Self-Induced Transparency in Warm and Strongly Interacting Rydberg Gases

We study dispersive optical nonlinearities of short pulses propagating in high number density, warm atomic vapors where the laser resonantly excites atoms to Rydberg $P$ states via a single-photon transition. Three different regimes of the light-atom interaction, dominated by either Doppler broadening, Rydberg atom interactions, or decay due to thermal collisions between ground state and Rydberg atoms, are found. We show that using fast Rabi flopping and strong Rydberg atom interactions, both in the order of gigahertz, can overcome the Doppler effect as well as collisional decay, leading to a sizable dispersive optical nonlinearity on nanosecond timescales. In this regime, self-induced transparency (SIT) emerges when areas of the nanosecond pulse are determined primarily by the Rydberg atom interaction, rather than the area theorem of interaction-free SIT. We identify, both numerically and analytically, the condition to realize Rydberg SIT. Our study contributes to efforts in achieving quantum information processing using glass cell technologies.

Figure 1

Light-atom interactions in thermal gases. (a) Nanosecond laser pulses excite atoms from the ground state to Rydberg states. (b) In a gas of warm atoms, the excitation is affected by thermal motions, Rydberg atom interactions, and inelastic collisions between ground state (black dots) and Rydberg (yellow balls) atoms. The latter two depend on the density of the atoms. (c) Level scheme. The laser (Rabi frequency $\mathrm{\Omega }$) resonantly couples ground state $|1⟩$ and Rydberg state $|2⟩$. The latter experiences strong, long-range van der Waals interactions $V_r({\mathbf{r}}_{jk})$ and collisional decay (rate ${\gamma }_{21}^{\mathrm{c}}$). See text for details.

Figure 2

Collisional cross section and decay rate in Rydberg $nP$ states. The cross section increases with higher $n$ (a) and temperature (b). Collisional decay rates monotonically increase with $n$ (c) and temperature (d). At room temperature, the rate is a few gigahertz for high Rydberg states that is comparable to the Doppler broadening ($k{v}_T$). Here the atomic density is $\mathcal{N}=5\times {10}^{15}{\mathrm{cm}}^{-3}$, and $s$-wave scattering length of Cs atoms $a_s\approx 21.7a_B$ ($a_B$ the Bohr radius).

Figure 3

Transmission of the pulses. The pulse duration (a) and temperature (b) of the medium affect the transmission. When $\tau \sim 1\mathrm{ns}$, $\eta \sim 1$ almost independent of the temperature. Notable absorption is found when $\tau \gg 1\mathrm{ns}$ in (a). Transmission varies with temperature nonmonotonically for very long pulses, e.g., $\tau =100\mathrm{ns}$ in (b). The imaginary ${\tilde{\chi }}_i=\mathrm{Im}[\tilde{\chi }(T)]/\mathrm{Im}[{\tilde{\chi }}_s]$ (c) and real part ${\tilde{\chi }}_r=\mathrm{Re}[\tilde{\chi }(T)]/\mathrm{Re}[{\tilde{\chi }}_s]$ (d) of static susceptibility $\tilde{\chi }(T)$ at temperature $T$, scaled with respect to ${\tilde{\chi }}_s=\tilde{\chi }(T=1\mathrm{K})$. The maximal ${\tilde{\chi }}_i$ and maximal absorption for $\tau =100\mathrm{ns}$ in (b) both locate around $T=10\mathrm{K}$. The absorption is suppressed at low and high temperatures, due to less Rydberg excitations (hence, decay) caused by the Rydberg blockade and Doppler effect [58], respectively. The Rydberg interaction gives large real part ${\tilde{\chi }}_r$, especially at low temperatures. The legend in (c) and (d) is the same. We consider Rydberg state $|30P⟩$ with lifetime $27.79\mu \mathrm{s}$, $L=400\mu \mathrm{m}$, and $\mathcal{N}=5\times {10}^{15}{\mathrm{cm}}^{-3}$.

Figure 4

Rydberg SIT and the optimal area. The pulse is distorted when $\theta (0)=2\pi$ (a) and stable when $\theta (0)=0.35\pi$ (b), corresponding to Rydberg SIT. (c) The transient dynamics of atoms at $T=1\mu \mathrm{K}$ (upper panel) and 300 K (lower panel). $\mathrm{Im}({\rho }_{21})$ is symmetric with respect to $t_0$. The time average of $\mathrm{Im}({\rho }_{21})$ is negligibly small at 300 K, which is important to the formation of Rydberg SIT. (d) Fidelity $F$ as a function of initial area $\theta (0)$. Maximal fidelities appear at Rydberg-state-dependent optimal areas. (e) Optimal area (filled circle) and corresponding fidelity at $1\mu \mathrm{K}$ (star) and 300 K (empty circle). The MF (dashed line) and numerical calculation agree well. (f) Three regimes of nanosecond pulses, dominated by either the Doppler broadening (DB), Rydberg interactions, or optical absorption (OA). Rydberg SIT forms in the Rydberg interaction dominant region. The color bar shows the ratio of the sum of the Rydberg interaction and Doppler broadening over the collisional decay rate. In panels (a)–(c) and (f), $n=30$. In panels (d) and (e), the pulse area is varied by changing ${\mathrm{\Omega }}_s$. Other parameters are $t_0=5\mathrm{ns}$, $\tau =1\mathrm{ns}$, $L=400\mu \mathrm{m}$, and $T=300\mathrm{K}$.