Quantum limits, nonseparable transformations, and nonlinear optics

Lie-type transformations and effective Hamiltonians in nonlinear quantum optics: applications to multilevel systems

We reelaborate on a general method for diagonalizing a wide class of nonlinear Hamiltonians describing different quantum optical models. This method makes use of a nonlinear deformation of the usual su(2) algebra and when some physical parameter, dictated by the particular model under consideration, becomes small, it gives a diagonal effective Hamiltonian that describes correctly the dynamics f...

Physics 673 : Nonlinear and Quantum Optics

Nonlinear quantum optics mediated by Rydberg interactions

By mapping the strong interaction between Rydberg excitations in ultra-cold atomic ensembles onto single photons via electromagnetically induced transparency, it is now possible to realize a medium which exhibits a strong optical nonlinearity at the level of individual photons. We review the theoretical concepts and the experimental state-of-the-art of this exciting new field, and discuss first...

The beginning of quantum nonlinear optics [Invited]

When asked to talk at the symposium celebrating the fiftieth birthday of nonlinear optics in Kauai last July, I needed to decide on an interesting approach beyond that of rehashing the, by now familiar, scientific facts. The work that I will describe has to do with the quantum mechanical formalism for nonlinear optics. Although the implications of this theory are fundamental and continue to unf...

Nonlinear optics quantum computing with circuit QED.

One approach to quantum information processing is to use photons as quantum bits and rely on linear optical elements for most operations. However, some optical nonlinearity is necessary to enable universal quantum computing. Here, we suggest a circuit-QED approach to nonlinear optics quantum computing in the microwave regime, including a deterministic two-photon phase gate. Our specific example...