Improvement of the memory quality of optical pulse pairs in atomic systems via four-wave mixing

Datang Xu, Chao Hang, and Guoxiang Huang

Phys. Rev. A 98, 043848 – Published 25 October 2018

Abstract

We present a scheme to improve the memory quality of linear and nonlinear optical pulse pairs via four-wave mixing (FWM) in an atomic gas. We show that in a linear regime the efficiency and fidelity of the memory of the probe and Stokes pulses can be largely improved through an elimination of the fast-light mode (and hence the suppression of the optical gain induced by the FWM process). We also show that in a nonlinear regime the system may support stable optical soliton pairs with ultraslow propagation velocity and ultralow generation power, which can also be stored and retrieved with a better quality. The improved optical pulse pair memory suggested here may have promising applications in optical information processing and transformation.

Received 20 August 2018

DOI:https://doi.org/10.1103/PhysRevA.98.043848

Physics Subject Headings (PhySH)

Electromagnetically induced transparency Nonlinear optics

Atomic, Molecular & Optical

Authors & Affiliations

Datang Xu^1,2, Chao Hang^1,3, and Guoxiang Huang^1,3

¹State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200062, China
²School of Physics and Electronic Engineering, Changshu Institute of Technology, Changshu 215500, China
³NYU-ECNU Joint Institute of Physics at NYU-Shanghai, Shanghai 200062, China

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Vol. 98, Iss. 4 — October 2018

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Images

Figure 1
(a) Energy-level diagram and excitation scheme of the double- $Λ$ system. $Ω_{p}$ and $Ω_{s}$ ( $Ω_{c 1}$ and $Ω_{c 2}$ ) are respectively half Rabi frequencies of the probe and Stokes fields (control field 1 and control field 2); $Δ_{j}$ ( $j = 2, 3, 4$ ) are detunings; $Γ_{3}$ and $Γ_{4}$ are respectively decay rates of the levels $| 3 〉$ and $| 4 〉$ . Black dots mean that the population is initially prepared at the state $| 1 〉$ . For light propagation the system has two eigenmodes, i.e., slow-light and fast-light modes, which are collective (normal) modes of the system with linear dispersion relations respectively given by $K_{+}$ and $K_{-}$ . (b) $Im (K_{\pm}$ ) as functions of $ω$ [25] for $Δ_{2} = Δ_{3} = 0$ and $Δ_{4} = 0.5 GHz$ . The dashed (solid) blue line is for $Ω_{c 1} = Ω_{c 2} \equiv Ω_{c} = 1.0 \times 10^{8} Hz$ ( $1.5 \times 10^{8} Hz$ ); dashed-dotted (dashed-dotted-dotted) red line is for $K_{-}$ mode for $Ω_{c} = 1.0 \times 10^{8} Hz$ ( $1.5 \times 10^{8} Hz$ ). The inset shows the detail of $Im (K_{\pm}$ ) near $ω = 0$ . (c) $Re (K_{\pm}$ ) as functions of $ω$ . $K_{+}$ is an absorptive (slow-light) mode, whereas $K_{-}$ is a gain (fast-light) mode which contributes to the FWM gain in the optical memory (see text for more detail).
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Figure 2
Propagation of linear probe pulse (blue) and Stokes pulse (red). In each panel, the upper (lower) part is for the probe (Stokes) field, with the dashed line for the input (at $z = 0$ ) and solid line for the output (at $z = 5$ cm). (a) Propagation without the suppression of the $K_{-}$ mode. In this case, the probe and Stokes pulses contain both the slow- and fast-light modes, and a large deformation occurs during propagation. (b) Propagation with the suppression of the $K_{-}$ mode. In this case, both the probe and Stokes pulses contain only the slow-light mode and thus can keep their wave shapes during propagation (except for some decay due to the absorption of the slow-light mode).
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Figure 3
Storage and retrieval of linear optical pulse pair. (a) The case without suppression of the fast-light ( $K_{-}$ ) mode. The upper (lower) part is the result of the memory of the probe (Stokes) pulse. In each part, lines 1 to 6 are for the pulse propagating to $z = 0$ , 1, 2, 3, 4, and 5 cm, respectively. The solid and dashed magenta lines are curves of $| Ω_{c 1} τ_{0} |$ and $| Ω_{c 2} τ_{0} |$ , respectively; they (when overlapped completely) represent the switching off and on of the two control fields. In this case the Stokes pulse has a bad retrieval [lower part of (a)]. (b) The same as (a) but with suppression of the fast-light mode. In this case the memory efficiency and fidelity of the Stokes pulse is improved greatly compared with the case in (a) where the fast-light mode is not suppressed.
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Figure 4
Storage and retrieval of the ultraslow optical soliton pair. (a) Evolution of $| Ω_{p} τ_{0} |$ for the probe soliton component as a function of time $t$ for different propagation distance $z$ . Lines 1 to 6 are for the soliton propagating to $z = 0$ , 1, 2, 3, 4, and 5 cm, respectively; the solid and dashed purple lines are curves of $| Ω_{c 1} τ_{0} |$ and $| Ω_{c 2} τ_{0} |$ , respectively; they (when overlapped completely) represent the switching off and on of the two control fields. (b) The same as (a) but for $| Ω_{s} τ_{0} |$ , i.e., the Stokes soliton component.
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