Coherent perfect absorption in a homogeneously-broadened two-level medium

In recent works, it has been shown rather generally that the time-reversed process of lasing at threshold realizes a coherent perfect absorber (CPA). In a CPA, a lossy medium in an optical cavity with a specific degree of dissipation, equal in modulus to the gain of the lasing medium, can perfectly absorb coherent optical waves that are the time-reversed counterpart of the lasing field. Here the time-reversed process of lasing is considered in details for a homogeneously-broadened two-level medium in an optical cavity, and the conditions for CPA are derived. It is shown that, owing to the dispersive properties of the two-level medium, exact time-reversal symmetry is broken and the frequency of the field at which CPA occurs is generally different than the one of the lasing mode. Moreover, at a large cooperation parameter the observation of CPA in the presence of bistability requires to operate in the upper branch of the hysteresis cycle.