Azimuthal quantum number dependent two dimensional atom microscopy, via atom cavity coupling

zimuthal quantum number dependent two dimensional atom microscopy via atom cavity coupling is investigated in this manuscript. The study finds that the number of localization peaks is closely tied to the azimuthal quantum number and the phase of the control field. Specifically, increasing the value of the azimuthal quantum number in the control field leads to a significant enhancement of the localization peaks in the absorption spectrum within a unit wavelength range. The degree of enhancement of the localization peaks follows a quadratic relationship with l^2 at control field phases of φ =0,π ,2π , and also with 2l^2 at a control field phase of φ =π /2 . The spatial resolution of the localized peaks in the absorption spectrum is found to be proportional to λ /3l×λ /3l . These findings could have practical applications in atom trapping and nano-lithography technology.