We use time-domain terahertz spectroscopy to measure the low energy conductivity and magnons in RuCl$_3$ under external magnetic field. At zero field, an oscillation with a frequency of 0.62 THz is clearly observed in time-domain spectrum below T$_N$, which is identified as a magnon excitation in the magnetic order state. The magnon excitation is not affected by the external magnetic field $textbf{H}_{DC}$ when it is applied along the c-axis, but is clearly suppressed when $textbf{H}_{DC}$ is applied within ab plane. More interestingly, when the magnetic component of THz wave $textbf{h}(t)$ is perpendicular to the applied in-plane magnetic field, we observe another coherent oscillation at slightly higher energy scale at the field above 2 T, which is eventually suppressed for $H_{DC}>$5 T. The measurement seems to indicate that the in-plane magnetic field can lift the degeneracy of two branches of low energy magnons at $Gamma$ point. The low energy optical conductivity calculated from the measured transmission spectrum is dominated by a broad continuum contribution, which is not affected by changing either temperature or external magnetic field. The continuum is likely to be related to the fractional spin excitation due to dominated Kitaev interaction in the material.
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