Optimized Phase Masks for Absorption of Ultra-Broadband Pulses by Narrowband Atomic Ensembles

Abstract

By combining genetic algorithm and a spatial light modulator we theoretically analyse how to improve a two-photon cascade absorption in atomic ensembles, inspecting the impact of various configurations and parameters in the optimized phase mask. At low atomic densities, we compare the cases of sequential transitions with the two photons coming from the same pulse or from two different pulses. For the former, we predict an enhancement by a factor of $9.5$, similar to what was previously reported in the literature [Phys. Rev. Lett. {\bf 86}, 47 (2002)]. For the later, on the other hand, we obtain an enhancement factor of $26$ times. This absorption of two photons by different pulses is of particular interest for the storage of ultra-broadband single photons by atomic ensembles, in which case the second photon would come from a control pulse. We investigate this process as a function of the atomic density, demonstrating enhancements by factors up to 3 for the two-photon absorption after propagating through large optical depths. However, for the experimental conditions considered in the previous work by Carvalho {et al.} [Phys. Rev. A {\bf 101}, 053426 (2020)], in terms of control power and optical depths, we show that this enhancement in two-photon absorption would still result in just a modest increase of the absorption of a weak probe pulse.

Figures (8)

• Figure 1: (a) Two-photon cascade absorption by a single laser in rubidium atoms. The laser, centered at 778.1 nm with 18 nm bandwidth, excite both 5S-5P (780.2 nm) and 5P-5D (776.0 nm) transitions. (b) Two-photon cascade absorption by two laser pulses. Each laser is resonant with only one transition and the signal pulse alone goes through the SLM to be optimized. The control pulse is centered at 762 nm with 10.4 nm bandwidth, and the signal pulse is centered at 795 nm with 7.5 nm bandwidth.
• Figure 2: Genetic Algorithm optimized results for Eq. (\ref{['EQU Silb']}) and the parameters of Fig. \ref{['f1']}(a). Panel (a) shows the phase mask that achieved the best outcome, out of our 48 simulations, in solid blue. The dotted black curve is the pulse spectrum and the dashed black line provides the phase mask from Ref. dudovich2001transform. The arrows point to the vertical axis of each curve. Panel (b) displays the resulting pulse shape, in solid blue, from the mask in (a). For comparison, in dashed black is the pulse resulting from the phase mask implemented in reference dudovich2001transform and, in dotted black, the original FTL pulse. The inset shows the distribution of absorption optimization achieved by all 48 simulations.
• Figure 3: GA optimized results for Eq. (\ref{['EQU Thin p.v.']}) with $\tau = 0$. Panel (a) presents the phase mask that achieved the best outcome, in solid blue. The pulse spectrum is shown by the dashed black line, for reference. The arrows point to the vertical axis of each curve. Panel (b) plots the pulse shape, in solid blue, resulting from the phase mask in (a). The dashed black curve is the initial FTL pulse. This spectral phase mask increased the absorption by 26 times.
• Figure 4: Typical characteristics of a zero-area pulse. (a) The blue solid line plots the spectral phase of the pulse leaving a sample of length $l$, described by the imaginary part of Eq. (\ref{['EQU Zero Area']}). The atomic resonance ($\omega_a$) is set to zero. The modifications in the spectral phase can be compared to the dashed line, representing the pulse spectrum. The arrows point to the vertical axis of each curve. The inset is the shape of the pulse leaving the sample, in solid blue. The black dashed line is the shape of the FTL pulse before entering the atomic sample. (b) Spectrum of a $0\pi$ pulse, described by the real part of Eq. (\ref{['EQU Zero Area']}), for different OD.
• Figure 5: Impact of OD in the optimized two-photon cascade absorption with a zero-area pulse. The black squares are the results with a $0\pi$ pulse without optimization. The blue circles plot the absorption with delay ($\tau$) optimization alone. The red down triangles have only phase optimization ($\tau = 0$). The golden triangles are the results with phase and delay optimization. The purple diamonds are $0\pi$ pulses modified by a $\pi$ step phase with delay optimization. The normalization is relative to the absorption of a FTL pulse. The insets show two examples of the phase masks obtained by the GA for the downward triangles.