A giant electro-optic effect using polarizable dark states

Abstract

The electro-optic effect, where the refractive index of a medium is modified by an electric field, is of central importance in non-linear optics, laser technology, quantum optics and optical communications. In general, electro-optic coefficients are very weak and a medium with a giant electro-optic coefficient would have profound implications for non-linear optics, especially at the single photon level, enabling single photon entanglement and switching. Here we propose and demonstrate a giant electro-optic effect based on polarizable dark states. We demonstrate phase modulation of the light field in the dark state medium and measure an electro-optic coefficient that is more than 12 orders of magnitude larger than in other gases. This enormous Kerr non-linearity also creates the potential for precision electrometry and photon entanglement.PACS numbers: 32.80.Rm, 42.50.Gy In 1875 Kerr showed that the refractive index (n r ) of a medium can be changed by applying an electric field [1] according to ∆n r = λ 0 B 0 E 2 0 , where λ 0 is the wavelength of the light field, E 0 is the applied electric field and B 0 is the electro-optic Kerr coefficient. Subsequently, the Kerr effect, or quadratic electro-optic effect, and the related linear electro-optic effect have become widely used in photonic devices such as electro-optic modulators (EOMs) [2,3]. The ac Kerr effect where the electric field is produced by another light beam is the basis of Kerr lens mode-locking [4], and has led to the development of femto and attosecond pulses [5]. Outside these successes, the wider applicability of the Kerr effect is limited by the fact that, in general, the Kerr non-linearity is very small. A larger non-linearity occurs close to a resonance, but at the expense of higher absorption of the signal light. A way around this problem is to use electromagnetically induced transparency (EIT) [6,7,8] where an additional light field, the coupling beam, renders a medium transparent on resonance. Enhanced ac Kerr non-linearities were predicted [9], and have been studied in experiments on Bose Einstein condensates [10] and cold atoms [11]. However, such an EIT medium produces insufficient non-linearity to implement single photon non-linear optics [8]. In addition, the potential to implement all-optical quantum computation using the ac Kerr effect [12] is limited by pulse distortion effects [13], so a new Kerr mechanism based on interactions [14] is desirable.In this paper, we demonstrate a giant dc electro-optic effect in an EIT medium by coupling to a highly excited Rydberg state which has a large polarizability. This renders the transmission through the medium highly sensitive to electric fields produced either externally or internally due to interparticle interactions. The Rydberg states have a polarizability that scales as the principal quantum number, n 7 , and the interactions between Rydberg atoms scale with an even higher power (n 11 for van der Waals interactions) [15]. These strong interac-tions lead to strongly correlated quantum st...

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