Excitation of Rydberg wave packets with chirped laser pulses

We study Rydberg wave packets produced by pairs of time separated femtosecond laser pulses. The time separation ranges from femtosecond to picosecond time scales. The wave packets consist predominantly of $f$ states of principal quantum numbers $n=22$–32 in Li. With a direct analysis of the field ionization spectra the $n$-level-resolved classical orbit times are displayed. By chirping the second excitation pulse we demonstrate controlled amplitude oscillations of $n$-level amplitudes on femtosecond time scales.

Figure 1

Experimental setup for cross-correlated interferogram measurements. M, mirror; BS, beam splitter; R, retrorefractor.

Figure 2

Retrieved characterization of the used femtosecond laser pulses from FROG measurements. (a) Time profile and temporal phase of the Fourier-transform-limited pulse. (b) Spectrum and spectral phase of the Fourier-transform-limited pulse. (c) Time profile and temporal phase of the down-chirped pulse, (d) Spectrum and spectral phase of the down-chirped pulse.

Figure 3

SFI signals. Upper thick lines: SFI spectra of atoms excited to superposition of Rydberg states by femtosecond laser pulses with central wavelengths of 831 and 838 nm. Lower lines: SFI spectra of $n=22$ to $n=33$ $f$ states excited individually by tunable nanosecond laser pulses with narrow spectral bandwidth. The vertical lines indicate the values of $t_{\mathrm{SFI}}$ used in the state resolution analysis in Figs. 5, 6, 7.

Figure 4

Plot of the function $0.5[2+\cos Mt+\cos (M+1\left)t\right]$ of $t$ illustrating the formula Eq. (5) from adding two probabilities of Eq. (4) for the incoherent sum of two interference patterns, here for $M=20$. The envelope curves $(1\pm \cos t/2)$ remain the same for all $M$. Our realistic values would be of the order between $M\approx 900$ and $M\approx 1500$; the faster oscillations would appear to fill the envelope.

Figure 5

(a) Map of SFI spectra as a function of picosecond scale time delay $\Delta$$t$ between two Fourier-transform-limited femtosecond laser pulses. (b) SFI signal from the population of two neighboring $nf$ states (labeled on the right side) as a function of the time delay $\Delta$$t$. Curves were substracted as horizontal cuts from the map (a) at the SFI times indicated in Fig. 3. Note that the apparent oscillations in panels (b) and (c) are only the result of sampling, the real oscillations are of much higher frequency (cf. Fig. 4). The gray curves are the theoretical envelopes. (c) Theoretical simulation of the population of the pairs of neighboring $nf$ states as a function of time delay $\Delta$$t$ between two femtosecond laser pulses. The densely oscillating curve is sampled at the same times as the measured ones. The envelopes (cf. Fig. 4) are plotted in gray and are the same in panels (b) and (c).

Figure 6

(a) Map of SFI spectra as a function of the femtosecond-scale time delay $\Delta$$t$ between two Fourier-transform-limited femtosecond laser pulses. (b) SFI signal from the population of two neighboring $nf$ states (labeled on the right side) as a function of the time delay $\Delta$$t$. Curves were substracted as horizontal cuts from the map (a) at the SFI times indicated in Fig. 3. (c) Theoretical simulation of evolution of the population of different pairs of neighboring $nf$ states as a function of time delay $\Delta t$ between the two femtosecond laser pulses. The scale of the time delay is adjusted to reproduce the observed Ramsey interference displayed by in panel (b).

Figure 7

(a) Map of SFI spectra as a function of the femtosecond-scale time delay $\Delta$$t$ between one Fourier-transform-limited femtosecond laser pulse and one down-chirped femtosecond laser pulse. (b) SFI signal from the population of two neighboring $nf$ states (labeled on the right side) as a function of the time delay $\Delta$$t$. Curves were substracted as horizontal cuts from the map (a) at the SFI times indicated in Fig. 3. (c) Theoretical simulation of evolution of the population of different pairs of neighboring $nf$ states as a function of time delay $\Delta t$ between the two femtosecond laser pulses. The scale of the time delay is adjusted to reproduce the observed Ramsey interference displayed in panel (b).