Autler-Townes spectroscopy with interaction-induced dephasing

We study the effects of Rydberg-atom interactions on Autler-Townes (AT) spectra in a dense gas of ultracold cesium atoms. The $6S_{1/2}$ and $6P_{3/2}$ levels of cesium are strongly coupled (Rabi frequency ${\Omega }_c)$, and the resultant AT spectra are probed via excitation into a Rydberg level. Van der Waals interactions between the atoms in the probe Rydberg level give rise to a dephasing rate $\left({\gamma }_3\right)$. The interaction-induced dephasing is found to cause characteristic changes in the AT spectra, including a reduction or elimination of the AT splitting, an increase in the critical ${\Omega }_c$ above which AT splitting occurs, and an increase in the width of the AT spectral lines. Rydberg-atom interactions are controlled by varying the principal quantum number $n$ of the probe Rydberg level; larger values of $n$ correspond to higher dephasing rates ${\gamma }_3$. Results of numerical calculations are in good agreement with the experiments.

Figure 1

(a) Level scheme. A coupling laser (Rabi frequency ${\Omega }_c)$ is applied to the $6S_{1/2}\leftrightarrow 6P_{3/2}$ and a probe laser (Rabi frequency ${\Omega }_p$ and detuning ${\delta }_p)$ to the $6P_{3/2}\to n{S}_{1/2}$ transition. ${\Gamma }_{re}$ and ${\Gamma }_{eg}$ are the natural decay rates of the Rydberg and $6P_{3/2}$ state, respectively. (b) Time sequence of the experiment (schematic). (c) Sketch of the experimental setup. The 852-nm coupling and 510-nm probe lasers are counter-propagated and focused into the cold-atom cloud.

Figure 2

(a) Calculated AT spectra for ${\gamma }_3=2\pi \times 20$ MHz, ${\Omega }_p=2\pi \times 200$ kHz, and ${\Gamma }_{re}=2\pi \times 1.6$ kHz vs the coupling laser Rabi frequency ${\Omega }_c$ and ${\delta }_p$, for the pulse sequence shown in Fig 1. The relative Rydberg-atom population ${\rho }_{33}$ is displayed on a linear scale. The horizontal (red) line marks the boundary between the domain of split AT line pairs and that of only one peak; the boundary occurs at ${\Omega }_{c0}\approx 2\pi \times 15$ MHz. The dot-dashed (white) and the dashed (orange) lines mark the positions of AT line peaks for ${\gamma }_3=0$ MHz and ${\gamma }_3=2\pi \times 20$ MHz, respectively. (b) Calculated critical ${\eta }_0$ values (circles) vs ${\gamma }_3$ and the fit explained in the text. The curve separates the plane into an upper-right region, in which AT splitting occurs, and a lower-left one, in which it does not. The dashed vertical line marks the dephasing on the $|1\rangle -|2\rangle$ transition, ${\gamma }_2=2\pi \times 5.2$ MHz. The thin dashed curve shows ${\eta }_0$ for continuous coupling and probe fields. The (blue) squares refer to figure numbers and show experimental data explained in the text.

Figure 3

(a)–(c) Measured normalized AT spectra (symbols) and calculated fits (solid lines), probed by excitation into the $49S_{1/2}$ level. Experimental ${\Omega }_c$ values are $2\pi \times 2.0$ MHz (a), $2\pi \times 12.6$ MHz (b), and $2\pi \times 32.6$ MHz (c). Fit results for ${\gamma }_3$ and ${\Omega }_c$ are given in the text. (d), (e) Measurements (symbols) and fits (solid lines) of AT spectra for $49S_{1/2}$ with experimental Rabi frequency ${\Omega }_c=2\pi \times 40.7$ MHz (d) and $71S_{1/2}$ with ${\Omega }_c=2\pi \times 37.9$ MHz (e). Dashed (blue) lines show spectra calculated with ${\gamma }_3=0$.

Figure 4

Measured and calculated (solid lines) AT-peak separations vs ${\Omega }_c$ for probing into $49S_{1/2}$ [(blue) squares] and $71S_{1/2}$ [(red) circles]. Experimental and simulated probe Rabi frequencies are ${\Omega }_p=2\pi \times 2.2$ MHz $\left(49S_{1/2}\right)$ and $2\pi \times 1.3$ MHz $\left(71S_{1/2}\right)$, respectively.