Unraveling the Spin Polarization of the ν = 5/2 Fractional Quantum Hall State

Toward Quantum Computing Quantum computers are expected to be able to tackle problems that would take classical computers many lifetimes to solve. Nonabelian states of matter can store quantum information in their topology, making them immune to environmental perturbations. A physical system expected to possess this unusual property is the fractional quantum Hall state at filling factor ν = 5/2. Tiemann et al. (p. 828, published online 26 January) used nuclear magnetic resonance to measure the polarization of the 5/2 state and found that it is fully polarized—a finding consistent with a nonabelian state—keeping hopes for topological fault-tolerant quantum computing alive. Nuclear magnetic resonance shows that an exotic state of matter may have the properties necessary for error-free quantum computing. 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.

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