  In this paper, the first femtoscopic analysis of pion-kaon correlations at
the LHC is reported. The analysis was performed on the Pb-Pb collision data at
$\sqrt{s_{\rm{NN}}}$ = 2.76 TeV recorded with the ALICE detector. The
non-identical particle correlations probe the spatio-temporal separation
between sources of different particle species as well as the average source
size of the emitting system. The sizes of the pion and kaon sources increase
with centrality, and pions are emitted closer to the centre of the system
and/or later than kaons. This is naturally expected in a system with strong
radial flow and is qualitatively reproduced by hydrodynamic models. ALICE data
on pion-kaon emission asymmetry are consistent with (3+1)-dimensional viscous
hydrodynamics coupled to a statistical hadronization model, resonance
propagation, and decay code THERMINATOR 2 calculation, with an additional time
delay between 1 and 2 fm$/c$ for kaons. The delay can be interpreted as
evidence for a significant hadronic rescattering phase in heavy-ion collisions
at the LHC.
