Efficient isolation of multiphoton processes and detection of collective resonances in dilute samples

A phase modulation technique to sensitively and selectively isolate multiple-quantum coherences in a femtosecond pump-probe setup is presented. By detecting incoherent observables and incorporating lock-in amplification, even weak signals of highly dilute samples can be acquired. Applying this method, efficient isolation of one- and two-photon quantum beats in a rubidium-doped helium droplet beam experiment is demonstrated and collective resonances are observed in a potassium vapor for the first time up to fourth order. Our approach provides promising perspectives for coherent time-resolved experiments in the deep UV and multidimensional spectroscopy schemes, in particular when mass-selective detection of particles in dilute gas-phase targets is possible.

Figure 1

Simplified diagram of the phase-modulated WPI scheme used for the detection of MQCs. The optical setup is shown in panel (a), diagrammatic WP excitation for a one- and $n$-photon transition is shown in panel (b), and a respective Feynman diagram for the $n$-photon transition is shown in panel (c).

Figure 2

Interferograms recorded in a single measurement referenced to the first and second harmonic of ${\mathrm{\Omega }}_{21}$. The downshifting by ${\omega }_M$ and $2{\omega }_M$, respectively, results in similar oscillation periods with respect to the pump-probe delay $\tau$.

Figure 3

Level diagram of the involved Rb electronic states (a). Fourier-transformed spectra of the measured time domain interferograms referenced to ${\omega }_M$ [panel (b)] and $2{\omega }_M$ [panels (c) and (d)]. Dashed vertical lines show tabulated transitions [28].

Figure 4

Time-domain interferograms of collective energy states in a potassium vapor, detected with first- to fourth-harmonic lock-in demodulation (labeled 1H–4H).

Figure 5

Collective resonances in potassium vapor for first- to fourth-harmonic lock-in demodulation (labeled 1H–4H). Black dashed lines indicate the predicted energies of the collective states. Their labels correspond to the notation introduced in Fig. 6. Peaks with gray labels correspond to leak signals from the first harmonic.

Figure 6

Level diagram for atomic potassium and wave numbers for the excited $D_1$ and $D_2$ lines in panel (a) [28], and corresponding collective energy states for an ensemble of four potassium atoms described in a product basis in panel (b). For clearer visualization in panel (a), states lying between the $6^{2}S$ and the ionic potential are not shown. Since the laser is only resonant to the $D1$ and $D2$ line transitions, only these excitations are considered for the collective energy levels.