Photoexcitation of $n\simeq 305$ Rydberg states in the presence of an rf drive field

The response of highly excited potassium Rydberg states with $n$ $\sim 305$ to a sinusoidal electric drive field in the radio frequency (100–300 MHz) regime is examined by photoexcitation from the $4s$ ground state using a uv probe beam. The drive field couples many Rydberg levels simultaneously and results in a coherent response that leads to a variety of multiphoton processes. The excitation spectra are analyzed within the framework of Floquet theory and reveal signatures of quantum optical phenomena such as electromagnetically induced transparency and Autler-Townes splitting seen with few-level systems.

Figure 1

Comparison between the standard three-level ladder scheme for coherent excitation of Rydberg levels utilizing two optical transitions with frequencies ${\omega }_{1,2}$ (a) and the coherent excitation of a multilevel Rydberg atom through rf driving that is probed using a uv laser pulse (b).

Figure 2

Schematic diagram of the apparatus. The inset shows a partial term diagram for potassium depicting the two Rydberg series of interest here that originate on the $F=1$ and $F=2$ ground hyperfine states. The arrows indicate the energy separations between neighboring $s$ and $p$ levels.

Figure 3

Floquet energies (a),(d) of the three-level driven harmonic oscillator [Eq. (9)] and excitation spectra (b),(c),(e),(f) of the three-level Rydberg atom ($306s$, $306p$, $307s$) driven by an rf field. The drive frequency is ${\omega }_{\mathrm{rf}}=233$MHz in (a)–(c) and 116 MHz in (d)–(f). The excitation strengths $\mathrm{Im}\chi$ of the Floquet states are estimated as $\mu ({\mathcal{E}}_k,N)$ [Eq. (6)] when the laser is tuned to the frequency ${\mathcal{E}}_k+N{\omega }_{\mathrm{rf}}$. The spectra are summed over all Floquet states and photon numbers $N$ and convolved with a Gaussian to match with Doppler broadening $(\Delta \sim 15$MHz) seen experimentally. The laser frequency resonant with excitation of the $306p$ state is defined as zero detuning. Excitation strengths calculated both with (b),(e), and without (c),(f) use of the RWA are included.

Figure 4

Floquet energies (a),(d) of the three-level driven harmonic oscillator [Eq. (9)] and excitation spectra (b),(c),(e),(f) of the three-level Rydberg atom ($306p$, $307s$, $307p$) driven by an rf field. The driving frequency is ${\omega }_{\mathrm{rf}}=233$ MHz in (a)–(c) and 116 MHz in (d)–(f). In (a),(d) the dashed lines correspond to the Floquet energies ${\mathcal{E}}_i$ $(i=1,2,3)$ in Eq. (10) with $N=0$, the red (dark gray) lines with $N=1$, and the light blue (light gray) lines with $N=-1$. The excitation strengths are calculated and arranged as in Fig. 3.

Figure 5

Evolution of the photoexcitation spectrum near $n\sim 305$ as a function of rf drive field amplitude for a drive frequency ${\omega }_{\mathrm{rf}}=233$ MHz. (a) Excitation strengths [Eq. (14)] derived from the expansion coefficients $\mu ({\mathcal{E}}_k,N)$ calculated within the finite basis $284\le n\le 324$, $0\le \ell \le 10$, and $m=0$. (b) Comparison of experimental data (black lines) with simulated spectra [blue (gray) lines] obtained by making cuts through (a) at selected field strengths within the white dashed rectangle. The positions of the zero-field resonances are indicated.

Figure 6

Evolution of the photoexcitation spectrum near $n\sim 305$ as a function of rf drive field amplitude for a drive frequency ${\omega }_{\mathrm{rf}}=116$ MHz. The excitation strengths are calculated, and the figure is arranged, as in Fig. 5.

Figure 7

Growth of the features seen in Fig. 5b associated with excitation of (a) $304d$, $306s$ and (b) $305d$, $307s$ states as a function of rf drive field amplitude: $\blacksquare$, experimental data; —–, integrated excitation strengths [Eq. (14)]. The integration ranges are (a) ${\delta }_{305d}-20$MHz $<{\omega }_{\mathrm{uv}}<{\delta }_{307s}+20$MHz and (b) ${\delta }_{304d}-20$MHz $<{\omega }_{\mathrm{uv}}<{\delta }_{306s}+20$MHz.

Figure 8

Evolution of the potassium photoexcitation spectrum in the vicinity of $n\sim 305$ as a function of the frequency of an rf drive field of amplitude $\sim$3 mV cm${}^{-1}$. The excitation strengths are calculated, and the figure is arranged, as in Fig. 5. The processes responsible for excitation at the crossings labeled A, B, and C in (a) are shown schematically in the bottom frame (see text).