Quantum optics on a chip - photon counters and NOON states

Circuit quantum electrodynamics is a maturing field in which the physics of
quantum optical setups is realized in cryogenic electric circuits, profiting
from large achievable coupling strengths. Elements like cavities, artificial
atoms, mirrors, and beamsplitters have been successfully demonstrated. The
missing element is a single-photon counter as microwave photons are usually
amplified instead of counted, and as most of these amplifiers are noisy. I will
present the Josephson Photomultiplier, a simple device that allows single photon
counting at high efficiency and bandwidth. Quantum optics with multiple modes
has highlightes NOON states - states in which N photons are in a superposition 
of two arms of an interferometer for quantum-enhanced metrology. I am going to
show how these can be created deterministically in circuit QED. The success of
such an experiment is difficult to determine as the reconstruction of a two-mode
density matrix at large photon number is forbiddingly cumbersome. We are going
to show that it is much more efficient to test for a hypothesis state and then
estimate the overlap between the hypothetical state and the physical state
using nonlinear programming.