  We present deep imaging of Sirius B, the closest and brightest white dwarf,
to constrain post-main-sequence planetary evolution in the Sirius system. We
use Keck/NIRC2 in L'-band (3.776 $\mu$m) across three epochs in 2020 using the
technique of angular differential imaging. Our observations are speckle-limited
out to 1 AU and background-limited beyond. The 5$\sigma$ detection limits from
our best performing epoch are 17 to 20.4 L' absolute magnitude. We consider
multiple planetary formation pathways in the context of Sirius B's evolution to
derive mass sensitivity limits, and achieve sub-Jupiter sensitivities at sub-AU
separations, reaching 1.6 $\mathrm{M_J}$ to 2.4 $\mathrm{M_J}$ at 0.5 AU down
to a sensitivity of 0.7 $\mathrm{M_J}$ to 1.2 $\mathrm{M_J}$ at >1 AU.
Consistent with previous results, we do not detect any companions around Sirius
B. Our strong detection limits demonstrate the potential of using high-contrast
imaging to characterize nearby white dwarfs.
