Effects of imperfect pulses on dynamical decoupling using quantum trajectory method<xref rid="cpb_27_12_120303fn1" ref-type="fn">*</xref><fn id="cpb_27_12_120303fn1"><label>*</label><p>Project supported by the National Basic Research Program of China (Grant No. 2016YFA0301903), the National Natural Science Foundation of China (Grant Nos. 11174370, 11304387, 61632021, 11305262, and 61205108), and the Research Plan Project of the National University of Defense Technology (Grant No. ZK16-03-04).</p></fn>

Effects of imperfect pulses on dynamical decoupling using quantum trajectory method**

Project supported by the National Basic Research Program of China (Grant No. 2016YFA0301903), the National Natural Science Foundation of China (Grant Nos. 11174370, 11304387, 61632021, 11305262, and 61205108), and the Research Plan Project of the National University of Defense Technology (Grant No. ZK16-03-04).

He Lin-Ze^{1, 2, 3}, Zhang Man-Chao^{1, 2, 3}, Wu Chun-Wang^{1, 2, 3}, Xie Yi^{1, 2, 3}, Wu Wei^{1, 2, 3}, Chen Ping-Xing^{1, 2, 3, †}

(color online) (a) Threshold behavior of detuning with imperfections increasing in 6- and 30-pulse situations. Several data points are adopted to show the difference of fringe contrast from the analytical result. For certain detuning imperfections, the fringe contrast difference is increased for the 30-pulse situation because of error accumulation. For the threshold of detuning, the point where the curve rises sharply is around the threshold. As is seen, the detuning threshold for the 6-pulse situation is 5 × 10⁴ Hz and for the 30-pulse situation it is around 3 × 10⁴ Hz. The accumulation of pulses can continuously decrease the thresholds. (b) Threshold behavior of coupling strength, as well as intensity, with imperfections increasing in the 6- and 30-pulse situations. We select many data points that range from 10³ Hz to 7 × 10⁵ Hz. It is shown that the threshold for the 6-pulse situation is around 1.5 × 10⁵ Hz and for 30 pulses, it is about 3 × 10⁴ Hz. (c) Threshold behavior of phase with imperfections increasing in the 6- and 30-pulse situations. It is shown that the threshold of the phase is 0.05 rad for the 6-pulse situation and 0.01 rad for the 30-pulse situation.