  Flux ladders constitute the minimal setup enabling a systematic understanding
of the rich physics of interacting particles subjected simultaneously to strong
magnetic fields and a lattice potential. In this paper, the ground-state phase
diagram of a flux-ladder model is mapped out using extensive density-matrix
renormalization-group simulations. The emphasis is put on parameters which can
be experimentally realized exploiting the internal states of potassium atoms as
a synthetic dimension. The focus is on accessible observables such as the
chiral current and the leg-population imbalance. Considering a particle filling
of one boson per rung, we report the existence of a Mott-insulating Meissner
phase as well as biased-ladder phases on top of superfluids and Mott
insulators. Furthermore, we demonstrate that quantum quenches from suitably
chosen initial states can be used to probe the equilibrium properties in the
transient dynamics. Concretely, we consider the instantaneous turning on of
hopping matrix elements along the rungs or legs in the synthetic flux-ladder
model, with different initial particle distributions. We show that clear
signatures of the biased-ladder phase can be observed in the transient
dynamics. Moreover, the behavior of the chiral current in the transient
dynamics is discussed. The results presented in this paper provide guidelines
for future implementations of flux ladders in experimental setups exploiting a
synthetic dimension.
