Recovering the Homogeneous Absorption of Inhomogeneous Media

Ohr Lahad, Ran Finkelstein, Omri Davidson, Ohad Michel, Eilon Poem, and Ofer Firstenberg

Phys. Rev. Lett. 123, 173203 – Published 25 October 2019

Abstract

The resonant absorption of light by an ensemble of absorbers decreases when the resonance is inhomogeneously broadened. Recovering the lost absorption cross section is of great importance for various applications of light-matter interactions, particularly in quantum optics, but no recovery mechanism has yet been identified and successfully demonstrated. Here, we formulate the limit set by the inhomogeneity on the absorption, and present a mechanism able to circumvent this limit and fully recover the homogeneous absorption of the ensemble. We experimentally study this mechanism using two different level schemes in atomic vapors and demonstrate up to fivefold enhancement of the absorption above the inhomogeneous limit. Our scheme relies on light shifts induced by auxiliary fields and is thus applicable to various physical systems and inhomogeneity mechanisms.

Received 18 April 2019

DOI:https://doi.org/10.1103/PhysRevLett.123.173203

Physics Subject Headings (PhySH)

Light-matter interaction

Atomic ensemble Atoms

Electric moment

Optical absorption spectroscopy

Atomic, Molecular & Optical

Authors & Affiliations

Ohr Lahad^*, Ran Finkelstein^*, Omri Davidson, Ohad Michel, Eilon Poem, and Ofer Firstenberg

Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100, Israel

^*These authors contributed equally to this work.

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Vol. 123, Iss. 17 — 25 October 2019

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Images

Figure 1
Induced inhomogeneous broadening (left) and compensation (right). (a) Inhomogeneous broadening of the optical transition $| s ⟩ \leftrightarrow | e ⟩$ (purple shading) leads to broadening of the two-photon transition $| g ⟩ \leftrightarrow | s ⟩$ (red shading) due to a distribution of light shifts introduced by the far-detuned coupling field. (b) Calculations showing the two-photon resonances for different absorbers (different colors; enlarged in the inset). The resulting absorption spectrum (black), obtained by summing over all absorbers, is bounded by the inhomogeneous limit (red horizontal line). (c) A recovery field driving a second optical transition $| g ⟩ \leftrightarrow | r ⟩$ removes the inhomogeneity of the two-photon transition by introducing similar light shifts. (d) With inhomogeneous compensation, the two-photon resonances of different absorbers are aligned (see inset), potentially recovering the absorption of the homogeneous system (magenta asterisk). Along with the merging of the two-photon resonances, a transmission window akin to the Autler-Townes splitting opens up around the enhanced peak.
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Figure 2
Experimental demonstration of absorption enhancement with inhomogeneous compensation. The absorption spectra of the probe field exhibit both the one-photon resonance $| g ⟩ \to | e ⟩$ near zero detuning, and the two-photon (Raman) resonance $| g ⟩ \to | s ⟩$ induced by the coupling field around $Δ = - 270 MHz$ . Without the recovery field (blue curve), the absorption on both resonances is bounded by the inhomogeneous limit (dashed red). With the recovery field (green curve), the absorption peak grows substantially, exceeding the inhomogeneous limit by a factor of $β = 4.8 \pm 0.4$ . In this measurement, $Ω = 29$ , $Ω_{r} = 29.6$ , and $Δ_{r} = - 300 MHz$ .
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Figure 3
Enhancement of absorption $β$ , defined with respect to the inhomogeneous limit. (a) Measured enhancement for several coupling-field intensities ( $Δ = - 270 MHz$ , and $Δ_{r}$ is optimized to maximize $β$ ). (b) Measured enhancement (circles) vs the detuning $Δ_{r}$ ( $Δ = - 270 MHz$ , and $Ω$ , $Ω_{r}$ are optimized to maximize $β$ ). The maximal enhancement is obtained at $Ω_{r} \approx Ω$ [in (a)] and at $Δ_{r} \approx Δ$ [in (b)], which together satisfy the compensation condition (1). The data are consistent with full calculations [dashed blue in (b)], which include the nonidealities of the experiment (see main text).
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Figure 4
Enhancement of absorption $β$ vs the coupling Rabi-frequency $Ω$ in terms of $μ = Ω \sqrt{(γ + γ_{r}) / [(Δ^{2} + σ^{2}) γ_{s g}]}$ . The experimental data (red circles) agree with the full calculation (dashed blue), which includes the nonidealities of the experiment; here $Δ = - 270 MHz$ , and $Ω_{r}$ and $Δ_{r}$ are chosen to maximize $β$ . The nonidealities limit the enhancement to $β \approx 5$ . In a calculation of an ideal far-detuned ( $Δ = - 5 GHz$ ) four-level system (solid green), the enhancement approaches $β_{0} γ / (γ + γ_{r})$ ( $β_{0} = 60$ and $γ \approx γ_{r}$ ), as described by Eq. (2). Reaching this upper limit (solid black) requires strong coupling and recovery fields $μ^{2} ≫ 1$ .
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Figure 5
Inhomogeneous compensation for a ladder system with a Rydberg level. The absorption spectrum in the absence of the recovery field (blue) is bounded by the inhomogeneous limit (dashed red). The addition of the recovery field significantly enhances the absorption of the probe (green) above this limit. In this measurement, the driving lasers with $Ω = 55$ and $Ω_{r} = 45 MHz$ are tuned to resonance.
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