Quantum Field Theory of Atoms and Photons

John Avery

Matti J. Lassas, Medet Nursultanov, Lauri Oksanen +1 more

We consider the quantum field theory for a scalar model of the electromagnetic field interacting with a system of two-level atoms. In this setting, we show that it is possible to uniquely determine the density of atoms from measurements of the source to solution map for a system of nonlocal partial differential equations, which describe the scattering of a two-photon state from the atoms. The required measurements involve correlating the outputs of a point detector with an integrating detector, thereby exploiting information about the entanglement of the photons.

B. K. Agarwal

Maciej Lewenstein, Li You, J. Cooper +1 more

We discuss theoretical foundations of the emerging area of quantum-optical studies of many-body systems: a quantum field theory of atoms interacting with photons. This theory is designed to describe quantum-statistical systems of cooled and trapped atoms undergoing spontaneous and stimulated emission processes. Formulated in the framework of the second quantization, this theory accounts fully for quantum-statistical properties of atoms as bosons or fermions. In particular, it applies to a description of the formation of the Bose-Einstein condensate in bosonic systems, as well as the spectroscopy and other quantum optical properties of the Bose-Einstein condensate. We derive the general second quantized Hamiltonian of this theory and discuss in detail various approximations.

Weiping Zhang, Daniel F. Walls

A vector quantum field theory is developed to describe the interaction of an ultracold atomic ensemble with a laser field. The ultracold atomic ensemble is composed of either bosonic atoms or fermionic atoms. The photon exchanges between different ultracold atoms result in a long-range interatom interaction. Under appropriate conditions, such a many-body interaction leads to an effective ``Kerr-type'' nonlinearity of atomic waves. In terms of the nonlinearity, we construct a general formalism of nonlinear atom optics for an ultracold atomic beam. Applying the formalism to the diffraction of an ultracold atomic beam composed of bosonic atoms by a standing-wave laser field, we find that the many-body nonlinearity induces self-phase and cross-phase modulation of diffracted atomic waves. As a result, a standing-wave laser acts as a nonlinear atomic grating which diffracts atoms in the same way as a nonlinear periodic medium diffracts photons.