Realization of a Time-Domain Fresnel Lens with Coherent Control

Perturbative chirped pulse excitation leads to oscillations of the excited state amplitude. These coherent transients are governed by interferences between resonant and off-resonant contributions. Control mechanisms in both frequency and time domain are used to modify these dynamics. First, by applying a phase step in the spectrum, we manipulate the phase of the oscillations. By direct analogy with Fresnel zone lenses, we then conceive highly phase-amplitude modulated pulse shapes that slice destructive interferences out of the excitation time structure and enhance the final population.

Figure 1

(a) Excitation scheme of rubidium. $\tau$ is the pump-probe delay. (b) Experimental setup. The shaper is shown with lenses for clarity. CPA: regenerative amplifier; LC-SLM: liquid crystal spatial light modulator; PM: photomultiplier.

Figure 2

Experimental (dotted) and numerical (solid) results: chirped pump pulse (black), and $\pi$-step shaped chirped pulse (gray). Here ${\varphi }^{\prime \prime }=-9.4\times {10}^5{\mathrm{f}\mathrm{s}}^2$ corresponding to ${\tau }_c\simeq 21\mathrm{p}\mathrm{s}$. Here ${\lambda }_{\mathrm{s}\mathrm{t}\mathrm{e}\mathrm{p}}=2\pi c/{\omega }_{\mathrm{s}\mathrm{t}\mathrm{e}\mathrm{p}}=795.23\mathrm{n}\mathrm{m}$.

Figure 3

Fresnel zone lens analogy: Excited transient population with unshaped chirped pump pulse (black line) and with calculated shaped pulse (solid gray line). Inset: Corresponding shaped temporal envelope of the pump pulse.

Figure 4

(a) Calculated (black) and realized (gray) spectra. Original spectrum (dashed line). ${\lambda }_{eg}=794.95\mathrm{n}\mathrm{m}$. (b) Transient population measurements (dots) and numerical solution (line) obtained with the experimental spectrum (gray), together with the normal CT (black). Here ${\varphi }^{\prime \prime }=-4.9\times {10}^5{\mathrm{f}\mathrm{s}}^2$ corresponding to ${\tau }_c\simeq 12.4\mathrm{p}\mathrm{s}$.