  Luttinger liquids (LLs) arise by coupling left- and right-moving particles
through interactions in one dimension. This most natural partitioning of LLs is
investigated by the momentum-space entanglement after a quantum quench using
analytical and numerical methods. We show that the momentum-space entanglement
spectrum of a LL possesses many universal features both in equilibrium and
after a quantum quench. The largest entanglement eigenvalue is identical to the
Loschmidt echo, i.e. the overlap of the disentangled and final wavefunctions of
the system. The second largest eigenvalue is the overlap of the first excited
state of the disentangled system with zero total momentum and the final
wavefunction. The entanglement gap is universal both in equilibrium and after a
quantum quench. The momentum-space entanglement entropy is always extensive and
saturates fast to a time independent value after the quench, in sharp contrast
to a spatial bipartitioning.
