Four-level atomic interferometer driven by shaped ultrafast laser pulses

We analyze the behavior of a four-state, two-path atomic interferometer driven by shaped ultrafast laser pulses. The laser pulses interact with atomic rubidium, exciting the atoms to the $5D$ state via two intermediate resonances (the $5P_{1/2}$ and $5P_{3/2}$). The relative phase of the two paths can be modified by applying a varying spectral phase at the wavelength corresponding to one of the resonant transitions for each pathway. We trace out the behavior of the system from the simplest case of weak-field excitation with resonant fields to strong-field excitation with a broadband source. Our measurements and analysis reveal that while interference is observed for all field strengths and spectral widths, the character of the interference changes substantially.

Figure 1

Grotrian diagram and illustration of the laser spectrum. (a) Grotrian diagram showing the two-path interferometer in atomic rubidium with the relevant transition wavelengths. (b) Illustration of the electric field amplitude $|E(\omega )|$, the four resonant transition frequencies, and the spectral phase $\phi (\omega )$. (c) Illustration of the electric field with only the resonant frequencies and the spectral phase.

Figure 2

$5D$ population as a function of spectral phase on the 775.94 nm $5P_{3/2}\to 5D_{3/2}$ transition. The dotted black curve corresponds to the case where only the resonant frequencies in the broadband pulse were present and all other frequencies were blocked. The solid red curve corresponds to weak-field excitation with the full spectrum and the blue dot-dashed curve corresponds to strong-field excitation with the full spectrum.

Figure 3

Measured and calculated $5D$ population as a function of phase applied to 794.76 nm while blocking 780.02 nm in the case of the full laser spectrum.

Figure 4

Wigner plots of the phase-shaped pulses. (a) The Wigner plot of a pulse with a $\pi$ phase window located at 775.94 nm (386.6 THz). (b) The Wigner plot of a pulse with a $\pi$ phase window located at 780.02 nm (384.6 THz). (c) The absolute value of the electric field envelope.

Figure 5

Populations dynamics as a function of time for phase-shaped pulses. The dynamics in panel (a) correspond to the interference minimum in Fig. 3. The dynamics in panel (b) correspond to the interference maximum in Fig. 3.