  We study the emission spectrum of two distant qubits strongly coupled to a
waveguide by using the numerical and analytical approaches, which are beyond
the Markovian approximation and the rotating-wave approximation (RWA). The
numerical approach combines the Dirac-Frenkel time-dependent variational
principle with the multiple Davydov $D_{1}$ ansatz. A transformed RWA (TRWA)
treatment and a standard perturbation (SP) are used to analytically calculate
the emission spectrum. It is found that the variational approach and the TRWA
treatment yield accurate emission spectra of the two distant qubits in certain
strong coupling regimes while the SP breaks down. The emission spectrum is
found to be asymmetric irrespective of the two-qubit distance and exhibits a
single peak, doublet, and multipeaks depending on the two-qubit distance as
well as the initial states. In sharply contrast with the single-qubit case, the
excited-state populations of the two qubits can ultraslowly decay due to the
subradiance even in the presence of a strong qubit-waveguide coupling, which in
turn yields ultranarrow emission line. Our results provide insights into the
emission spectral features of the two distant qubits in the strong light-matter
coupling regime.
