We report on the analysis of a deep Chandra observation of the high-magnetic field pulsar (PSR) J1119-6127 and its compact pulsar wind nebula (PWN) taken in October 2019, three years after the source went into outburst. The 0.5-7 keV post-outburst (2019) spectrum of the pulsar is best described by a two-component blackbody plus powerlaw model with a temperature of 0.2pm0.1 keV, photon index of 1.8pm0.4 and X-ray luminosity of ~1.9e33 erg s^{-1}, consistent with its pre-burst quiescent phase. We find that the pulsar has gone back to quiescence. The compact nebula shows a jet-like morphology elongated in the north-south direction, similar to the pre-burst phase. The post-outburst PWN spectrum is best fit by an absorbed powerlaw with a photon index of 2.3pm0.5 and flux of ~3.2e-14 erg cm^{-2} s^{-1} (0.5-7 keV). The PWN spectrum shows evidence of spectral softening in the post-outburst phase, with the pre-burst photon index of 1.2pm0.4 changing to 2.3pm0.5, and pre-burst luminosity of ~1.5e32 erg s^{-1} changing to 2.7e32 erg s^{-1} in the 0.5-7 keV band, suggesting magnetar outbursts can impact PWNe. The observed timescale for returning to quiescence, of just a few years, implies a rather fast cooling process and favors a scenario where J1119 is temporarily powered by magnetic energy following the magnetar outburst, in addition to its spin-down energy.
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