  We calculate the ground state of a Bose gas trapped on a two-leg ladder where
Raman-induced hopping mimics the effect of a large magnetic field. In the
mean-field limit, where there are large numbers of particles per site, this
maps onto a uniformly frustrated two-leg ladder classical spin model. The net
particle current always vanishes in the ground state, but generically there is
a finite "chiral current", corresponding to equal and opposite flow on the two
legs. We vary the strength of the hopping across the rungs of the ladder and
the interaction between the bosons. We find three phases: (1) A "saturated
chiral current phase" (SCCP), where the density is uniform and the chiral
current is simply related to the strength of the magnetic field. In this state
the only broken symmetry is the $U(1)$ condensate phase. (2) A "biased ladder
phase" (BLP), where the density is higher on one leg than the other. The fluid
velocity is higher on the lower density leg, so the net current is zero. In
addition to the $U(1)$ condensate phase, this has a broken $Z_2$ reflection
symmetry. (3) A "modulated density phase" (MDP), where the atomic density is
modulated along the ladder. In addition to the $U(1)$ condensate phase, this
has a second broken $U(1)$ symmetry corresponding to translations of the
density wave. We further study the fluctuations of the condensate in the BLP,
finding a roton-maxon like excitation spectrum. Decreasing the hopping along
the rungs softens the spectrum. As the energy of the "roton" reaches to zero,
the BLP becomes unstable. We describe the experimental signatures of these
phases, including the response to changing the frequency of the Raman
transition.
