Stern-Gerlach effect of weak-light ultraslow vector solitons

Chao Hang and Guoxiang Huang

Phys. Rev. A 86, 043809 – Published 5 October 2012

Abstract

We propose a scheme to exhibit Stern-Gerlach deflection of high-dimensional vector optical solitons at a weak-light level in a cold atomic gas via electromagnetically induced transparency. We show that the propagating velocity and generation power of such solitons can be reduced to $10^{- 6} c$ ( $c$ is light speed in vacuum) and lowered to magnitude of nanowatt, respectively. The stabilization of the solitons is realized by using an optical lattice potential formed by a far-detuned laser field, and trajectories of them are deflected significantly by using a transversal Stern-Gerlach gradient magnetic field. Deflection angles of the solitons can be of magnitude of $10^{- 3}$ rad when propagating several millimeters. Different from atomic Stern-Gerlach deflection, deflection angles of the solitons can be distinct for different polarization components and can be manipulated in a controllable way. The result obtained can be described in terms of the Stern-Gerlach effect for vector optical solitons with quasispin and effective magnetic moment.

Received 20 June 2012

DOI:https://doi.org/10.1103/PhysRevA.86.043809

Authors & Affiliations

Chao Hang and Guoxiang Huang^*

State Key Laboratory of Precision Spectroscopy and Department of Physics, East China Normal University, Shanghai 200062, China

^*gxhuang@phys.ecnu.edu.cn

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Issue

Vol. 86, Iss. 4 — October 2012

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Images

Figure 1
(a) Double EIT scheme. $E_{p}$ and $E_{c j}$ ( $j = 1, 2$ ) are probe and control fields, respectively; $δ_{p}$ , $δ_{p} + Δ$ , and $δ_{c j}$ are detunings. (b) A possible experimental arrangement, where an inhomogeneous static magnetic field $B (y) = \hat{z} (B_{0} + B_{1} y)$ removes the degeneracy of ground states $| j 〉$ ( $j = 1, 3, 5$ ) and excited states $| l 〉$ ( $l = 2, 4$ ), and causes Stern-Gerlach deflection of probe-field components. $θ_{1}$ and $θ_{2}$ are, respectively, deflection angles of $σ^{-}$ polarization component (i.e., $E_{p 1}$ ) and $σ^{+}$ polarization component (i.e., $E_{p 2}$ ) of high-dimensional vector optical soliton, which has a quasispin and an effective magnetic moment. The curved thick arrow represents the far-detuned optical lattice field $E (x, t) = \hat{x} E_{0} \cos [x / (2 R_{⊥})] \cos (ω_{L} t)$ used to stabilize the soliton.Reuse & Permissions
Figure 2
(a) Im $K_{j} (ω)$ and (b) Re $K_{j} (ω)$ as functions of $ω$ . The solid and dotted lines correspond to the $σ^{-}$ ( $j = 1$ ) and $σ^{+}$ ( $j = 2$ ) polarization components of the probe field, respectively.Reuse & Permissions
Figure 3
(a) and (b) Evolutions of $| u_{1} |^{2}$ , respectively, at $t = 0$ and $t = 3 τ_{0}$ for the single-peaked VOS. (c) and (d) Evolutions of $| u_{1} |^{2}$ , respectively, at $t = 0$ and $t = 3 τ_{0}$ for the multiple-peaked VOS. The SG gradient magnetic field is absent (i.e., $B_{1} = 0$ ). The stability of the VOS is achieved by the far-detuned optical lattice. Result for $| u_{2} |^{2}$ is similar to that for $| u_{1} |^{2}$ thus not shown.Reuse & Permissions
Figure 4
SG effect of ultraslow VOS. (a) and (b) Symmetric deflection (on $y$ axis) of $| u_{1} |^{2}$ and $| u_{2} |^{2}$ when propagating from $z = 2 L_{Diff}$ to $z = 8 L_{Diff}$ (corresponding respectively to the subfigure from left to right), respectively. (c) Asymmetric deflection of $| u_{2} |^{2}$ [ $| u_{1} |^{2}$ is the same as (a) thus not shown]. (d), (e), and (f) The corresponding evolution of two polarization components in a linear case.Reuse & Permissions
Figure 5
(a) Deflection angles of the VOS as functions of medium length $L$ for magnetic field $B_{1} = 0.7$ mG/ $μ$ m. The solid line with positive (negative) slope is the analytical result of $θ_{1}$ ( $θ_{2}$ ) for the symmetric case. Dashed line is the analytical result of $θ_{2}$ for the asymmetric case ( $θ_{1}$ is the same as the symmetric case thus not shown). Points labeled by “x” and “ $+$ ” are center positions of the VOS polarization components obtained numerically. (b) Deflection angles of the VOS as functions of $B_{1}$ for $L = 0.8$ cm. The solid line of positive (negative) slope is the result for $θ_{1}$ ( $θ_{2}$ ) in the symmetric case. Dashed line is the result of $θ_{2}$ in the asymmetric case ( $θ_{1}$ is the same as the symmetric case hence not shown).Reuse & Permissions

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