Double-Λmicroscopic model for entangled light generation by four-wave mixing

Abstract

Motivated by recent experiments, we study four-wave-mixing in an atomic double-Λ system driven by a far-detuned pump. Using the Heisenberg-Langevin formalism, and based on the microscopic properties of the medium, we calculate the classical and quantum properties of seed and conjugate beams beyond the linear amplifier approximation. A continuous variable approach gives us access to relative-intensity noise spectra that can be directly compared to experiments. Restricting ourselves to the cold-atom regime, we predict the generation of quantum-correlated beams with a relative-intensity noise spectrum well below the standard quantum limit (down to -6 dB). Moreover entanglement between seed and conjugate beams measured by an inseparability down to 0.25 is expected. This work opens the way to the generation of entangled beams by four-wave mixing in a cold atomic sample.PACS numbers:

Relative intensity squeezing by four-wave mixing with loss: an analytic model and experimental diagnostic

“…Earlier theoretical investigations of this system have applied numerical methods [3] and the Heisenberg-Langevin formalism [8] to predict the resulting degree of squeezing. The numerical model demonstrated excellent agreement with experimental results, but it can be difficult to gain insight into the competing processes from numerical calculations.…”

Theory of noise suppression inΛ-type quantum memories by means of a cavity

“…The complex decay rates κ s,a account for dispersion, absorption and other scattering losses as the fields propagate. Strictly the losses in (4) should be accompanied by Langevin noise operators which maintain the bosonic commutation relations of the field operators [46]. But vacuum noise entering due to losses experienced by the signal field does not contribute to the signal intensi-ties or autocorrelations that we will compute, and antiStokes absorption and atomic decoherence are negligible in the Λ-memory configuration considered, thus we neglect Langevin forces [32].…”

Overcoming classical measurement limits through entanglement in photon number: an introduction

“…For this purpose, a source of correlated beams exploiting four wave mixing (4WM) in hot atomic vapor is a good candidate [19][20][21][22]. Four-wave mixing is indeed a known source of intense nonclassical twin beams: in fact, the first experimental demonstration of squeezed light was actually made using 4WM with sodium atoms [23].…”