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

Advances in Optics, Photonics, Spectroscopy & Applications VI ISSN 1859 - 4271(0)In Fig. 2, we plot the results of the numerical calculations for the radial component Frand(0)the axial component Fzof the force on a motionless atom. The FBG cavity length is L = 102cm. The FBG mirror reflectivity is | R | = 0.9 , which corresponds to the finesse2F = π | R | /(1− | R | ) ≅ 30 , a moderate value. The parameters of the atom correspond to the D2-line transition 6S 1/2F= 4, M = 4 ↔ 6P3/2F′= 5, M ′ = 5 of cesium, with the wavelength λ0= 852nm and the natural linewidth γ0/2π= 5.25 MHz. For the parameters used, we find the atomcavitycoupling coefficient G ( r,z)|r= a,z=0= 5.33γ0, the cavity damping rate κ = 7.02γ0, and theatomic decay rate γ ( r ) |r = a= 1.73γ0. It is clear that the s<strong>trong</strong>-coupling condition 2 | G |> κ, γ issatisfied when the atom is close to the fiber and to an an<s<strong>trong</strong>>tin</s<strong>trong</strong>>ode of the cavity standing-wave field.The input probe power is Pin= 1 pW. For the parameters used, the mean number of intracavity<strong>ph</strong>otons N0in the absence of the atom is very small, namely, N0= 0.037 in the case of Fig. 2.We observe from the figure that the spatial dependence of the force is rather complicated. Onereason is that the coupling between the atom and the fiber-guided cavity field is periodic in theaxial direction and has the evanescent-wave nature in the radial direction. Another reason is thepresence of the van der Waals potential, which not only leads to the van der Waals force but alsoaffects the optical force through the shift of the atomic transition frequency. Figure 2(a) shows(0)that in the close vicinity of the fiber surface ( r − a < 100 nm), the radial component Frof theforce varies quickly and is negative as it is mainly determined by the spatial gradient of the van(0)der Waals potential in this region. For large distances r − a , the radial force component Frismainly determined by the spatial gradient of the coupling between the atom and the fiber-guided(0)cavity field. We observe from Fig. 2(d) that the axial component Fzof the force changes itssign at the nodes ( βcz = ± π/2,± 3π/2,K ) and an<s<strong>trong</strong>>tin</s<strong>trong</strong>>odes ( βcz = 0, ± π , ± 2π, K) of the cavitystanding-wave field.B, Friction forceIn general, the force F on the atom depends on the atomic velocity v = ( vr, vϕ, vz) due to theDoppler shift of the atomic transition frequency and the gradient of the field. To calculate theeffect of a small velocity v on the force, we perform a simple linearization procedure [23]. For amoving atom, the total force is(0) (1)F = F + F ,(12)(0)(1)where F is the force on a motionless atom and F is the friction force. We can present the(1)components F , with i = r,ϕ , z , of the friction force F in the form(1)iF(1)i= −∑j=r,ϕ,zβ vijj.(13)Here βijwith i , j = r,ϕ , z are the friction coefficients. Due to the cylindrical symmetry, wehave β β = 0.iϕ= ϕi66