The phonon propagation dynamics in a phononic crystal waveguide, realized via a suspended onedimensional membrane array with periodic air holes, is investigated as function of its geometry. The bandstructure of the phononic crystal waveguide can be engineered by modifying the characteristics of the phonon waves by varying the waveguide width and the pitch of the air holes. This enables the phonon transmission bands, the bandgaps, the velocity and the nonlinear dispersion in the phononic crystal to be controlled. Indeed the engineered bandstructure can even be tuned to sustain multiple phonon modes in a given branch which while being spectrally degenerate can be temporally resolved via their differing group velocities. Furthermore, the ability to tune the bandstructure and thus the nonlinear dispersion can be harnessed to efficiently activate nonlinear phenomena such as mechanical four wave mixing. This systematic study reveals the key geometric parameters that enable the phonon transport in phononic crystal waveguides to be fully controlled.

We give a complete proposal showing how to detect the non-classical nature of photonic states with naked eyes as detectors. The enabling technology is a sub-Poissonian photonic state that is obtained from single photons, displacement operations in phase space and basic non-photon-number-resolving detectors. We present a detailed statistical analysis of our proposal including imperfect photon creation and detection and a realistic model of the human eye. We conclude that a few tens of hours are sufficient to certify non-classical light with the human eye with a p-value of 10%.

We formulate a Bardeen-Cooper-Schriffer (BCS) theory of quasiparticles in a degenerate Fermi gas strongly coupled to photons in a optical cavity. The elementary photonic excitations of the system are cavity polaritons, which consist of a cavity photon and an excitation of an atom within the Fermi sea. The excitation of the atom out of the Fermi sea leaves behind a hole, which together results in a loosely bound Cooper pair, allowing for the system to be written by a BCS wavefunction. As the density of the excitations is increased, the excited atom and hole become more strongly bound, crossing over into the molecular regime. This thus realizes an alternative BCS to BEC crossover scenario, where the participating species are quasiparticle excitations in a Fermi sea consisting of excited atoms and holes.