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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The fractional quantum Hall (FQH) effect at filling factor ν = 5/2 has recently come under close scrutiny, as its ground state may possess quasi-particle excitations obeying nonabelian statistics, a property sought for topologically protected quantum operations. However, its microscopic origin remains unknown, and candidate model wave functions include those with undesirable abelian statistics. We report direct measurements of the electron spin polarization of the ν = 5/2 FQH state using resistively detected nuclear magnetic resonance. We find the system to be fully polarized, which unambiguously rules out the most likely abelian contender and lends strong support for the ν = 5/2 state being nonabelian. Our measurements reveal an intrinsically different nature of interaction in the first excited Landau level underlying the physics at ν = 5/2.

The model of interacting fermion systems in one dimension known as a Tomonaga-Luttinger liquid (TLL) provides a simple and exactly solvable theoretical framework that predicts various intriguing physical properties. Evidence of a TLL has been observed as power-law behaviour in electronic transport on various types of one-dimensional conductor. However, these measurements, which rely on d.c. transport involving electron tunneling processes, cannot identify the long-awaited hallmark of charge fractionalization, in which an injection of elementary charge e from a non-interacting lead is divided into the non-trivial effective charge e* and the remainder, e-e* (refs 6, 7, 8). Here, we report time-resolved transport measurements on an artificial TLL composed of coupled integer quantum Hall edge channels, in which we successfully identify single charge fractionalization processes. A wave packet of charge q incident from a non-interacting region breaks up into several fractionalized charge wave packets at the edges of the artificial TLL, from which transport eigenmodes can be evaluated directly. These results are informative for elucidating the nature of TLLs and low-energy excitations in the edge channels.

Macroscopic order appears as the collective behaviour of many interacting particles. Prime examples are superfluidity in helium 1 , atomic Bose-Einstein condensation 2 , s-wave 3 and d-wave superconductivity 4 and metal-insulator transitions 5. Such physical properties are tightly linked to spin and charge degrees of freedom and are greatly enriched by orbital structures 6. Moreover, high-orbital states of bosons exhibit exotic orders distinct from the orders with real-valued bosonic ground states 7. Recently, a wide range of related phenomena have been studied using atom condensates in optical lattices 8-10 , but the experimental observation of highorbital orders has been limited to momentum space 11,12. Here we establish microcavity exciton-polariton condensates as a promising alternative for exploring high-orbital orders. We observe the formation of d-orbital condensates on a square lattice and characterize their coherence properties in terms of population distributions both in real and momentum space. Exciton-polaritons emerge from the strong light-matter coupling in semiconductor quantum wells embedded in a planar microcavity structure. They behave as degenerate Bose gases in the low-density and low-temperature limit 13. Exciton-polaritons have undergone a dynamic phase transition, in which a macroscopic number of particles are accumulated in the lowest-energy single-particle state with a long-range order 14-17. Owing to their very light effective mass, the phase transition temperatures of exciton-polaritons are eight to nine orders of magnitude higher than those of atomic Bose-Einstein condensates. Coherence properties of exciton-polariton condensates have been characterized by the direct optical access in spatial and momentum spaces 14-16,18. Modern solid-state physics has studied quantum many-body phenomena whose properties reflect exotic orbital nature, another intrinsic degree of freedom, which interplays with charge and spin degrees of freedom. Its energy degeneracy and spatial anisotropy generate rich dynamics in weakly interacting many-body systems. For example, a key role of d-orbital nature has been actively investigated in salient phenomena including metal-insulator transitions 5 , colossal magnetoresistance 6,19 , and recently discovered iron-pnictide superconductors 20,21. These orbital ordering phenomena originate from the strong correlation effects of electrons in the anisotropic degenerate d-orbitals. Theoretical modelling of such