Intrinsic optical bistability in a strongly driven Rydberg ensemble

We observe and characterize intrinsic optical bistability in a dilute Rydberg vapor. The bistability is characterized by sharp jumps between states of low and high Rydberg occupancy with jump-up and -down positions displaying hysteresis depending on the direction in which the control parameter is changed. We find that the shift in frequency of the jump point scales with the fourth power of the principal quantum number. Also, the width of the hysteresis window increases with increasing principal quantum number, before reaching a peak and then closing again. The experimental results are consistent with predictions from a simple theoretical model based on semiclassical Maxwell–Bloch equations including the effects of interaction-induced broadening and level shifts. These results provide insight into the dynamics of driven dissipative systems.

Figure 1

(a) Three-photon excitation scheme to Rydberg states in cesium. (b) Schematic of experimental setup. The three excitation lasers copropagate through a 2 mm vapor cell. An interference filter is used to selected the transmission signal of the probe beam. (c) Simplified two-level model system.

Figure 2

(a) Experimental optical response, the transmission of the probe beam as a function of the Rydberg laser detuning for the same Rabi frequency ${\mathrm{\Omega }}_{\mathrm{r}}/2\pi =(80\pm 10)$ MHz and different Rydberg levels $n=34,35$, and 37. ${\mathrm{\Omega }}_{\mathrm{p}}/2\pi =(140\pm 10)$ and ${\mathrm{\Omega }}_{\mathrm{c}}/2\pi =(170\pm 10)$ MHz. (b) Measurement of the frequency shift of the phase transition as a function of principal quantum number $n$, of the Rydberg level $n{P}_{3/2}$. The solid (red) line is a fit showing that the shift scales with ${(n-\delta )}^{\alpha }$, where $\delta$ is the quantum defect of the Rydberg state $n{P}_{3/2}$ and $\alpha =3.8\pm 0.3$.

Figure 3

(a) Experimental optical response; the transmission of the probe beam as a function of the Rydberg laser detuning for the same Rabi frequency ${\mathrm{\Omega }}_{\mathrm{r}}/2\pi =(130\pm 10)$ MHz and different Rydberg levels. (b) Theoretical Rydberg-state population ${\rho }_{\mathrm{rr}}$ from the model as a function of the laser detuning for different Rydberg levels. Theoretical parameters are ${\mathrm{\Omega }}_{\mathrm{r}}/2\pi =40$ MHz and ${\mathrm{\Gamma }}_{\mathrm{rg}}/2\pi =3$ MHz.

Figure 4

Bistability width as a function of the principal quantum number for two atomic densities, $N=(2.0\pm 0.5){\mathrm{cm}}^{-3}$ (purple squares) and $(3.0\pm 0.5)\times {10}^{11}{\mathrm{cm}}^{-3}$ (green circles), for the same Rydberg Rabi frequency, ${\mathrm{\Omega }}_{\mathrm{r}}/2\pi =(120\pm 10)$ MHz. The column bars are the theoretical results considering the interaction-broadening effect, ${\beta }^{\prime }/2\pi =(2.0\pm 0.2)\times {10}^{-9}\mathrm{Hz}{\mathrm{cm}}^3$ and the parameters ${\mathrm{\Gamma }}_{\mathrm{rg}}/2\pi =13.5$ MHz and $\mathrm{\Omega }/2\pi =(140\pm 5)$ MHz.

Figure 5

Bistability width as a function of the Rydberg laser power for $n=28$ and three different atomic densities $N=\{3.0\left(\mathrm{O}\right);1.0(\square );0.7\left(▵\right)\}\pm 0.5\times {10}^{11}{\mathrm{cm}}^{-3}$. The solid lines are the theoretical calculation using the parameters ${\beta }^{\prime }/2\pi =(1.6\pm 0.2)\times {10}^{-9}\mathrm{Hz}{\mathrm{cm}}^3, {\mathrm{\Gamma }}_{\mathrm{rg}}/2\pi =13.5$ MHz, and $\mathrm{\Omega }/2\pi =(137\pm 2)\sqrt{P}$ MHz, where $P$ is the Rydberg laser power.