Virtual single-photon transition interrupted: Time-gated optical gain and loss

The response of matter to an optical excitation consists essentially of absorption and emission. Traditional spectroscopy accesses the frequency-resolved and time-integrated response, while the temporal evolution stays concealed. However, we will demonstrate here that the temporal evolution of a virtual single-photon transition can be mapped out by a second pulsed electromagnetic field. The resulting optical signal shows optical gain and loss, which can be gated and controlled via the relative delay of the electromagnetic fields.

Figure 1

Time-frequency analysis of the dipole response of the two-level system for off-resonant excitation. (a) depicts the time-frequency representation of the dipole response. Red represents a positive and blue a negative response. In (a) and (c) the dashed line shows the energetic position of the excited state $\left|e\right.〉$. (b) shows the time-integrated dipole response for negative times (dashed gray) and positive times (dotted purple). They differ only in the sign, which results in a zero TIDR when integrating over positive and negative times (solid light blue). (c) presents the dipole response with a loss term added to the model and a control pulse arriving 15 fs after the exciting pulse. The dipole response for positive times (dotted purple) in (d) is significantly reduced. Therefore, the temporal integration of the dipole response (solid light blue) is nonzero with positive and negative contributions.

Figure 2

Investigated spectral window and transmitted XUV signal for different delays between the XUV and IR pulse. (a) The transmitted XUV signal shows strong absorption (about 50$\%$) when both pulses overlap (∼0 fs delay) due to a two-photon absorption [also shown in (b)]. (b) The 15th harmonic is energetically located between the excited 1$s$3$p$ and 1$s$4$p$ states of He. Additionally the energy is below the ionization potential of He (24.59 eV). The small peak at 24.2 eV is an effect due to higher-order diffraction of the grating's spectrometer.

Figure 3

Change of absorption (a) and calculated time-integrated dipole response (b) for different delays between the pulses. The change in optical density at XUV frequencies is plotted for different delays between the two pulses. For positive delays the XUV pulse is preceding the IR pulse. Red corresponds to a positive dipole response and is related to absorption, whereas blue stands for a negative dipole response (net emission, optical gain). On top of (a) the spectrum of the XUV pulse is shown. We also detect significant optical gain in spectral regions where the intensity of the original XUV pulse signal has already decreased to the noise level.