Experimental investigation of the transition between Autler-Townes splitting and electromagnetically-induced-transparency models

Two phenomena can affect the transmission of a probe field through an absorbing medium in the presence of an additional field: electromagnetically induced transparency (EIT) and Autler-Townes splitting (ATS). Being able to discriminate between the two is important for various practical applications. Here we present an experimental investigation into a method that allows for such a disambiguation as proposed by Anisimov, Dowling, and Sanders in Phys. Rev. Lett. 107, 163604 (2011). We apply the proposed test based on Akaike's information criterion to a coherently driven ensemble of cold cesium atoms and find a good agreement with theoretical predictions, therefore demonstrating the suitability of the method. Beyond the applicability of the test, our results demonstrate that the transition features are highly sensitive to the properties of the medium under study, potentially providing a practical characterizing tool for complex systems.

Figure 1

Absorption in a $\Lambda$-type system. (a) Experimental setup: a weak probe beam and a control beam travel through a cloud of cold cesium atoms. The atoms are initially in the ground state $|g\rangle$. The probe field is close to the $|g\rangle \to |e\rangle$ transition (detuning $\delta$) while the control field drives the $|s\rangle \to |e\rangle$ transition on resonance. PD is a high-gain photodiode. (b) Absorption profiles are displayed as a function of the detuning $\delta$ for a control Rabi frequency $\Omega$ between $0.1\Gamma$ and $4\Gamma$, where $\Gamma$ is the natural linewidth. (c) Experimental splitting as a function of $\sqrt{P}$, where $P$ is the measured control power, fit by a linear function.

Figure 2

Absorption profiles and model fits for two values of the control Rabi frequency $\Omega$. Experimental data (blue dots) are presented together with the best fits of functions $A_{\mathrm{EIT}}(C_{+},C_{-},\epsilon ,{\gamma }_{+},{\gamma }_{-})$ (red solid lines) and $A_{\mathrm{ATS}}(C_1,C_2,{\delta }_1,{\delta }_2,{\gamma }_1,{\gamma }_2)$ (green solid lines). Parameters $C_{+},C_{-},C_1,C_2$ representing the amplitudes of the absorption curves are in dimensionless units, while the parameters $\epsilon ,{\gamma }_{+},{\gamma }_{-}$ and ${\delta }_1,{\delta }_2,{\gamma }_1,{\gamma }_2$ representing detunings and widths are in MHz. (a) $\Omega =0.2\Gamma$. In this case $A_{\mathrm{EIT}}(3.52,3.14,1.45\times {10}^{-2},5.71,0.239)$ fits the experimental data much better than $A_{\mathrm{ATS}}(2.01,2.04,1.84,1.84,4.14,4.08)$. (b) $\Omega =2.3\Gamma$. Here $A_{\mathrm{ATS}}(2.05,1.64,5.86,5.67,3.94,4.68)$ fits the data better than $A_{\mathrm{EIT}}(1.59\times {10}^5,1.59\times {10}^5,1.45\times {10}^{-7},8.17,8.17)$.

Figure 3

Experimental Akaike weights $w_j$ as a function of Rabi frequency $\Omega$ for ATS model [green triangles, curve (1)] and for EIT model [red triangles, curve (2)]. Experimental per-point weights ${\overline{w}}_j$ for ATS model [green dots, curve (3)] and for EIT model [red dots, curve (4)]. The grey area indicates the EIT-ATS model transition. Error bars include the uncertainty on the coefficient $\alpha$ and on the measured power. The solid lines give the theoretical per-point weights for a pure three-level system [curves (5) and (6)].

Figure 4

Theoretical simulations with Zeeman sublevels and Doppler broadening. (a) Level scheme for the Cs $D_2$ line and the six three-level transitions involving Zeeman sublevels. Inset shows the population distribution.(b) Per-point weights for a system with two ground states and taking into account all the hyperfine sublevels of the $6P_{3/2}$ manifold (gray solid lines), for a system involving additionally Zeeman sublevels (dotted lines), for a system involving Zeeman sublevels and residual Doppler broadenings ${\Gamma }_{\text{D}}/\left(2\pi \right)=0.6$ MHz (dashed lines) and ${\Gamma }_{\text{D}}/\left(2\pi \right)=1.3$ MHz (dash-dotted lines).