Quantum nonlinear optics provides a means to generate and manipulate light at the quantum level, with applications in enhanced sensing and metrology, and in quantum information processing and networking. Nonlinear optics requires a nonlinear medium to interact with the light, and we take two approaches to generating, controlling and exploiting quantum properties light using atomic vapors as the nonlinear medium. First, we have developed a 4-wave mixing technology in thermal atomic vapors for generating non-classical light. This system allows us to generate squeezed light in a straightforward way that is not technically demanding. ("Squeezed light" is light with noise properties below the "standard quantum limit" achievable with a coherent state; the coherent state being the closest possible approximation to a classical state.) This light has properties that, in turn, can be used to enhance optical trace-detection capabilities, as well as to enhance interferometry. Our technique allows the squeezed light to be generated in multiple spatial modes (images) and this allows us to directly apply such sub-shot-noise advantages to image processing applications. In addition the light is narrow in frequency and can interact strongly with laser-cooled atoms and can thus be used in quantum information processing and quantum memory applications. In a second approach, we use strong interactions between Rydberg-excited atoms in an ensemble of trapped, laser cooled atoms to generate strong nonlinearities at the two-photon level. Such few-photon nonlinearities can be either dissipative or coherent, and can be used for a variety of applications, from single photon sources to quantum gates between pairs of photons.
We have generated "twin beams" of light using four-wave mixing (4WM) that are correlated at a level better than can be displayed by classical radiators. One particularly useful feature of the 4WM technique is that the light can easily be made in multiple spatial modes. That is, images with quantum correlations can be produced. Pixel-by-pixel, the light in these pairs of images is correlated to levels better than the shot noise of the photon numbers involved. Light in the corresponding pixels is not just correlated in intensity, but also in phase. The intensity-difference and the phase-sum are quadrature variables displaying quantum entanglement at levels that violate the inequality expressing the Einstein-Podolsky-Rosen paradox. Measurements of the phase involve generating "local oscillator" phase references with the 4-wave mixing as well. Quantum-correlated and entangled images can be used for faint-object detection (a small absorption or scattering from one of the beams, even at a level below the shot noise, can be detected in the differencing between the beams). Another use of such images is in information storage. The parallel storage of quantum information in images is important for quantum information processing applications. The correlated and quantum-entangled beams that we generate are entangled in continuous variables (phase and amplitude rather than discrete variables like polarization, which has only two possibilities). The fields of quantum communications and quantum information processing using continuous variables are relatively less-developed than the corresponding discrete-variable studies. Our ability to generate entangled beams of narrowband light near atomic resonance frequencies will allow us to pursue the study of continuous-variable quantum communications. Not only can this light interact readily with hot atoms in a vapor cell, but also with laser-cooled atoms, and the generation and transfer of quantum information between sources and memory devices can be studied. In addition, we have studied the effect of optical dispersion (group velocities both slower and faster than the speed of light in vacuum) on the propagation of quantum information. The effects in both phase-sensitive (noiseless) and phase-insensitive optical amplifiers are being studied.