We perform a joint BAO and RSD analysis using the eBOSS DR16 LRG and ELG samples in the redshift range of $zin[0.6,1.1]$, and detect a RSD signal from the cross power spectrum at a $sim4sigma$ confidence level, i.e., $fsigma_8=0.317pm0.080$ at $z_{rm eff}=0.77$. Based on the chained power spectrum, which is a new development in this work to mitigate the angular systematics, we measurement the BAO distances and growth rate simultaneously at two effective redshifts, namely, $D_{rm M}/r_{rm d} (z=0.70)=17.96pm0.51, D_{rm H}/r_{rm d} (z=0.70)=21.22pm1.20, fsigma_8 (z=0.70) =0.43pm0.05$, and $D_{rm M}/r_{rm d} (z=0.845)=18.90pm0.78, D_{rm H}/r_{rm d} (z=0.845)=20.91pm2.86, fsigma_8 (z=0.845) =0.30pm0.08$. Combined with BAO measurements including those from the eBOSS DR16 QSO and Lyman-$alpha$ sample, our measurement has raised the significance level of a nonzero $Omega_{rm Lambda}$ to $sim11sigma$.
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