  This paper considers ground states of mass subcritical rotational nonlinear
Schr\"{o}dinger equation \begin{equation*} -\Delta
u+V(x)u+i\Omega(x^\perp\cdot\nabla u)=\mu u+\rho^{p-1}|u|^{p-1}u \,\ \text{in}
\,\ \mathbb{R}^2, \end{equation*} where $V(x)$ is an external potential,
$\Omega>0$ characterizes the rotational velocity of the trap $V(x)$, $1<p<3$
and $\rho>0$ describes the strength of the attractive interactions. It is shown
that ground states of the above equation can be described equivalently by
minimizers of the $L^2-$ constrained variational problem. We prove that
minimizers exist for any $\rho\in(0,\infty)$ when $0<\Omega<\Omega^*$, where
$0<\Omega^*:=\Omega^*(V)<\infty$ denotes the critical rotational velocity of
$V(x)$. While $\Omega>\Omega^*$, there admits no minimizers for any
$\rho\in(0,\infty)$. For fixed $0<\Omega<\Omega^*$, by using energy estimates
and blow-up analysis, we also analyze the limit behavior of minimizers as
$\rho\to\infty$. Finally, we prove that up to a constant phase, there exists a
unique minimizer when $\rho>0$ is large enough and $\Omega\in(0,\Omega^*)$ is
fixed.
