Coherent THz-wave emission from voltage- and number-controlled intrinsic Josephson junctions in Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+\delta }$

Intense and coherent terahertz electromagnetic wave (THz-wave) emission from the intrinsic Josephson junctions (IJJs) in single crystalline high-$T_{c}$ superconductor Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+\delta }$ (Bi-2212) was reported in 2007 [L. Ozyuzer \textit{et al}., Science \textbf{318}, (2007) 1291.]. In the present work, we demonstrate the relationship between the bias condition and the resonance state by controlling both the applied voltage, $V$, and the number of resistive junctions, $N$. We directly observed that if $N$ junctions are in resistive state, the resonance frequency, $f_{J}$, varies in accordance with the ac-Josephson relation; $f_{J}$ = (2$\vert e\vert $/$h)V$/$N$, although frequency $f_{J}$ has previously been thought to be uniquely determined by the geometrical condition due to the cavity resonance effect [M. Tsujimoto \textit{et al}., Phys. Rev. Lett. \textbf{105}, (2010) 037005.]. We also found that the emission intensity varies as a function of both $f_{J}$ and $N$.