(12)2.2. The Rabi Oscillation StabilizationWhen external coherent laser field was applied, the vacuum-field-induced coherence effects will be replaced by the microwave-field-induced coherence effects. The decoherence effect caused by spontaneous this site emission in the system can be suppressed by the introduction of the control of the laser field. Furthermore, the method for implementing the decoherence suppression is to change the Rabi oscillation frequency. According to the previous strategy, the transfer function of the system is constructed and then the decoherence suppression is realized through the compensation of the transfer function.We can infer from (11) that the underdamped Rabi oscillation is a typical second-order system and the open-loop transfer function is (0 < �� < 1):G(s)=K0��n2s2+2��ns+��n2.

(13)Hence, the unit step response of the open-loop system described by (10) is as follows:y(t)=K0[1?(cos??��dt+��1?��2sin?��dt)e?��nt],��d=1?��2��n.(14)Comparing formula (11) and (14), the parameters in the transfer function of damping Rabi oscillation can be obtained as follows:K0=|��|24��2+2|��|2,(15)��=3��4��2+9��2,��n=124��2+9��2.(16)If we put the open-loop transfer function (13) into a unit negative feedback system, the root locus of the closed-loop system is as Figure 2(a) shows. And the damping system is compensated on this basis. The basic idea is to make the unit step response of the compensated system become an equal amplitude oscillation through open-loop gain setting and pole-zero configuration.

The problem is how to design the compensated system so that the root locus of the closed-loop system will pass through the imaginary axis, and at the same time, the operating point of the system is at the intersection of the root locus AV-951 with the imaginary axis. A feasible solution to the problem is as follows.Add a pole s = ?p in the negative half real axis, where p > ��n. After this step, the root locus of the system is as Figure 2(b) shows.Considering that the compensated system is sensitive to the open-loop gain after step (1), then we add a zero s = ?z to locate the asymptotes of the root locus in the right side of the imaginary axis. Let ��x > 0 be the intersection of the asymptotes and the real axis. To meet the requirements of the asymptote (?p ? 2��n + z)/2 = ��x, we get z = p+2��n + 2��x, where ��x should be moderately selected to avoid causing the open-loop gain to be too large. After this step, the root locus of the system is as Figure 2(c) shows.Figure 2The root locus comparison before and after the compensation. (a) Origin root locus of the system. (b) Root locus of the system after step (1). (c) Root locus of the system after step (2).