  We present experimental results on the sub-Doppler Rydberg spectroscopy of
potassium in a hot cell and cold atoms, performed with two counter-propagating
laser beams of 405 nm and 980 nm in the inverted ladder-type system
(4S1/2-5P3/2-nS1/2 and nD3/2;5/2). Such an inverted ladder-type scheme is
predicted to be without sub-Doppler electromagnetically induced transparency
(EIT) feature in a thermal ensemble under the weak-probe approximation.
Instead, we utilized a strong probe field and successfully observed a
transparency window with a width narrower than 50~MHz. Our all-order numerical
simulation is in satisfactory agreement with the experimental results. This
narrow linewidth allows us to measure the energy levels of the Rydberg levels
from $n$=20-70 with improved accuracy. The deduced ionization energy agrees
with the previous measurements. Furthermore, the two-photon Rydberg excitation
scheme was applied to the cold ensembles to study the ground-state atoms
population decrease in the MOT for various Rydberg states. Our experimental
observations suggested two distinct regimes of the trap losses under different
probe detuning conditions. While the far off-resonance case (\delta p>>0) can
be described by the picture of dressed atom, the on-resonance case (\delta p~0)
reveals more interesting results. The higher Rydberg states suffer larger trap
loss. Besides, even with similar level energies, the excitation to nD states
result in faster escape of the ground-state atom from trap than nearby nS
states.
