We theoretically investigate rapid adiabatic passage(RAP)-based
super-resolution imaging in a two-level quantum dot system interacting with two
structured beams. To understand the physical mechanism behind the formation of
super-resolution for the experiment of Kaldewey {\it et. al.,}[Nature Photonics
10.1038/s41566-017-0079-y (2018)], we first use Liouville's density matrix
where photon-mediated radiative and non-radiative decays are incorporated. A
suitably chosen spatiotemporal envelope of the structured beams enables the
formation of a super-resolution image. We also find that the feature size of
the image depends on the intensity of the Laguerre Gaussian beam(LG). However,
the created image resolution undergoes distortion due to the existence of a
low-intensity circular ring. The unwanted circular ring arises from the
dominance of the LG beam tail over the super-Gaussian(SG) beam tail, initiating
the residual population transfer from the ground state to the excited state.
This limitation can be overcome by using the Bessel-modulated truncated
structured LG and SG beams. We next study the dynamics of the semiconductor
quantum dot system at finite temperatures wherein the phonon interaction
becomes imperative. We employ the polaron-transformed master equation to
explore the system at higher temperatures. Our numerical results confirm that
the sharpness of the image remains intact at low temperatures with weak phonon
coupling. Hence, the proposed scheme may open up applications in nano-scale
imaging with quantum dots.Comment: 14 pages, 12 figure