Quantum theory of resonantly enhanced four-wave mixing: mean-field and exact numerical solutions

Abstract

We present a full quantum analysis of resonant forward four-wave mixing based on electromagnetically induced transparency (EIT). In particular, we study the regime of efficient nonlinear conversion with low-intensity fields that has been predicted from a semiclassical analysis. We derive an effective nonlinear interaction Hamiltonian in the adiabatic limit. In contrast to conventional nonlinear optics this Hamiltonian does not have a power expansion in the fields and the conversion length increases with the input power. We analyze the stationary wave-mixing process in the forward scattering configuration using an exact numerical analysis for up to $10^3$ input photons and compare the results with a mean-field approach. Due to quantum effects, complete conversion from the two pump fields into the signal and idler modes is achieved only asymptotically for large coherent pump intensities or for pump fields in few-photon Fock states. The signal and idler fields are perfectly quantum correlated which has potential applications in quantum communication schemes. We also discuss the implementation of a single-photon phase gate for continuous quantum computation.

10 pages, 11 figures

References in corpus (1)

• Resonant nonlinear optics in coherently prepared media: full analytic solutions

Cited by in corpus (10)

• Multiphoton Quantum Optics and Quantum State Engineering
• Low-light-level nonlinear optics with slow light
• Buffer-gas induced absorption resonances in Rb vapor
• Storing quantum information using dark state polaritons
• Phase-dependent light propagation in atomic vapors
• Arrayed and checkerboard optical waveguides controlled by the electromagnetically-induced transparency
• Efficient photon counting and single-photon generation using resonant nonlinear optics
• Full quantum solutions to the resonant four-wave mixing of two single-photon wave packets
• Analysis of Quantum Light Memory in Atomic Systems
• An integrable (classical and quantum) four-wave mixing Hamiltonian system