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

Four-wave mixing near resonance in an atomic vapor can produce relative intensity squeezed light suitable for precision measurements beyond the shot-noise limit. We develop an analytic distributed gain/loss model to describe the competition of mixing and absorption through the non-linear medium. Using a novel matrix calculus, we present closed-form expressions for the degree of relative intensity squeezing produced by this system. We use these theoretical results to analyze experimentally measured squeezing from a $^{85}$Rb vapor and demonstrate the analytic model's utility as an experimental diagnostic.Comment: 10 pages, 5 figure

Double-lambda microscopic model for entangled light generation by four-wave-mixing

Motivated by recent experiments, we study four-wave-mixing in an atomic double-{\Lambda} 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 conju- gate 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.Comment: 11 pages, 6 figures, submitted to PR

Broadband quadrature-squeezed vacuum and nonclassical photon number correlations from a nanophotonic device

We report the first demonstrations of both quadrature squeezed vacuum and photon number difference squeezing generated in an integrated nanophotonic device. Squeezed light is generated via strongly driven spontaneous four-wave mixing below threshold in silicon nitride microring resonators. The generated light is characterized with both homodyne detection and direct measurements of photon statistics using photon number-resolving transition edge sensors. We measure $1.0(1)$~dB of broadband quadrature squeezing (${\sim}4$~dB inferred on-chip) and $1.5(3)$~dB of photon number difference squeezing (${\sim}7$~dB inferred on-chip). Nearly-single temporal mode operation is achieved, with raw unheralded second-order correlations $g^{(2)}$ as high as $1.87(1)$ measured (${\sim}1.9$~when corrected for noise). Multi-photon events of over 10 photons are directly detected with rates exceeding any previous quantum optical demonstration using integrated nanophotonics. These results will have an enabling impact on scaling continuous variable quantum technology.Comment: Significant improvements and updates to photon number squeezing results and discussions, including results on single temporal mode operatio