  The Josephson junction is typically tuned by a magnetic field or
electrostatic gates to realize a superconducting transistor, which manipulates
the supercurrent in integrated superconducting circuits. However, this tunable
method does not achieve simultaneous control for the supercurrent phase (phase
difference between two superconductors) and magnitude. Here, we propose a novel
scheme for the light-controlled superconducting transistor, which is composed
of two superconductor leads linked by a coherent light-driven quantum dot. We
discover a Josephson-like relation for supercurrent
$I_{\mathrm{s}}=I_{c}(\Phi)\,\sin\Phi$, where both supercurrent phase $\Phi$
and magnitude $I_{c}$ could be entirely controlled by the phase, intensity, and
detuning of the driving light. Additionally, the supercurrent magnitude
displays a Fano profile with the increase of the driving light intensity, which
is clearly understood by comparing the level splitting of the quantum dot under
light driving and the superconducting gap. Moreover, when two such
superconducting transistors form a loop, they make up a light-controlled
superconducting quantum interference device (SQUID). Such a light-controlled
SQUID could demonstrate the Josephson diode effect, and the optimized
non-reciprocal efficiency achieves up to $54\%$, surpassing the maximum record
reported in recent literature. Thus, our feasible scheme delivers a promising
platform to perform diverse and flexible manipulations in superconducting
circuits.
