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We proposed utilizing a medium with a high optical depth (OD) and a Rydberg state of low principal quantum number, $n$, to create a weakly-interacting many-body system of Rydberg polaritons, based on the effect of electromagnetically induced transparency (EIT). We experimentally verified the mean field approach to weakly-interacting Rydberg polaritons, and observed the phase shift and attenuation induced by the dipole-dipole interaction (DDI). The DDI-induced phase shift or attenuation can be viewed as a consequence of the elastic or inelastic collisions among the Rydberg polaritons. Using a weakly-interacting system, we further observed that a larger DDI strength caused a width of the momentum distribution of Rydberg polaritons at the exit of the system to become notably smaller as compared with that at the entrance. In this study, we took $n =32$ and the atomic (or polariton) density of 5$\times10^{10}$ (or 2$\times10^{9}$) cm$^{-3}$. The observations demonstrate that the elastic collisions are sufficient to drive the thermalization process in this weakly-interacting many-body system. The combination of the $\mu$s-long interaction time due to the high-OD EIT medium and the $\mu$m$^2$-size collision cross section due to the DDI suggests a new and feasible platform for the Bose-Einstein condensation of the Rydberg polaritons.

The effect of electromagnetically induced transparency (EIT) combined with Rydberg-state atoms provides high optical nonlinearity to efficiently mediate the photon-photon interaction. However, the decay rate of Rydberg coherence, i.e., the decoherence rate, plays an important role in optical nonlinear efficiency and can be largely influenced by laser frequency fluctuation. In this work, we carried out a systematic study of the effect of laser frequency fluctuation on the decoherence rate. We derive an analytical formula that quantitatively describes the relationship between the decoherence rate and laser frequency fluctuation. The formula is experimentally verified by using the $\mathrm{\ensuremath{\Lambda}}$-type EIT system of laser-cooled $^{87}\mathrm{Rb}$ atoms, in which one can either completely eliminate or controllably introduce the effect of laser frequency fluctuation. We also include the effect of Doppler shift caused by the atomic thermal motion in the formula, which can be negligible in the $\mathrm{\ensuremath{\Lambda}}$-type EIT experiment but significant in the Rydberg-EIT experiment. Utilizing the atoms of 350 $\ensuremath{\mu}\mathrm{K}$, we study the decoherence rate in the Rydberg-EIT system involving the state of $|32{D}_{5/2}\ensuremath{\rangle}$. The experimental data are consistent with the predictions from the formula. We are able to achieve a rather low decoherence rate of $2\ensuremath{\pi}\ifmmode\times\else\texttimes\fi{}48$ kHz at a moderate coupling Rabi frequency of $2\ensuremath{\pi}\ifmmode\times\else\texttimes\fi{}4.3$ MHz.

The coherent control of optical images has garnered attention because all information embedded in optical images is expected to be controlled in a parallel way. One of the most important control processes is switch for information delivery. We experimentally demonstrated phase-controlled optical image switching in a double-Lambda system where the transmission of the image through a medium was switched. Two independent laser sources were adopted for a double-Lambda system such that images inscribed in two weak probe light beams were incoherent with each other. Arbitrary phase was added to the optical images to show that switching could be accomplished just with the relative phase difference between the probe pixels. (C) 2013 Optical Society of America

Phase-controlled optical image switching with low light intensity was demonstrated in a double-Λ system. Switching by interference in a double-Λ system was observed as having a 90 % switching depth between incoherent image pixels.

We theoretically studied a triple-Λ system comprising three pairs of coupling-probe fields. Three probe fields were phase-dependently switched with a switching depth above 80%, at which the group-velocity matching of all probe pulses was available under slow light-propagation conditions. We considered the probe susceptibility as the superposition of three-photon transitions to systematically understand the multi-photon interference in a triple-Λ system, which can be applied to systems with N−Λ (N≥1). This helped us to tailor the probe susceptibility by adjusting the detuning and phases of the coupling and probe fields. This work can be applied to all-optical switching gates for triple-photons and can enhance the speed of processing optical information.

Multi-photon interference effects of the optical loop in a double-Λ/V system aid coherent photon control, especially all-optical switching between single photons. In the multi-photon interference, phase fluctuations induced by the mechanical vibration of the optical components should be removed to observe the high fidelity of photon controls. We solved this problem by overlapping coupling and probe beams that have opposite phase shifts in the optical loop system to cancel out phase fluctuation induced by mechanical vibration. We used two independent laser sources to generate two pairs of coupling-probe fields that are resonant on a double-Λ system. The removal of vibrational phase fluctuation was confirmed by comparison with a normal phase-dependent light-switching experiment.

We have demonstrated anticorrelated light switching between multiphoton transition channels in a nonresonant double-Λ system. Two-color probe transitions, using rubidium D1 (795 nm) and D2 (780 nm), were included in our double-Λ system. In anticorrelated light switching, one of two probe transitions is selected as transparent while the other is selected as opaque. In this configuration, we observed completely different behavior from that seen in a resonant double-Λ system, in which both probe transmissions are transparent or opaque simultaneously. Furthermore, we observed a noise correlation between two-color probe transmissions when the phase fluctuation of the two probe lasers was converted to the intensity fluctuation. The relative phase fluctuation between the two probe lasers induced an anticorrelation between the intensity noises of two probe lasers in a nonresonant double-Λ system, while a correlation was induced in a resonant double-Λ system. The intensity fluctuation (correlated or anticorrelated) was easily controlled by detuning the double-Λ system. The noise anticorrelation effect is clearly interpreted as arising from the anticorrelated light switching in a nonresonant double-Λ system. This system can be used for noise control as well as optical switching between incoherent two-color laser lights.

We showed experimentally interference could be occurred between incoherent lights in a double-Λ lambda transition implemented with rubidium atomic vapor. Switching of probe transmission was controlled by the phases of two independent probe lasers with low light intensity. More than 70 % of the probe transmission could be switched by ultra-weak incoherent field. We suggested optically cryptic information could be delivered by the phase-controlled switching with incoherent fields in a double-Λ system.