  Experimental realizations of chimera patterns, characterized by coexisting
regions of phase coherence and incoherence, have so far only been achieved for
non-conservative systems with dissipation. Moreover, theoretical studies of
chimera patterns have also been limited either to the non-conservative case or
to simplified models that describe the dynamics only in terms of a scalar phase
field. Here, we show for the first time explicitly that the formation of
chimera patterns can also be observed in conservative Hamiltonian systems with
nonlocal hopping in which both energy and particle number are conserved, and
where the local phase and amplitude are non-separable even in the weak coupling
regime. Effective nonlocality can be realized in a physical system with only
local coupling if different time scales exist, which we illustrate by a minimal
conservative model with an additional mediating channel. Finally, we show that
chimera patterns should be observable in ultracold atomic systems: Nonlocal
spatial hopping over up to tens of lattice sites with independently tunable
hopping strength and on-site nonlinearity can be implemented in a two-component
Bose-Einstein condensate with a spin-dependent optical lattice, where the
untrapped component serves as the matter-wave mediating field.
