The effect of quantum statistics in quantum gases and liquids results in observable collective properties among many-particle systems. One prime example is Bose-Einstein condensation, whose onset in a quantum liquid leads to phenomena such as superfluidity and superconductivity. A Bose-Einstein condensate is generally defined as a macroscopic occupation of a single-particle quantum state, a phenomenon technically referred to as off-diagonal long-range order due to non-vanishing off-diagonal components of the single-particle density matrix. The wavefunction of the condensate is an order parameter whose phase is essential in characterizing the coherence and superfluid phenomena. The long-range spatial coherence leads to the existence of phase-locked multiple condensates in an array of superfluid helium, superconducting Josephson junctions or atomic Bose-Einstein condensates. Under certain circumstances, a quantum phase difference of pi is predicted to develop among weakly coupled Josephson junctions. Such a meta-stable pi-state was discovered in a weak link of superfluid 3He, which is characterized by a 'p-wave' order parameter. The possible existence of such a pi-state in weakly coupled atomic Bose-Einstein condensates has also been proposed, but remains undiscovered. Here we report the observation of spontaneous build-up of in-phase ('zero-state') and antiphase ('pi-state') 'superfluid' states in a solid-state system; an array of exciton-polariton condensates connected by weak periodic potential barriers within a semiconductor microcavity. These in-phase and antiphase states reflect the band structure of the one-dimensional polariton array and the dynamic characteristics of metastable exciton-polariton condensates.

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Polariton lasers do not rely on stimulated emission of cavity photons, which sets stringent conditions on the threshold current in a conventional laser. Indeed, it has been demonstrated in optically pumped systems, that bosonic polariton lasers can outperform standard lasers in terms of their threshold power. The polaritons, which are part light and part matter quasiparticles, can undergo a condensation process into a common energy state. The radiated light from such a system shares many similarities with the light emitted from a conventional photon laser, even though the decay of the polaritons is a spontaneous process.We discuss properties of polariton lasers and condensates in GaAs based microcavities. Special emphasis is given to the system's response to an applied magnetic field. We introduce the magnetic field interactions as a reliable tool to distinguish a polariton laser from a conventional photon laser device. In particular, we will discuss the first successful realization of an electrically pumped polariton laser, which marks a promising step towards the exploitation of polaritonic devices in the real world. We believe that our work can be extended to devices operated at room temperature by transferring the technology to large bandgap semiconductors, or even to GaAs samples with a modified layer design.

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and is made available as an electronic reprint (preprint) with permission of Society of Photo-optical Instrumentation Engineers (SPIE).