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Two beams of light can be quantum mechanically entangled through correlations of their phase and intensity fluctuations. For a pair of spatially extended image-carrying light fields, the concept of entanglement can be applied not only to the entire images but also to their smaller details. We used a spatially multimode amplifier based on four-wave mixing in a hot vapor to produce twin images that exhibit localized entanglement. The images can be bright fields that display position-dependent quantum noise reduction in their intensity difference or vacuum twin beams that are strongly entangled when projected onto a large range of different spatial modes. The high degree of spatial entanglement demonstrates that the system is an ideal source for parallel continuous-variable quantum information protocols.

Non-degenerate forward four-wave mixing in hot atomic vapors has been shown to produce strong quantum correlations between twin beams of light [McCormick et al, Opt. Lett. 32, 178 (2007)], in a configuration which minimizes losses by absorption. In this paper, we look at the role of the phase-matching condition in the trade-off that occurs between the efficiency of the nonlinear process and the absorption of the twin beams. To this effect, we develop a semi-classical model by deriving the atomic susceptibilities in the relevant double-lambda configuration and by solving the classical propagation of the twin-beam fields for parameters close to those found in typical experiments. These theoretical results are confirmed by a simple experimental study of the nonlinear gain experienced by the twin beams as a function of the phase mismatch. The model shows that the amount of phase mismatch is key to the realization of the physical conditions in which the absorption of the twin beams is minimized while the cross-coupling between the twin beams is maintained at the level required for the generation of strong quantum correlations. The optimum is reached when the four-wave mixing process is not fully phase matched., 10 pages, 9 figures

We perform theoretical and experimental studies of the effect of phase matching on the generation of entangled twin beams with four-wave mixing. We find that it plays a critical role on the optimum parameters for the process.

We show that non-degenerate four-wave mixing in an atomic vapor can be used as a quantum delay line for multi-spatial-mode twin beams. This makes it possible to delay continuous variable entangled images without significant degradation.

We have observed a violation of the Cauchy-Schwarz inequality in the macroscopic regime by more than 8 standard deviations. The violation has been obtained while filtering out only the low frequency noise of the quantum-correlated beams that results from the technical noise of the laser used to generate them. We use bright intensity-difference squeezed beams produced by four-wave mixing as the source of the correlated fields. We also demonstrate that squeezing does not necessarily imply a violation of the Cauchy-Schwarz inequality., 5 pages, 4 figures

We use a four-wave mixing process in an atomic system to delay quantum correlations in twin beams. We have obtained a delay of 13 ns without a significant degradation of the intensity-difference squeezing.

Entangled multi-spatial-mode fields have interesting applications in quantum information, such as parallel quantum information protocols, quantum computing, and quantum imaging. We study the use of a nondegenerate four-wave mixing process in rubidium vapor at 795 nm to demonstrate generation of quantum-entangled images. Owing to the lack of an optical resonator cavity, the four-wave mixing scheme generates inherently multi-spatial-mode output fields. We have verified the presence of entanglement between the multi-mode beams by analyzing the amplitude difference and the phase sum noise using a dual homodyne detection scheme, measuring more than 4 dB of squeezing in both cases. This paper will discuss the quantum properties of amplifiers based on four-wave-mixing, along with the multi mode properties of such devices., Comment: 11 pages, 8 figures. SPIE Optics and Photonics 2008 proceeding (San Diego, CA)

We have measured ?6.3 dB of relative intensity squeezing at 795 nm, generated by stimulated, nondegenerate four-wave mixing in a hot rubidium vapor. This scheme is of interest for experiments involving cold atoms or atomic ensembles.

We have observed a very clean slow light effect and matched pulse propagation in nondegenerate four-wave mixing in hot atomic vapor. Locking between probe and conjugate pulses gives some insight in the nonlinear dynamics.

We show that a simple scheme based on nondegenerate four-wave mixing in a hot atomic vapor behaves like a near-perfect phase-insensitive optical amplifier, which can generate bright twin beams with a measured quantum noise reduction in the intensity difference of more than 8 dB, close to the best optical parametric amplifiers and oscillators. The absence of a cavity makes the system immune to external perturbations, and the strong quantum noise reduction is observed over a large frequency range., 4 pages, 4 figures. Major rewrite of the previous version. New experimental results and further analysis

We use nondegenerate four-wave mixing in hot atomic vapor to measure up to -7.1dB of relative-intensity squeezing. This narrowband, squeezed light near an atomic resonance is of interest for experiments involving atomic ensembles. Article not available.

We demonstrate multi-spatial-mode, nondegenerate four-wave mixing in hot atomic Rb vapor. We generate images with strong intensity-difference squeezing between the amplified probe and the generated conjugate beams. Measurements to quantify the multi-mode nature of the beams will be presented. We also report on progress in improving the relative-intensity squeezing. This narrowband, squeezed light near an atomic resonance is also of interest for experiments involving atomic ensembles.

We use a four-wave mixing process to generate relative-intensity squeezing. We are able to significantly modify the squeezing spectrum by controlling the relative delay between the probe and conjugate beams.

We have observed the ultraslow propagation of matched pulses in nondegenerate four-wave mixing in a hot atomic vapor. Probe pulses as short as 70 ns can be delayed by a tunable time of up to 40 ns with little broadening or distortion. During the propagation, a probe pulse is amplified and generates a conjugate pulse which is faster and separates from the probe pulse before getting locked to it at a fixed delay. The precise timing of this process allows us to determine the key coefficients of the susceptibility tensor. The presence of gain in this system makes this system very interesting in the context of all-optical information processing., Comment: 5 pages, 4 figures

We report our progress towards the realization of a tunable and narrow-band source of correlated photons for coherent manipulation of cold atoms, using a combination of four-wave mixing and electromagnetically induced transparency.

We have demonstrated 3dB relative intensity squeezing from a non-degenerate four-wave mixing scheme in hot atomic rubidium vapor. The generated twin beams are narrowband and are suitable for atomic manipulation.

We present experimental results showing that quantum correlated light can be produced using non-degenerate, off-resonant, four-wave mixing (4WM) on both the D1 (795 nm) and D2 (780 nm) lines of (85)Rb and (87)Rb, extending earlier work on the D1 line of (85)Rb. Using this 4WM process in a hot vapor cell to produce bright twin beams, we characterize the degree of intensity-difference noise reduction below the standard quantum limit for each of the four systems. Although each system approximates a double-lambda configuration, differences in details of the actual level structure lead to varying degrees of noise reduction. The observation of quantum correlations on light produced using all four of these systems, regardless of their substructure, suggests that it should be possible to use other systems with similar level structures in order to produce narrow frequency, non-classical beams at a particular wavelength.

Quantum Optics: It is now possible to conduct optical experiments on systems that exhibit strongly correlated behavior.