Observation of picosecond superfluorescent pulses in rubidium atomic vapor pumped by 100-fs laser pulses

We study the superfluorescence (SF) from a gas of rubidium atoms. The atoms of a dense vapor are excited to the $5D$ state from the $5S$ state by a two-photon process driven by 100-fs laser pulses. The atoms decay to the $6P$ state and then to the $5S$ state. The SF emission at 420 nm on the $6P$–$5S$ transition is recorded by a streak camera with picosecond time resolution. The time duration of the generated SF is tens of picoseconds, which is much shorter than the time scale of the usual relaxation processes, including spontaneous emission and atomic coherence dephasing. The dependence of the time delay between the reference input pulse and SF is measured as a function of laser power. The experimental data are described quantitatively by a simulation based on the semiclassical atom-field interaction theory. The observed change in scaling laws for the peak intensity and delay time can be elucidated by an SF theory in which the sample length is larger than the cooperation length.

Figure 1

The rubidium atomic level scheme. After essentially instantaneous two-photon excitation of the input 778 nm pulse from the ground state ($5S$) to the upper level ($5D$), the atoms emit SF light at 5 $\mu$m which triggers SF at 420 nm.

Figure 2

Diagram of experimental setup. OPA: optical parametric amplifier, 778 nm: input laser beam, BS: beam splitter, T: translation stage, M: mirror, L: lens, F: filter which is transparent for the 420 nm beam and blocks the 778 nm beam, SC: streak camera, S: spectrometer, Ref: timing reference beam, Rb: rubidium vapor cell.

Figure 3

The power dependence of the magnitude at 420 nm from the recorded spectra.

Figure 4

The streak camera data for the reference and 420 nm pulses. The input beam power was varied from 0.3 to 2.1 mW.

Figure 5

The relation between the relative time delay with respect to the arrival time of the reference pulse and input power.

Figure 6

A model of a five-level atomic system, see text for detail.

Figure 7

The time evolution of the normalized intensities $\left|{\Omega }_{\mathit{ab}}\right|{}^2$ (5 $\mu$m pulse) and $\left|{\Omega }_{\mathit{bc}}\right|{}^2$ (420 nm pulse) for an input Gaussian pulse with amplitude ${\Omega }_0=3$.

Figure 8

The simulations for delay times of the 5 $\mu$m and 420 nm pulses as functions of the amplitude of the input Gaussian pulse. The parameters are the same as used in Fig. 7, but ${\Omega }_0=2.5,2.75,3,3.25,3.5,4$, and $4.5$.

Figure 9

The time evolution of the normalized intensity $\left|{\Omega }_{\mathit{bc}}\right|{}^2$ for different input pulse amplitudes. The input Gaussian pulse amplitudes are ${\Omega }_0=2.5,3.5,4.5,5.5$, and $6.5$.

Figure 10

The measured relative delay time for the 420 nm pulse as a function of input power (full circles) and simulations for both the 5 $\mu$m (dotted curve) and 420 nm (solid curve) pulses with scaling factor $\alpha =0.0480$.

Figure 11

The log-log scaled relations of the population of the excited state $max({\rho }_{\mathit{aa}})$ (full circles) and its fit with function $\left|{\Omega }_0\right|{}^{3.6}$ (solid curve) and input intensity.

Figure 12

The power dependence of the magnitude at 420 nm from the recorded spectra for the 420 nm SF light (full circles) and its fit with function $P^{2.0}$ (solid line) in a log-log scale.

Figure 13

A log-log plot that shows the 420 nm SF delay time relative to the reference pulse as a function of input power (full circles). A fit is given by $\propto P^{-0.7}$ (solid line). The data are also compared to functions $P^{-2}$ (dotted line) and $P^{-1}$ (dashed line).