Four-wave mixing involving Rydberg states in thermal vapor

We present experimental results on nondegenerate four-wave mixing in a thermal vapor cell of rubidium atoms via highly excited Rydberg states. We observe sub-Doppler spectral features and a large sensitivity of the mixed light mode to small electric fields due to the large polarizabilities of the involved Rydberg state. We observe a saturation of the optical response due to the nonlinear four-level physics. The strong interaction between Rydberg atoms and the associated Rydberg blockade could potentially increase the nonlinearity dramatically.

Figure 1

(a) The four atomic states and the three coupling lasers used in the experiment. The emitted light has a wavelength of $795\mathrm{nm}$. For the simulations we set the spontaneous decay rates of ${\Gamma }_1={\Gamma }_4=6\times 2\pi \mathrm{MHz}$ and ${\Gamma }_2={\Gamma }_3=0.5\times 2\pi \mathrm{MHz}$ representing dominant transit effects. (b) In our setup we overlap the two blue laser beams by a holographic grating and the 780-nm laser beam afterwards by a dichroic mirror. To separate the mixed signal beam from the coupling beams after the cell we use a blazed holographic grating (1200 lines/mm) and detect the light at 795 nm with a photomultiplier tube.

Figure 2

(a) Measured signal for the parameters $P_{780}=200\mu \mathrm{W}$, $P_{480}=24\mathit{mW}$, and $P_{474}=43\mathit{mW}$ for the $30S$ state and (b) the corresponding simulation including the full velocity distribution in combination with the peak coupling strengths ${\Omega }_{780}=300\mathrm{MHz}$, ${\Omega }_{480}=50\mathrm{MHz}$, ${\Omega }_{474}=50\mathrm{MHz}$ at the threefold focal spot. The detuning ${\Delta }_{480}$ was fixed to $100\times 2\pi \mathrm{MHz}$. The qualitative structures in (b) are in good agreement with the measurements shown in (a), despite some additional broadening induced by the actual intensity distribution of the three Gaussian beams. Simulated fraction of the population in the Rydberg state (c) and $5P_{1/2}$ state (d) based on the same parameters including black contours representing the mixed intensity (b).

Figure 3

Saturation effects of the maximum signal for increasing 780-nm Rabi frequency on the $30S$ [solid blue (upper) line] and $42S$ [solid red (lower) line] state. The dotted lines are simulations with the calculated peak Rabi frequencies for both Rydberg excitation lasers and were scaled to the corresponding atomic density. The simulation of the 30S state was fitted to the maximum of the measurement with constant scaling factor, which was also applied to the simulation of the 42S state. The insets show measurements on the 30S state for the powers $P_{780}=(25,200,500)\mu \mathrm{W}$, $P_{480}=24\mathit{mW}$, and $P_{474}=43\mathit{mW}$. The axes are scaled as in Fig. 2.

Figure 4

Measured stark effect on a 42S state. By taking the locked 480-nm laser and Doppler effects into account this leads to the shift of the Rydberg state (red square) with a quadratic fit (dashed green line). Applying a shielding factor of $0.8$ for the electric field (not shown here), the measurement is in good agreement with the theory (solid blue line). The nearly vertical lines of the theory belong to an $f$-state manifold.