Quantum coherence, control and distinguishability in experiments with atoms and photons

The past few years have seen a great deal of work on characterization of quantum states and prevention or correction of errors in quantum systems. In this talk I will discuss some of the complications which arise in real systems, in particular, multi-photon entangled states constructed by combining photons from different sources in single- mode fibre, and laser-cooled atoms trapped in the wells of an optical lattice. We have been generating 3-photon entangled states by combining photon pairs from spontaneous parametric down-conversion with single laser photons in a non-unitary process. We are studying a variety of states potentially useful for metrology applications. In order to fully characterize and optimize this system, taking into account background rates made inevitable by the non-single-photon nature of the sources as well as the imperfect indistinguishability of the photons, we carry out tomographic analysis of the polarization state of the resulting "triphoton." I will discuss how one can carry out "complete" characterization of a state about which one can extract only incomplete information, and specifically the role played by the distinguishability of the component photons. In parallel, we have been studying techniques to control and characterize the quantum state of centre-of-mass motion of Rubidium-85 atoms trapped in an optical lattice, along with applications to quantum chaos. We have developed novel techniques to carry out state and process tomography, and to directly observe the lattice oscillations at the quantum level. I will present new theory and experiment on the problem of efficiently coupling the lattice bands in the presence of broadening due to uncertain quasimomentum as well as intensity fluctuations in the lattice. I will also describe our most recent results on pulse-echo in the lattice and some open questions about dephasing mechanisms and bath memory times in the system.