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

Advances in Optics, Photonics, Spectroscopy & Applications VI ISSN 1859 - 4271Here the quasistationary conditions have been assumed and the notation δ Xˆ≡ Xˆ− 〈 Xˆ〉 hasbeen introduced.Fig. 5: Diffusion coefficient D as a function of (a) the atom-to-surface distance r − a and (b) theaxial position z for the parameters of Fig. 2, where ωp= ωc= ω0.We again consider the case where the probe field is so weak that the excited state is hardlyoccupied and there is at most one <strong>ph</strong>oton in the cavity. We plot the diffusion coefficient D inFig. 5 for the parameters of Fig. 2. Figure 5(a) shows that D has a peak when the atom-tosurfacedistance r − a is small enough but not too small. The appearance of such a peak is aresult of the balance between the compe<s<strong>trong</strong>>tin</s<strong>trong</strong>>g effects of the van der Waals potential and the atomcavitycoupling.V. CENTER-OF-MASS MOTION OF THE ATOMThe classical motion of the center of mass of the atom is governed by the equationsM & z= F z+ p&z(D)(M r& = Mr & ϕ + F r+ p&r,2 D),(D)Mr & ϕ= − 2Mr&& ϕ + F + p&.(16)ϕϕHere M is the mass of the atom, Fr, F ϕ , and Fzare the cylindrical-coordinate components(D) (D)(D)of the force F , and p&r, p&ϕ , and p&zare the random variables that characterize themomentum diffusion.We use the method of Ref. [6] to solve Eqs. (??). In every time step ∆ t of the numerical( D)integration of p , a stochastic term ∆p = rˆR ( 6 ) ˆrDr∆t+ ϕRϕ( 6Dϕ∆t) + zˆRz( 6Dz∆t) isadded. Here rˆ , ϕˆ , and ẑ are the unit vectors for the cylindrical coordinates r , ϕ , and z ,respectively. The quantity Rj( p), where j = r,ϕ , z , produces a random number between − pand p . The coefficients Dr, D ϕ , and Dzare the cylindrical-coordinate components of thediffusion coefficient D = Dr+ D ϕ + Dz, which are responsible for the motion along the rˆ , ϕˆ ,and ẑ directions, respectively.68