Observation and Symmetry-Based Coherent Control of Transient Two-Photon Absorption: The Bright Side of Dark Pulses

We present and experimentally demonstrate for the first time the observation and femtosecond coherent control over the temporal evolution of a transient population that is excited via nonresonant two-photon absorption. Based on symmetry properties of the two-photon absorption process, the exciting femtosecond pulses are phase-shaped to photoinduce different evolutions of the transient excited population for a given final excited population. As a study case, we focus here on the attractive case of two-photon dark pulses that, although inducing zero final population (hence, the terminology of “dark pulses”), they induce a transient excited population during the pulse irradiation that can significantly deviate from zero. This nonzero transient population can be viewed as the bright side of such dark pulses. The symmetry-based coherent control is demonstrated first with dark pulses that we shape to induce transient excited population that at all times is kept below different target levels. Then, it is further demonstrated with pairs of dark pulses where one is rationally shaped to induce temporal evolution of the transient excited population that is the inverse of the evolution induced by the other. The work is conducted in the weak-field regime with the sodium atom as the model system. The approach developed here is general, conceptually simple, and very effective.

Figure 1

The excitation scheme of Na for the study of symmetry-based coherent control of transient two-photon absorption.

Figure 2

Experimental (circles) and calculated (black solid lines) results for basic symmetry-based phase control of transient two-photon absorption. Different temporal evolutions of the $4s$ transient population are photoinduced for a given final population that is (a),(b) maximal, and (c),(d) zero (dark pulses). The components of the spectral phase of the different shaped pulses, the base phase pattern (blue line) and antisymmetric phase addition (red line), are shown in the insets. The temporal intensity of the different pulses (gray dotted-dashed lines) are also shown.

Figure 3

Experimental results for time-inversion symmetry-based transient coherent control with pairs of two-photon dark pulses that photoinduce time-inverted evolutions of the $4s$ transient population. Each row corresponds to a different pair of dark pulses: the induced traces are presented individually in the first two panels of each row [(a),(b), (d),(e), and (g),(h)], while the third panel of each row [(c), (f), and (i)] compares them by presenting the first one as is (black line) and the second one after its numerical time-inversion (red line). See text for details.