  $^{133}$Cs, which is the only stable cesium (Cs) isotope, is one of the most
investigated elements in atomic spectroscopy and was used to realize the atomic
clock in 1955. Among all atomic clocks, the cesium atomic clock has a special
place, since the current unit of time is based on a microwave transition in the
Cs atom. In addition, the long lifetime of the $6{\text{P}}_{3/2}$ state and
simple preparation technique of Cs vapor cells have great relevance to quantum
and atom optics experiments, which suggests the use of the $6{\text{S}} -
6{\text{P}}$ D2 transition as an optical frequency standard. In this work,
using one laser as the local oscillator and Cs atoms as the quantum reference,
we realized two atomic clocks in the optical and microwave frequencies,
respectively. Both clocks could be freely switched or simultaneously output.
The optical clock based on the vapor cell continuously operated with a
frequency stability of $3.89 \times {10^{ - 13}}$ at 1 s, decreasing to $2.17
\times {10^{ - 13}}$ at 32 s, which was frequency stabilized by modulation
transfer spectroscopy and estimated by an optical comb. Then, applying this
stabilized laser for an optically pumped Cs beam atomic clock to reduce the
laser frequency noise, we obtained a microwave clock with a frequency stability
of $1.84 \times {10^{ - 12}}/\sqrt \tau $, reaching $5.99 \times {10^{ - 15}}$
at $10^5$ s. This study demonstrates an attractive feature for the
commercialization and deployment of optical and microwave clocks and will guide
further development of integrated atomic clocks with better stability. Thus,
this study lays the groundwork for future quantum metrology and laser physics.
