High-optical-depth, sub-Doppler-width absorption lines at telecom wavelengths in hot, optically driven rubidium vapor

Abstract

Doppler broadening presents a major limitation for high-resolution spectroscopy and nonlinear optics in room-temperature atomic vapors. Here, we demonstrate the suppression of Doppler broadening accompanied by pronounced absorption on the upper transition of a three-level ladder system, achieved by dressing the intermediate state with a strong control field. As a concrete realization, we study a hot vapor of $^{87}$Rb where the lower transition is driven by a strong control field resonant with the D2 line at a wavelength of 780 nm, while a weak counter-propagating probe field at the telecom C-band wavelength of 1529 nm ($5P_{(3/2)}\leftrightarrow 4D_{(5/2)}$) interrogates the dressed states. We observe absorption features with a resonant optical depth of approximately 4 and a full width at half maximum of about 17 MHz. Remarkably, this corresponds to an order-of-magnitude reduction relative to the Doppler width, while the optical depth on the upper transition of the ladder scheme exceeds that of the Doppler-broadened lower transition. The measured spectra are in good agreement with theoretical modeling. Combining high optical density with sub-Doppler-width absorption lines typically requires laser-cooled atoms, while our approach profits from the experimental simplicity of a hot-vapor platform.

Figures (10)

• Figure 1: Excitation scheme of a ladder-type three-level atom in the bare-state (a) and dressed-state (b) representations. (a) A strong control field with frequency $\omega_c$, wave-vector magnitude $k_c$, and Rabi frequency $\Omega_c$ drives the transition between the initially populated ground state $|1\rangle$ and the intermediate state $|2\rangle$ with transition frequency $\omega_{12}$. In the atomic rest frame, the Doppler-shifted detuning is $\tilde{\Delta}_c=\Delta_c+k_c v_z$, where $\Delta_c=\omega_{12}-\omega_c$ is the detuning from the center of the Doppler-broadened transition and $v_z$ denotes the atomic velocity component along the propagation direction of the control field. A weak probe field with frequency $\omega_p$, wave-vector magnitude $k_p$, and Rabi frequency $\Omega_p$ couples the transition $|2\rangle\!\leftrightarrow\!|3\rangle$ with Doppler-shifted detuning $\tilde{\Delta}_p=\Delta_p\pm k_p v_z$, where $\Delta_p=\omega_{23}-\omega_p$; the upper (lower) sign corresponds to co-propagating (counter-propagating) probe and control fields. (b) In the dressed-state picture, the control field mixes states $|1\rangle$ and $|2\rangle$ into dressed states $|+\rangle$ and $|-\rangle$, separated in energy by $\hbar\tilde{\Omega}_c=\hbar\sqrt{\tilde{\Delta}_c^2+\Omega_c^2}$. The dressed states are coupled to state $|3\rangle$ with effective Rabi frequencies $\Omega_{p,+}$ and $\Omega_{p,-}$ and detunings $\tilde{\Delta}_{p,+}$ and $\tilde{\Delta}_{p,-}$ [see Eqs. (\ref{['parameters1']})--(\ref{['parameters2']})]. Wavy arrows denote incoherent spontaneous decay processes with rates $\gamma_2$ and $\gamma_3$.
• Figure 2: Dependence of the full width at half maximum (FWHM) of a single Autler--Townes (AT) component on the ratio $k_p/k_c$ for three values of the control-field Rabi frequency $\Omega_c$, calculated for $\gamma_2=\gamma_3=\gamma$ and $k_c v_0 = 50\gamma$ (solid lines). Negative values of $k_p/k_c$ formally correspond to counter-propagating configurations of the probe and control fields. For parameter regimes where the AT components are not spectrally resolved, the FWHM of the resulting single spectral feature is shown by the corresponding dashed lines. As a resolution criterion, we require that the signal at $\Delta_p = 0$ does not exceed one half of the maximum absorption signal, which occurs at $\Delta_p \simeq \Omega_c/2$. The inset shows the FWHM on an expanded scale; the dotted and dashed blue curves indicate, respectively, the inner and outer half-widths at half maximum (see definitions in Fig. \ref{['shape']}) of an individual AT component for $\Omega_c = 50\gamma$.
• Figure 3: Shape of a single resolved AT component: the probe absorption coefficient $\alpha_p$, normalized to its maximum value $\alpha_m$, as a function of the probe detuning $\delta_p$ from the expected position of the AT component, $\delta_p=\Delta_p-\Omega_c/2$, for three values of the control-field Rabi frequency $\Omega_c$ ($\gamma_2=\gamma_3=\gamma$ and $k_c v_0=50\gamma$).
• Figure 4: Normalized probe absorption coefficient $\alpha/\alpha_{0p}$ as a function of the probe detuning $\Delta_p$ and the control-field Rabi frequency $\Omega_c$ for (a) counter-propagating and (b) co-propagating configurations, calculated for $k_p=0.5k_c$, $\gamma_2=\gamma_3=\gamma$, and $k_c v_0=50\gamma$.
• Figure 5: Normalized peak absorption $\alpha_{\max}/\alpha_{0p}$ of a single AT component as a function of the control-field Rabi frequency $\Omega_c$, expressed in units of the Doppler width $k_c v_0$, for the counter-propagating configuration. The curves are calculated for $k_p=0.5k_c$, $\gamma_2=\gamma_3=\gamma$, and $k_c v_0=50\gamma$.