Theory of Subradiant States of a One-Dimensional Two-Level Atom Chain

Recently, the subradiant states of one-dimensional two-level atom chains coupled to light modes were found to have decay rates obeying a universal scaling, and an unexpected fermionic character of the multiply-excited subradiant states was discovered. In this Letter, we theoretically obtain the singly-excited subradiant states, and by eliminating the superradiant modes, we demonstrate a relation between the multiply-excited subradiant states and the Tonks-Girardeau limit of the Lieb- Liniger model which explains the fermionic behavior. In addition, we identify a new family of states with correlations different from the fermionic ansatz.