Charge-induced optical bistability in thermal Rydberg vapor

We investigate the phenomenon of optical bistability in a driven ensemble of Rydberg atoms. By performing two experiments with thermal vapors of rubidium and cesium, we are able to shed light on the underlying interaction mechanisms causing such a nonlinear behavior. Due to the different properties of these two atomic species, we conclude that the large polarizability of Rydberg states in combination with electric fields of spontaneously ionized Rydberg atoms is the relevant interaction mechanism. In the case of rubidium, we directly measure the electric field in a bistable situation via two-species spectroscopy. In cesium, we make use of the different sign of the polarizability for different $l$ states and the possibility of applying electric fields. Both these experiments allow us to rule out dipole-dipole interactions and support our hypothesis of a charge-induced bistability.

Figure 1

Relevant transitions in the resonant two-photon excitation schemes for both isotopes. (a) ${\mathrm{EIT}}_{\mathrm{OB}}$ drives the optical bistability. (b) ${\mathrm{EIT}}_{\mathrm{FP}}$ acts as a probe for electric fields.

Figure 2

Setup of the rubidium experiment. Two pairs of lasers drive the two isotopes in the same volume using an EIT-like excitation scheme (see Fig. 1). One drives an optical bistability with the scheme ${\mathrm{EIT}}_{\mathrm{OB}}$, while the other probes for local fields with the scheme ${\mathrm{EIT}}_{\mathrm{FP}}$.

Figure 3

Setup of the cesium experiment. (a) Level scheme with the relevant cesium transitions. (b) Counterpropagating spectroscopy setup with a 3-mm-thick cesium vapor sample. The cell is placed between two electrodes, where the modulation is applied on one port while the other is $50\mathrm{\Omega }$ terminated. The laser polarization is parallel to the electric field between the plates.

Figure 4

Rubidium measurements. (a) Deformation of the 795-nm laser (${\mathrm{EIT}}_{\mathrm{OB}}$) transmission peak towards optical bistability. Scans across the resonance from blue to red detuning (dashed) and reverse (solid line). (b) ${\mathrm{EIT}}_{\mathrm{FP}}$ scans taken at a fixed detuning ${\mathrm{\Delta }}_{477}/2\pi =-35$ MHz [vertical dashed line in panel (a)]. The feature is shown for different Rabi frequencies of the ${\mathrm{EIT}}_{\mathrm{OB}}$ system (offset to discern the lines).

Figure 5

Rubidium interaction potentials. (a) Pair potentials for $32S-32S$. The color shading represents the projection on the unperturbed pair state. (b) Pair potentials for $41S-32S$. The avoided crossings arise from the interaction with different pair-states (not shown here). The $C_4/r^4$ potential is plotted as a red dashed line for the $32S$ state (a) and the $41S$ state (b). (c) Nearest-neighbor distribution for various densities (given in $\mu {\mathrm{m}}^{-3}$) of Rydberg atoms, corresponding to Rydberg fractions of 1% to 50%. The curves are normalized to the maximum density. Left: Projection of pair potentials weighted with distribution (c).

Figure 6

Rubidium measurements. (a) Example of a two-dimensional map showing the ${\mathrm{EIT}}_{\mathrm{FP}}$ traces against both detunings for ${\mathrm{\Omega }}_{477}/2\pi =14$ MHz. (b) Cuts along the dashed lines in panel (a). (c) Dependence of the fitted maximum in every row in panel (a) for different Rabi frequencies ${\mathrm{\Omega }}_{477}$. (d) Center frequency and amplitude of the curves in panel (c), determined via a Gaussian fit (uncertainty within marker size). The center frequency (blue dots) represents the shift in the ${\mathrm{EIT}}_{\mathrm{OB}}$ scheme, while the amplitude (red squares) illustrates the shift in the ${\mathrm{EIT}}_{\mathrm{FP}}$ scheme. The offsets are chosen such that the linear fits intersect at zero.

Figure 7

Cesium measurements. Transmission spectra with frequency scans towards the color of the respective line. (a), (b) Comparison between (a) the $23D$ state and (b) the $28S$ state. (c)–(h) Effect on the bistability for the $23D$ state by RF modulation with a sine wave of 3.2 V ${\mathrm{cm}}^{-1}$ amplitude and increasing frequency (10, 20, 50, 100, 200, and 500 MHz).