Optical conductivity of at−Jladder

The optical conductivity $\sigma \left(\omega \right)$ of a doped two-leg $t-J$ ladder is calculated for an electric field polarized parallel to the legs of the ladder. The low- and high-electron-density regimes behave differently, exhibiting Tomonaga-Luttinger-like and Luther-Emery-like behavior, respectively. We concentrate on the hole-doped region where the conductivity has a Drude weight proportional to the hole doping and an apparent threshold for absorption (a pseudogap) which may be associated with the energy to break a pair. This pseudogap in $\sigma \left(\omega \right)$ is present even though the pairs have a modified $d_{x^2-y^2}$-like wave function because the geometry of the ladder leads to quasiparticle states which probe the gap along an antinode.