Population transfer by multiphoton adiabatic rapid passage

The population of atoms in Rydberg states is efficiently transferred with a change in principal quantum number $n$ of up to ten via multiphoton adiabatic rapid passage through a single multiphoton resonance using a frequency-chirped microwave pulse. A quantum-mechanical picture of multiphoton adiabatic rapid passage in a one-dimensional atom using a Floquet approach provides a good description of most, but not all, of the observed phenomena.

Figure 1

(a) Energy levels for a sequence of ARP’s of single-photon $\Delta n=1$ transitions from $n=70$ to $80$. (b) Ten-photon avoided level crossing for a single ten-photon ARP from $n=70$ to $80$. The broken lines are the $n=70$ and $80$ Floquet levels in the absence of a microwave field, and the solid lines are the levels in the presence of a 3.7-V/cm microwave field. The avoided crossing may be traversed in either direction, as shown by the two arrows.

Figure 2

(a) Floquet energy levels as defined in Eq. (1) for $60⩽n⩽$ 90 vs microwave frequency in zero microwave field. The $n=72$–80 levels are labeled. The $\Delta n=1$ resonances are the highest-lying level crossings, and $\Delta n>1$ crossings are lower in energy. (b) With a microwave amplitude of 0.3 V/cm, the $\Delta n=k$, $k⩽5$, and $k⩽6$ avoided crossings become smooth curves in the higher and lower frequencies, respectively, the $\Delta n=6$ avoided crossings are recognizable as isolated avoided-level crossings, and the $\Delta n⩾7$ avoided crossings are invisible on this scale in the lower frequency region. (c) With a microwave amplitude of 1.0 V/cm, the $\Delta n=k$, $k⩽5$, and $k⩽6$ avoided crossings become smooth curves in the higher and lower frequencies, respectively, the $\Delta n=6$ avoided crossings are recognizable as isolated avoided-level crossings, and the $\Delta n⩾7$ avoided crossings are invisible on this scale in the lower frequency region.

Figure 3

A schematic diagram of the experimental setup with (a) aWR-62 waveguide and (b) a pair of field plates.

Figure 4

Time-resolved field ionization signals of the even $n$, $\mathit{np}$ states between $n=72$ and $84$. The odd $n$ state signals are interspersed.

Figure 5

Final-state distributions of $n=74$ atoms exposed to a 50 ns, 285 MHz positively chirped pulse. Field strength of the microwave pulse is changed from less than $0.02$ to $15$ V/cm. Principal quantum numbers $n$ of the initial and final states are defined experimentally using state-selective field ionization. Panels (a)–(j) show the $\Delta n=10$–1 transitions.

Figure 6

Plots of calculated and observed center frequencies of the 50-ns, 285-MHz chirped pulse for MARP of Li Rydberg atoms with (a) a positive chirp and (b) a negative chirp.

Figure 7

The $n=74$ and $84$ signals from Fig. 5a vs microwave field. The oscillatory structure of the $n=74$ signal at fields less than 2 V/cm is meaningless.

Figure 8

Plot of the fields at which $50\%$ of the maximum population transfer occurs vs $\Delta n$. The prediction of Eq. (6) is shown by the broken line.

Figure 9

Fits to the time-resolved ionization signals of the $\Delta n=$ 4,7, and 10 transitions of Fig. 5 to determine quantitatively the final-state distributions subsequent to MARP. The microwave field strengths are 2.67, 4.75, and 4.75 V/cm, respectively. The experimental data are plotted as solid curves and the fits as dashed curves. The rapid oscillations in both have no significance. Inset: histograms of the final-state distributions for each fit shown.

Figure 10

Gray-scale rendering of the final-state distributions of the MARP transitions shown in Fig. 5. The initial state is in all cases $n=74$, and the locus of the expected final state is shown by the dotted line. Typically $30\%$ of the population remains in the $n=74$ state, as shown by the obvious darkened bar at $n=74$. Most of the population that is transferred to higher $n$ states is typically found in two adjacent $n$ states.

Figure 11

Final-state distributions of $n=79$ atoms exposed to a 50-ns, 285-MHz negatively chirped pulse. The field strength of the microwave pulse is changed from less than $0.02$ to $10$ V/cm. Principal quantum numbers $n$ of the initial and final states are defined experimentally using the state-selective field-ionization method. Panels (a)–(g) show the $\Delta n=-7$ to $\Delta n=-1$ transitions. Panel (h) shows the $\Delta n=1$ transition to $n=80$.

Figure 12

Final-state distributions of $n=71$ atoms exposed to a 50-ns, 285-MHz (a) negative chirp pulse and (b) positive chirp pulse. The field strength of the MW pulse is changed from less than $0.02$ to $15$ V/cm. Note that the center frequency measured in the experiment is slightly different from the calculated value. (c) Floquet energy levels of Rydberg atoms exposed to a 300-MHz chirped Gaussian pulse having the center frequency of 15.9 GHz with a peak field of 4 V/cm. Eleven-photon $n=71$–82 avoided crossing at 14.9 GHz is circled.