The possibility of using incoherent photon echo in spectroscopy of optically dense impurity media is considered. A theoretical approach to description of this phenomenon is presented. The experimental data on incoherent photon echo in ruby at liquid-helium temperature, with transport of an excitation pulse through a fiber, are reported. The spectral dependence of the echo intensity is studied. The decay curve for an incoherent echo signal is investigated, and the phase relaxation time is found to be 98 ns.
The interaction between an intense radiation field and atoms that undergo collisions in an atomic vapor is studied. With the assumption that velocity-changing collisions are state independent and weak, we obtain an analytic expression for the time-dependent density-matrix elements by solving a quantum-mechanical transport equation using a dressed-state approach. Our analytical calculation is used to predict the form of the signal in an extended-pulse photon echo. The results show good agreement with an experiment carried out by Yodh et al. [Phys. Rev. Lett. 53, 659 (1984)]. It is found that the decay rate of the echo signal decreases rapidly with increasing duration of the second pulse in the pulse excitation sequence. A comparison between theory and experiment is presented and a physical interpretation of the results is given.
We have observed the effect of angled excitation beams on the photon echoes from the 22S1/2–22P1/2 transition of atomic lithium. The degradation of the echo from noncollinear excitations is not so great as had been feared. A calculation with the billiard-ball echo model is in good agreement with our experimental results. In a similar experiment in atomic-sodium vapor we have recorded a decay of echo intensity with increasing pulse separation over nearly 12 orders of magnitude, with the weakest signals coming from atoms that had been more than 23 lifetimes in their excited state.
An analytic theory and experimental studies of the accumulated photon echo is presented. We define a temporal correlation function
G~ of the excitation field E ( t ) as
G~(τ,t)=(1/T1)∫0∞dt′E(t−t′)E(t−t′−τ)⋅exp(−t′/T1), where T 1 is the population relaxation time of the sample, and call the width of
G~ with respect to τ a temporal correlation time
τ~c(t). It is proved that the echo intensity is written by the temporal correlation functions when (1) T 1 and the duration of the excitation light τ p are much longer than
τ~c(t) in order to make the function
G~((τ,t) well-defined, (2) T 1 and τ p are much longer than the homogeneous dephasing time T 2 , and (3) one can find a time interval Δ t such that
G~(τ,t) does not change much between t and t + Δ t , where
Δt≫τ~c. Then we can show that the time resolution of the accumulated photon echo is determined by the averaged
τ~c(t) over an interval of the integration of the echo signal. This discussion is valid for any excitation source if the above conditions are satisfied, and applies to almost all cases of the practical accumulated photon echo experiment. A discussion is also made on the spurious spike on the echo decay curve near zero delay time that appeared in an experiment with a high time resolution in Nd 3+ -doped silicate glass. It is shown that the most probable cause for this spike is uncorrelated inhomogeneous broadenings of the resonant lines of neodymium ions.
We report a measurement of the 5P3/2 excited-state lifetime using two-pulse photon echoes in Rb vapor. The measurement is precise to ∼1% and agrees with the best measurement of atomic lifetime in Rb. The results suggest that a measurement precise to ∼0.25% is possible through additional data acquisition and study of systematic effects. The experiment relies on short optical pulses generated from a cw laser using acousto-optic modulators. The excitation pulses are on resonance with the F=3-->F′=4 transition in Rb85 or the F=2-->F′=3 transition in Rb87. The resulting photon echo signal is detected using a heterodyne detection technique. The excited-state lifetime is determined by measuring the exponential decay of the echo intensity as a function of the time between the excitation pulses. We also present a study of the echo intensity as a function of excitation pulse area and compare the results to simulations based on optical Bloch equations. The simulations include the effects of spontaneous emission as well as spatial and temporal variations of the intensities of excitation pulses.
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.