Absorptionless self-phase-modulation via dark-state electromagnetically induced transparency

The closely related phenomena of dark states and electromagnetically induced transparency ~EIT! have greatly enriched the fields of nonlinear and quantum optics in recent years. Although these two processes produce similar effects, they have important distinctions. Atomic dark states @1,2# are coherent superpositions of the two lower levels in a threelevel lambda (L) system that are not coupled to the excited state by the two applied laser fields. An atom prepared in a dark state will not absorb the incident fields, have no excitedstate population, and thus no spontaneous emission. Unfortunately for many applications in nonlinear optics, self-phase modulation also vanishes along with absorption. Electromagnetically induced transparency @3,4# is a pump-probe effect that provides transparency in a variety of systems @5#. While dark states are specific to L configurations, EIT occurs more generally: in two-level @6#, cascaded three-level @7#, and four-level systems @8#. In these systems there can be large third-order susceptibility, and thus self-phase modulation, in the absence of absorption of the probe field @9#. Unfortunately, spontaneous emission cannot be eliminated completely in these systems. The presence of spontaneous emission with associated noise limits the use of these EIT systems for noise-sensitive applications such as squeezed-light generation @10#. One possible exception using four fields is the double lambda system @11#, which has been shown to produce a large third-order nonlinear susceptibility in the absence of absorption @9#. In this paper, we combine the benefits of dark states and two-level EIT to create a system that has no absorption, while still possessing large self-phase modulation ~SPM! of the signal field. There is no absorption of the pump fields and, in addition, spontaneous-emission noise is eliminated because there is no population in the excited state. Such a system would be useful for applications such as squeezedlight generation via self-phase modulation and spatial soliton propagation. It should be noted that there is a recent study on the linear absorption of such a system @12#. Gain profiles have also been studied in a lambda system, where a single