Nhng tin b trong Quang hc, Quang ph và ng dng VI ISSN 1859 - 4271

Những tiến bộ <strong>trong</strong> <strong>Quang</strong> học, <strong>Quang</strong> <strong>ph</strong>ổ và Ứng dụng VI ISSN 1859 - 4271Fig. 1: (Color online) An atom in the vicinity of a nanofiber with two fiber-Bragg-gra<s<strong>trong</strong>>tin</s<strong>trong</strong>>g mirrorsdriven by a weak guided probe light field.Next, we take into account the effect of the FBG mirrors on the mode functions. We assumethat the two FBG mirrors are identical, having the same complex reflection and transmissioncoefficients R and T , respectively, for the guided modes in a broad bandwidth around theatomic transition frequency ω0. Without loss of essential <strong>ph</strong>ysics, we assume that the gra<s<strong>trong</strong>>tin</s<strong>trong</strong>>gs2 2are lossless, that is, | R | + | T | = 1. Let the mirrors be located at the positions z = ± L/2alongthe fiber, where L is the distance between the mirrors. The mode functions of the cavitymodifiedguided modes are obtained, as usual in the Fabry-Perot theory, by summing thegeometric series resul<s<strong>trong</strong>>tin</s<strong>trong</strong>>g from the multiple reflections by the mirrors. We assume that the FBGmirrors do not reflect the radiation modes.We drive the FBG cavity by a classical probe light field propaga<s<strong>trong</strong>>tin</s<strong>trong</strong>>g along the fiber in aguided mode µp= ( ωp,fp,lp) . Let Pinbe the incident power. The power of the transmitted fieldis given by Pout= h ω pκN/2, where N is the mean intracavity <strong>ph</strong>oton number and2κ = (1−| R | ) vg/L | R | is the cavity damping coefficient. In the absence of the atom, the mean2 2 2number of <strong>ph</strong>otons in the cavity is N0 ≡η /( κ /4 + ∆c) , where ∆c= ωp−ωcis the detuning of1/2the probe field from the cavity resonance and η = ( κPin /2h ωp) is the cavity pumping rate. Weassume that the probe field excites a single fiber-guided cavity mode ( ωc,fc,lc), where fc= fpand l = l . Furthermore, we assume that the probe field and the cavity field arecpcounterclockwise circularly polarized, that is, l p= l c= + , and that the atomic transition ispolarized.In the vicinity of the fiber surface, the atom experiences the effects of the van der Waalspotential on the internal state energy and on the center-of-mass motion. Let Vgand Vebe the vander Waals potentials for the ground state | g〉and the excited state | e〉, respectively. In thepresence of the fiber, the atomic transition frequency is shifted from the bare frequency ω0andis given by ωa( r)= ω0 + Veg( r)/h , where Veg= Ve−Vg. It is clear that the effect of the van derWaals potential on the atomic transition frequency is negligible in the region of large distancesr − a but significant in the region of small distances r − a . In our numerical calculations, weassume for simplicity that the van der Waals potential from the fiber is the same as that from a3flat surface, that is, V α= −C3 α/( r − a), where α = g, e .It has been shown that the interaction between the atom and the fiber-guided cavity field canbe described in the interaction picture by the effective Hamiltonian [19]2p 1V†† †† e+ VgHeff= − h∆aσz− h∆caa − ihG(aσ− a σ ) − ihη(a − a ) + . (1)2M22+σ63