Control of Rydberg-state population with realistic femtosecond laser pulses

We investigate computationally a method for ultrafast preparation of alkali-metal atoms in their Rydberg states using a three-dimensional model potential in the single active electron approximation. By optimizing laser pulse shapes that can be generated with modern waveform synthesizers, we propose pulses for controlling the population transfer from the ground state to a preselected set of Rydberg states. Dynamical processes under the optimized pulses are shown to be much more complicated than in the traditional optical two-photon preparation of Rydberg states.

Figure 1

Total population of the target states as a function of the optimization iterations demonstrating the working principle of the two-step optimization scheme. After convergence of the first local optimization [orange (gray) curve], the global optimizer restarts the local optimizer in a different region of the search space [at iteration number 102, blue (black) curve]. Here we have targeted the states $n=7$, $l=0\cdots 2$.

Figure 2

(a) The optimized laser pulse for populating the $2p$ state, (b) the power spectral density of the laser electric field, and (c)–(e) the populations of the stationary states.

Figure 3

(a) The optimized laser pulse for populating the set of states $n=7$, $l=0\cdots 2$ using the channels 800, 700, 400, and 300 nm, (b) the power spectral density of the electric field, and (c)–(e) the populations of the stationary states.

Figure 4

(a) The optimized laser pulse for populating the set of states $n=7$, $l=4\cdots 6$ using the channels 2 $\mu \mathrm{m}$, 800 nm, 700 nm, and 400 nm, (b) the power spectral density of the electric field, and (c)–(j) the populations of the stationary states.

Figure 5

Same as Fig. 4, but without the 700-nm channel.

Figure 6

(a) The optimized laser pulse for populating the set of $l=4$ states with principal quantum numbers $n=7\cdots 10$ consists of first a few-cycle 700-nm primer followed by single-cycle 2-$\mu \mathrm{m}$ pulse, (b) the power spectral density of the electric field, and (c)–(g) the populations of the stationary states.

Figure 7

(a) The optimized laser pulse for populating the set of states $n=7\cdots 10$ using the channels 2 $\mu \mathrm{m}$, 800 nm, 700 nm, and 300 nm, (b) the power spectral density of the electric field, and (c) the final populations of the stationary states.