Macroscopic phase coherence is one of the most remarkable manifestations of quantum mechanics, yet it seems to be the inevitable ground state of interacting many-body systems. In the last two decades, the familiar examples of superfluid He and conventional superconductors have been joined by exotic and high temperature superconductors, ultra-cold atomic gases, both bosonic and fermionic, and recently systems of excitons, magnons, and exciton-photon superpositions called polaritons, the subject of this talk.

An exciton is the solid-state analogue of positronium, made up of an electron and a hole in a semiconductor, bound together by the Coulomb interaction. The idea that a dense system of electrons and holes would be unstable toward an excitonic (electrical) insulator is one of the key ideas underlying metal-insulator transition physics. The further possibility that an exciton fluid would be a Bose-Einstein condensate was raised over 40 years ago, and has been the subject of an extensive experimental search in a variety of condensed matter systems. Such a condensate would naturally exhibit phase coherence. Lately, some novel experiments with planar optical microcavities make use of the mixing of excitons with photons to create a composite boson called a polariton that has a very light mass, and is thus a good candidate for a high-temperature Bose condensate. Good evidence for spontaneous coherence has now been obtained[1], though there are special issues to resolve considering the effects of low dimensionality, disorder, strong interactions, and especially strong decoherence associated with decay of the condensate into environmental photons --- since the condensate is a special kind of laser[2].

Polariton systems also offer an opportunity to use optical pumping to study a system outside equilibrium. Methods of adiabatic rapid passage can be used to populate the energy spectrum, and therefore to excite many body collective modes in analogy to a quantum quench. In extended systems this is predicted to lead to instabilities of the strongly driven phase (Bogoliubov) and amplitude (Higgs) modes[3].

[1] For a brief review, see D.Snoke and P.B. Littlewood, Polariton Condensates, Physics Today, 63, 42-47 (2010)

[2] J. Keeling, F. M. Marchetti, M. H. Szymanska, P. B. Littlewood, Collective coherence in planar semiconductor microcavities, Semiconductor Science and Technology, 22, R1-26 (2007).

[3] R.T. Brierley, P.B. Littlewood, and P.R. Eastham, Amplitude mode dynamics of polariton condensates, Phys. Rev. Lett. 107, 040401 (2011)

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