  In this paper, we try to understand the pseudogap phenomenon observed in the
cuprate superconductor through a model study. Specifically, we explore the
so-called low-temperature pseudogap state by turning off the superconducting
off diagonal long range order in an ansatz state for the $t$-$J$ model [New
Journal of Physics {\bf 13}, 103039 (2011)]. Besides strong non-Gaussian
superconducting fluctuations, the resulting state also exhibits a systematic
pseudogap behavior in both spin and charge degrees of freedom, manifested in
the uniform spin susceptibility, specific heat, non-Drude resistivity, Nernst
effect, as well as the quantum oscillation associated with small Fermi pockets
emerging in strong magnetic fields, etc. These anomalous `normal state'
properties are found in qualitative consistency with experimental measurements
in the cuprates. Such a model study establishes an intrinsic connection between
the peculiar pseudogap properties and the non-BCS nature of the superconducting
ground state. Critical comparison with other approaches to the doped Mott
insulator is also made.
