Nonperturbative quantum solutions to resonant four-wave mixing of two single-photon wave packets

Abstract

We analyze both analytically and numerically the resonant four-wave mixing of two co-propagating single-photon wave packets. We present analytic expressions for the two-photon wave function and show that soliton-type quantum solutions exist which display a shape-preserving oscillatory exchange of excitations between the modes. Potential applications including quantum information processing are discussed.

Storing quantum information in a solid using dark-state polaritons

“…The first term on the right hand side of ( 30) is clearly a correction to the group velocity of the polariton pulse. Provided we remain in the regime given by (27) this results in a velocity correction factor close to unity.…”

“…Provided we remain in the regime given by (27) this results in a velocity correction factor close to unity.…”

“…We assume that both fields propagate parallel to the z direction, reducing the system to a 1D problem. Using a similar approach to [27], one can show that in the continuum limit the interaction Hamiltonian for this system is given bŷ…”

“…Furthermore, within the regime (27), Γ Ψ is bounded by γ 12 , the dephasing rate of the ground state coherence. This is logical, and indicates that the maximum storage time is limited by the lifetime of the ground state coherence.…”

Single-photon frequency conversion in nonlinear crystals

“…Bragg scattering in nonlinear fibers or FWM in atomic gases) as demonstrated for weak coherent fields [18,19] and heralded single photons [20,21]. We mention that the use of atomic ensembles as nonlinear media for single-photon frequency conversion is also being discussed [22,23], and has been experimentally demonstrated [21]. This latter approach offers a smaller bandwidth compared with nonlinear crystals, but also a better perspective for achieving coherent control [24].…”