Figure 10.6 — Stability diagram

Fig. 10.6 — Stability diagram
Figure 10.6 — Stability diagram. Stability diagram of a particle in a potential well as a function of the parameters γΩ/κ and Δκ/κ. The parameters corresponding to the white region are stable, i.e., satisfy the stability conditions given in Eq. (10.13). The dashed line represents Δκ = κ and the dotted line represents the Δκ = γ|Ω| curves. The standard PFM, discussed in Section 10.1, corresponds to Δκ = 0 and Ω = 0. When a rotational term is added, i.e., Ω ≠ 0 and Δκ = 0, the system remains stable. When there is no rotational contribution to the force field (Ω = 0), the equilibrium point becomes unstable as soon as Δκ ≥ κ , as this implicates that κy􏰚 < 0 and, therefore, the probe is not confined along the y-direction. In the presence of a rotational component (Ω ≠ 0), the stability region becomes larger, as the equilibrium point now becomes unstable only for Δκ ≥ (κ2 + γ2Ω2)0.5. The circles represent the parameters that are further investigated in Fig. 10.4 and the squares those that are investigated in Fig. 10.5.