  In a graphene bilayer with Bernal stacking both $n=0$ and $n=1$ orbital
Landau levels have zero kinetic energy. An electronic state in the N=0 Landau
level consequently has three quantum numbers in addition to its guiding center
label: its spin, its valley index $K$ or $K^{\prime}$, and an orbital quantum
number $n=0,1.$ The two-dimensional electron gas (2DEG) in the bilayer supports
a wide variety of broken-symmetry states in which the pseudospins associated
these three quantum numbers order in a manner that is dependent on both filling
factor $\nu $ and the electric potential difference between the layers. In this
paper, we study the case of $\nu =-1$ in an external field strong enough to
freeze electronic spins. We show that an electric potential difference between
layers drives a series of transitions, starting from interlayer-coherent states
(ICS) at small potentials and leading to orbitally coherent states (OCS) that
are polarized in a single layer. Orbital pseudospins carry electric dipoles
with orientations that are ordered in the OCS and have Dzyaloshinskii-Moriya
interactions that can lead to spiral instabilities. We show that the microwave
absorption spectra of ICSs, OCSs, and the mixed states that occur at
intermediate potentials are sharply distinct.
