Quasisimultons in Thermal Atomic Vapors

The propagation of two-color laser fields through optically thick atomic ensembles is studied. We demonstrate how the interaction between these two fields spawns the formation of copropagating, two-color solitonlike pulses akin to the simultons found by Konopnicki and Eberly [Phys. Rev. A 24, 2567 (1981)]. For the particular case of thermal Rb atoms exposed to a combination of a weak cw laser field resonant on the $D1$ transition and a strong sub-ns laser pulse resonant on the $D2$ transition, simulton formation is initiated by an interplay between the $5s_{1/2}-5p_{1/2}$ and $5s_{1/2}-5p_{3/2}$ coherences. The interplay amplifies the $D1$ field at the arrival of the $D2$ pulse, producing a sech-squared pulse with a length of less than $10\mu \mathrm{m}$. This amplification is demonstrated in a time-resolved measurement of the light transmitted through a thin thermal cell. We find good agreement between experiment and a model that includes the hyperfine structure of the relevant levels. With the addition of Rydberg dressing, quasisimultons may offer interesting prospects for strong photon-photon interactions in a robust environment.

Figure 1

(a) Schematic of the experiment (not to scale). A cw probe field (red) resonant with the $5s_{1/2}(F=3)-5p_{1/2}(F=3)$ transition of ${}^{85}\mathrm{Rb}$ copropagates with a pulsed coupling field (blue) resonant with the $5s_{1/2}(F=3)-5p_{3/2}(F=4)$ transition. The coupling field reshapes the probe into sech-squared pulses. (b) Inset: The level scheme indicating the probe and coupling fields. Main plot: A snapshot of the intensity of the probe field (relative to the incident intensity) calculated over a much longer propagation distance than achieved in the experiment, taken 0.05 ns after the coupling pulse reached its maximum at the front of the medium; the circles are calculated points and the solid line is a fit of these with a sech-squared pulse of width $8.6\mu \mathrm{m}$ (FWHM).

Figure 2

The change in the transmission at the probe frequency for a $2\mu \mathrm{m}$-long Rb vapor relative to the average transmission at $t<-1\mathrm{ns}$, vs the peak power of the incident coupling pulse. The pink curves represent the temporal intensity profile of the latter, at the back of the medium, for an initial peak power of 85 mW. The 0 of the color scale corresponds to no change compared to the transmission before the arrival of the coupling pulse. The temperature is $200°\mathrm{C}$. (a) As measured. (b) As predicted by the model described in the text.

Figure 3

Formation of quasisimultons in a three-state model of an isotopically pure ${}^{85}\mathrm{Rb}$ vapor, neglecting Doppler broadening and self-broadening. The atomic density corresponds to a temperature of $220°\mathrm{C}$. (a) The intensity of the probe field vs time and propagation distance within the medium. This field is resonant on the $D1$ transition and has a constant intensity of $10\mu \mathrm{W}{\mathrm{cm}}^{-2}$ at the entrance of the medium ($z=0$). The 0.8-ns coupling pulse is resonant on the $D2$ transition and has a peak intensity of $1\mathrm{kW}{\mathrm{cm}}^{-2}$ at $(t=0,z=0)$. The dashed green line indicates the trajectory that a pulse propagating at a constant speed of $2\times {10}^{-4}c$ would trace in the figure. (b) Enlargement of the small-$z$ region of panel (a). The blue curve represents the temporal profile of the coupling pulse (the intensity scale is arbitrary). (c) The same as (a) but for the coupling field.

Figure 4

(a) The intensity of the probe field in the three-state model of Fig. 3. This part of the figure is an enlargement of the small $|t-z/c|$, small-$z$ region of Fig. 3. (b) The same as (a) but with the full hyperfine structure of the $5s_{1/2}$, $5p_{1/2}$, and $5p_{3/2}$ states included in the calculation. (c) The same as (b) but now also including Doppler broadening and self-broadening. (d) The same as (c) but for the coupling field.

Figure 5

(a) The calculated probe field for the conditions of Fig. 2, now for a much longer propagation distance of $50\mu \mathrm{m}$. The peak power of the coupling pulse is 35 mW. (b) The corresponding coupling field.