cases using a density-matrix formalism. Our results are relevant to the recently observed phenomena of transient coherent Raman beats and steady-state two-photon absorption of oppositely directed laser beams. Lowest-order perturbation theories have shown that these processes are insensitive to the Doppler effect, and consequently the linewidth is unaffected by Doppler broadening and by elastic collisions that change molecular velocity. The solutions presented here are of the same form for the Raman and two-photon problems and reveal significant power-dependent frequency shifts and line broadening that correct the ideal Doppler-free solutions. For the transient case, we assume a molecular three-level quantum structure that can be switched in or out of optical resonance with cw laser radiation by means of a pulsed dc Stark field, but the solutions also apply when resonant optical pulses are introduced. During the resonant condition when the Stark pulse is on, the three levels are prepared in coherent superposition, and during the nonresonant condition following the Stark pulse, the laser field(s) stimulates the coherently prepared sample in a transient two-photon process. One of these processes, the Ramanbeat effect, has been observed in forward scattering, but the second one, transient two-photon emission, should be observable in backward scattering. Bloch-like equations are derived for this three-level problem that facilitate an exact pulse solution for state preparation. Following the pulse, transient decay is well-approximated by a perturbation calculation. For the steady-state case, an exact solution is also obtained and is of interest for continuous-wave spectroscopy or for transient experiments requiring an initial preparation of quantum states, prior to Stark switching. These solutions exhibit a power-dependent line broadening and a frequency shift of magnitude $\ensuremath{\sim}\frac{\ensuremath{\Delta}({\ensuremath{\alpha}}^{2}\ensuremath{-}{\ensuremath{\beta}}^{2})}{({\ensuremath{\Delta}}^{2}+\frac{1}{{T}_{2}^{2}})}$, in agreement with our earlier estimate, where $\ensuremath{\alpha}$ and $\ensuremath{\beta}$ are the Rabi flopping frequencies for the two intermediate transitions and $\ensuremath{\Delta}$ is the off-resonance tuning behavior for one of them.