Two-color optical nonlinearity in an ultracold Rydberg atom gas mixture

We report the experimental observation of strong two-color optical nonlinearity in an ultracold gas of ${}^{85}\mathrm{Rb}\text{−}{}^{87}\mathrm{Rb}$ atom mixture. By simultaneously coupling two probe transitions of ${}^{85}\mathrm{Rb}$ and ${}^{87}\mathrm{Rb}$ atoms to Rydberg states in electromagnetically induced transparency (EIT) configurations, we observe significant suppression of the transparency resonance for one probe field when the second probe field is detuned at $\sim 1\mathrm{GHz}$ and hitting the EIT resonance of the other isotope. Such a cross-absorption modulation to the beam propagation dynamics can be described by two coupled nonlinear wave equations we develop. We further demonstrate that the two-color optical nonlinearity can be tuned by varying the density ratio of different atomic isotopes, which highlights its potential for exploring strongly interacting multicomponent fluids of light.

Figure 1

(a) Schematic of the optical setup. A magnetic field $B=4.75\mathrm{G}$ pointing upward is applied to specify the quantization axis $z$. (b) Schematics of the atomic level diagram. A 780-nm probe light ${\mathcal{E}}_a$ of ${\sigma }_{-}$ polarization couples state ${|g\rangle }_a=|5S_{1/2},F=2,m_F=-2\rangle$ to ${|e\rangle }_a=|5P_{3/2},F=3,m_F=-3\rangle$ of ${}^{87}\mathrm{Rb}$ atoms, while a second probe light ${\mathcal{E}}_b$ of $\pi$ polarization connects ${}^{85}\mathrm{Rb}$ atoms from state ${|g\rangle }_b=|5S_{1/2},F=3,m_F=-3\rangle$ to ${|e\rangle }_b=|5P_{3/2},F=4,m_F=-3\rangle$. A 480-nm ${\sigma }_{+}$ polarized control field $\mathrm{\Omega }$ drives both ${}^{87}\mathrm{Rb}$ and ${}^{85}\mathrm{Rb}$ atoms from intermediate states ${|e\rangle }_a$ and ${|e\rangle }_b$ to Rydberg states $|43S_{1/2},m_J=-1/2\rangle$ (${|r\rangle }_a$ and ${|r\rangle }_b$) with Rabi frequencies ${\mathrm{\Omega }}_a$ and ${\mathrm{\Omega }}_b=0.79{\mathrm{\Omega }}_a$. The control field is kept on resonance with the ${\left|e\right.〉}_a\leftrightarrow {\left|r\right.〉}_a$ transition, while the probe field ${\mathcal{E}}_b$ is detuned by ${\mathrm{\Delta }}_b/2\pi =4.0\mathrm{MHz}$ from the ${|g\rangle }_b\leftrightarrow {|e\rangle }_b$ transition to satisfy the two-photon resonance condition for ${}^{85}\mathrm{Rb}$. The beam waists for fields ${\mathcal{E}}_a$, ${\mathcal{E}}_b$, and $\mathrm{\Omega }$ are 460, 2030, and $27\mu \mathrm{m}$, respectively. The radial radius of the atomic ensemble is estimated to be $\sim 100\mu \mathrm{m}$.

Figure 2

Transmission spectra of the probe light on ${}^{87}\mathrm{Rb}$ atoms at different atomic densities [41]: (a) ${\rho }_a=4.1\times {10}^{10}{\mathrm{cm}}^{-3}$ (${}^{87}\mathrm{Rb}$) and ${\rho }_b=6.1\times {10}^9{\mathrm{cm}}^{-3}$ (${}^{85}\mathrm{Rb}$); (b) ${\rho }_a=4.8\times {10}^{10}{\mathrm{cm}}^{-3}$ and ${\rho }_b=1.2\times {10}^{10}{\mathrm{cm}}^{-3}$; (c) ${\rho }_a=5.9\times {10}^{10}{\mathrm{cm}}^{-3}$ and ${\rho }_b=2.0\times {10}^{10}{\mathrm{cm}}^{-3}$. The control field is kept at ${\mathrm{\Omega }}_a/2\pi =$ 9.5 MHz, and Rabi frequencies for the input probe fields are ${\mathcal{E}}_a/2\pi =$ 1.1 MHz and ${\mathcal{E}}_b/2\pi =$ 0.0 MHz (black circles), ${\mathcal{E}}_a/2\pi =$ 1.6 MHz and ${\mathcal{E}}_b/2\pi =$ 0.0 MHz (blue triangles), ${\mathcal{E}}_a/2\pi =$ 1.1 MHz and ${\mathcal{E}}_b/2\pi =1.5\mathrm{MHz}$ (red squares). The eye-guiding solid lines in (a)–(c) connecting the experimental data points come from spline fitting with the error bars denoting standard deviation from five measurements.

Figure 3

On-resonance (${\mathrm{\Delta }}_a=0$) transmission as a function of input Rabi frequencies ${\mathcal{E}}_a$ (a) and ${\mathcal{E}}_b$ (b) for ${\mathcal{E}}_b=0$ in (a) and ${\mathcal{E}}_a/2\pi =1.2\mathrm{MHz}$ in (b). The blue (lower) and red (upper) dots are measured for different atomic densities ${\rho }_a=6.0\times {10}^{10}{\mathrm{cm}}^{-3}$, ${\rho }_b=3.2\times {10}^{10}{\mathrm{cm}}^{-3}$, $L=280\mu \mathrm{m}$ (blue dots), and ${\rho }_a=4.2\times {10}^{10}{\mathrm{cm}}^{-3}$, ${\rho }_b=3.6\times {10}^{10}{\mathrm{cm}}^{-3}$, $L=273\mu \mathrm{m}$ (red dots). The solid lines show theoretical model predictions with ${\mathrm{\Omega }}_a/2\pi =9.5\mathrm{MHz}$, ${\mathrm{\Gamma }}_a^{\prime }/2\pi ={\mathrm{\Gamma }}_b^{\prime }/2\pi =3.6\mathrm{MHz}$, and $\gamma /2\pi =300\mathrm{kHz}$, while the error bars refer to standard deviation from seven measurements.

Figure 4

(a) and (b) show schematics of the on- and off-mode of an all-optical switch. (c) The extinction ratio for the proposed optical switch as a function of insertion loss (determined solely by ${\rho }_a$ here). For demonstration purpose, we assume that the phase noise of two probe fields can be neglected (i.e., ${\mathrm{\Gamma }}_a^{\prime }/2\pi ={\mathrm{\Gamma }}_b^{\prime }/2\pi =3\mathrm{MHz}$) and Rydberg excitation has a small decoherence rate $\gamma /2\pi =100\mathrm{kHz}$. The calculations are performed with $L=400\mu \mathrm{m}$, ${\mathrm{\Omega }}_a/2\pi =5\mathrm{MHz}$, ${\mathrm{\Delta }}_a=0$, ${\mathrm{\Delta }}_b/2\pi =4\mathrm{MHz}$, ${\mathcal{E}}_a/2\pi =1\mathrm{MHz}$, and ${\mathcal{E}}_b/2\pi =1\mathrm{MHz}$ [for the off-mode shown in (b)].