  Entanglement asymmetry is a quantity recently introduced to measure how much
a symmetry is broken in a part of an extended quantum system. It has been
employed to analyze the non-equilibrium dynamics of a broken symmetry after a
global quantum quench with a Hamiltonian that preserves it. In this work, we
carry out a comprehensive analysis of the entanglement asymmetry at equilibrium
taking the ground state of the XY spin chain, which breaks the $U(1)$ particle
number symmetry, and provide a physical interpretation of it in terms of
superconducting Cooper pairs. We also consider quenches from this ground state
to the XX spin chain, which preserves the broken $U(1)$ symmetry. In this case,
the entanglement asymmetry reveals that the more the symmetry is initially
broken, the faster it may be restored in a subsystem, a surprising and
counter-intuitive phenomenon that is a type of a quantum Mpemba effect. We
obtain a quasi-particle picture for the entanglement asymmetry in terms of
Cooper pairs, from which we derive the microscopic conditions to observe the
quantum Mpemba effect in this system, giving further support to the criteria
recently proposed for arbitrary integrable quantum systems. In addition, we
find that the power law governing symmetry restoration depends discontinuously
on whether the initial state is critical or not, leading to new forms of strong
and weak Mpemba effects.
