Simple Route to Strong-Field Coherent Control

Coherent-control schemes to manipulate weak-field interactions are generally invalid at stronger fields, since strong-field interactions are accompanied by level power broadenings and level shifts that usually elude simple analytical treatments. Here we show that a broad subgroup of weak-field solutions (those with real fields, i.e., fields with only one quadrature in the complex plane) can be extended to the strong-field regime while retaining their properties. The salient feature of these fields is a symmetry that cancels out power broadening effects. Such fields can be generated from ultrashort coherent pulses or from incoherent broadband down-converted light. Weak-field coherent-control approaches based on these solutions can therefore be extended to the strong-field regime as we demonstrate in a two-photon absorption experiment in atomic cesium.

Figure 1

(a) Energy level diagram of the two-photon transition $6S\to 8S$ in atomic Cs. Wavelengths longer than 840 nm are blocked as they spectrally overlap the $5P_{3/2}$ level. (b) Outline of the experimental setup.

Figure 2

TPA measurement for periodic spectral phase functions for which ${\epsilon }^2(t)$ is real. Two spectral phase functions are applied: $\Phi (\omega )=\alpha \sin \mathbf{(}\beta (\omega -{\omega }_0/2)\mathbf{)}$ (black lines) and $\Phi (\omega )=\alpha \cos \mathbf{(}\beta (\omega -{\omega }_0/2)\mathbf{)}$ (gray lines). The TPA is measured as a function of the modulation depth $\alpha$ for pulse intensities (at the center of the beam) of $0.1I_{\mathrm{m}\mathrm{a}\mathrm{x}}$ (dotted line), $0.5I_{\mathrm{m}\mathrm{a}\mathrm{x}}$ (dashed-dotted line), $0.8I_{\mathrm{m}\mathrm{a}\mathrm{x}}$ (dashed line) and $I_{\mathrm{m}\mathrm{a}\mathrm{x}}$ (solid line).

Figure 3

TPA measurement for spectral phase function of $\Phi (\omega )=\alpha \sin \mathbf{(}\beta (\omega -{\omega }_0/2)+\pi /4\mathbf{)}$ for which ${\epsilon }^2(t)$ has an imaginary part. The TPA is measured as a function of the modulation depth $\alpha$ for pulse intensities (at the center of the beam) of $0.1I_{\mathrm{m}\mathrm{a}\mathrm{x}}$ (dotted line), $0.5I_{\mathrm{m}\mathrm{a}\mathrm{x}}$ (dashed-dotted line), $0.8I_{\mathrm{m}\mathrm{a}\mathrm{x}}$ (dashed line) and $I_{\mathrm{m}\mathrm{a}\mathrm{x}}$ (solid line).