  On the recent report of a magnetic field induced first order transition
between an even-parity superconductivity and an odd-parity superconductivity in
$\mathrm{CeRh_{2}As_{2}}$, the microscopic physics is still under
investigation. However, if, in the vicinity of this transition, the coupling
strengths of the even and odd pairing channels are comparable, a
particle-particle excitonic collective mode referred to as the
Bardasis-Schrieffer (BS) mode should generically exist below the pair-breaking
continuum. This BS mode can couple to the light and thus affect the optical
response of the superconductor, as it arises from a pairing channel with the
parity opposite to that of the ground state pairs. Here, by using a generic
bilayer model Hamiltonian for the electronic degree of freedom, which is
globally centrosymmetric despite each layer being locally non-centrosymmetric,
we study the change of the excitation gap of the BS mode with respect to the
out-of-plane magnetic fields and demonstrate that its coupling to the light is
possible even in the linear response regime. The linear coupling is attributed
to the presence of multiple electronic bands, which is a generic feature of a
bilayer system. Our result shows the microwave absorption as the signature of
the BS mode, and hence a smoking gun signature of the parity-switching at the
transition between two superconducting phases.
