  The two-layer square lattice quantum antiferromagnet with spins 1/2 shows a
magnetic order-disorder transition at a critical ratio of the interplane to
intraplane couplings. We investigate the dynamics of a single hole in a bilayer
antiferromagnet described by a t-J Hamiltonian. To model the spin background we
propose a ground-state wave function for the undoped system which covers both
magnetic phases and includes transverse as well as longitudinal spin
fluctuations. The photoemission spectrum is calculated using the spin-polaron
picture for the whole range of the ratio of the magnetic couplings. This allows
for the study of the hole dynamics of both sides of the magnetic order-disorder
transition. For small interplane coupling we find a quasiparticle with
properties known from the single-layer antiferromagnet, e.g., the dispersion
minimum is at (pi/2,pi/2). For large interplane coupling the hole dispersion is
similar to that of a free fermion (with reduced bandwidth). The cross-over
between these two scenarios occurs inside the antiferromagnetic phase which
indicates that the hole dynamics is governed by the local environment of the
hole.
