The quantum statistics of bosons or fermions are manifest through even or odd relative angular momentum of a pair. We show theoretically that, under certain conditions, a pair of certain test particles immersed in a fractional quantum Hall state possesses, effectively, a fractional relative angular momentum, which can be interpreted in terms of fractional braid statistics. We propose that the fractionalization of the angular momentum can be detected directly through the measurement of the pair correlation function in rotating ultra-cold atomic systems in the fractional quantum Hall regime. Such a measurement will also provide direct evidence for the effective magnetic field resulting from Berry phases arising from attached vortices, and of excitations with fractional particle number, analogous to fractional charge of electron fractional quantum Hall effect.PACS numbers: 03.65. Vf,03.75.Mn, While all particles in nature are either bosons or fermions, emergent particles in strongly correlated condensed matter systems can, in principle, obey fractional braid statistics [1,2], which refers to the property that their braiding produces phases that are non-integral multiples of 2π. It was proposed three decades ago [3,4] that the fractional quantum Hall effect [5] (FQHE) provides a platform for the realization of such entities. No convincing measurement of the fractional braid statistics has yet been made. In this Letter we consider a pair of test atoms in a background FQHE state of bosonic atoms. Under certain conditions, the test atoms capture vortices and the bound states of atoms and vortices behave effectively as particles with fractional braid statistics. Just as fermionic or bosonic statistics are reflected through an odd or even integer relative angular momentum for a pair of particles, fractional braid statistics are manifest through fractional relative angular momentum. We further show that the relative angular momentum can be deduced from the pair correlation function through determination of the radii of various quantized orbits of one test particle around another. This provides a method for measuring fractional braid statistics relying only on already existing experimental methods of introducing test atoms as well as of measuring their pair correlation function in ultra-cold bosons in rapidly rotating optical traps. No direct interferometric or phase measurement is necessary. In addition, our proposed experiment will provide a direct measurement of the effective magnetic field arising from a binding of vortices to bosons, as well as of excitations involving a fraction of a boson.Neutral bosons can in principle be driven into the FQHE regime by rapid rotation, which effectively amounts to application of a magnetic field. The strongly interacting regime is reached as the number of vortices (N V ) in a rotating Bose-Einstein condensate becomes comparable with the number of atoms N , which is parametrized by the filling factor ν = N/N V . Various methods have been developed for producing vorticity in atomic Bo...

The interplay between strongly correlated liquid and crystal phases for two-dimensional electrons exposed to a high transverse magnetic field is of fundamental interest. Through the nonperturbative fixed-phase diffusion Monte Carlo method, we determine the phase diagram of the Wigner crystal in the ν-κ plane, where ν is the filling factor and κ is the strength of Landau-level (LL) mixing. The phase boundary is seen to exhibit a striking ν dependence, with the states away from the magic filling factors ν=n/(2pn+1) being much more susceptible to crystallization due to Landau-level mixing than those at ν=n/(2pn+1). Our results explain the qualitative difference between the experimental behaviors observed in n- and p-doped gallium arsenide quantum wells and, in particular, the existence of an insulating state for ν<1/3 and also for 1/3<ν<2/5 in low-density p-doped systems. We predict that, in the vicinity of ν=1/5 and ν=2/9, increasing LL mixing causes a transition not into an ordinary electron Wigner crystal, but rather into a strongly correlated crystal of composite fermions carrying two vortices.

The spin transitions in the fractional quantum Hall effect provide a direct measure of the tiny energy differences between differently spin-polarized states and thereby serve as an extremely sensitive test of the quantitative accuracy of the theory of the fractional quantum Hall effect, and, in particular, of the role of Landau-level mixing in lifting the particle-hole symmetry. We report on an accurate quantitative study of this physics, evaluating the effect of Landau-level mixing in a nonperturbative manner using a fixed-phase diffusion Monte Carlo method. We find excellent agreement between our calculated critical Zeeman energies and the experimentally measured values. In particular, we find, as also do experiments, that the critical Zeeman energies for fractional quantum Hall states at filling factors ν=2-n/(2n±1) are significantly higher than those for ν=n/(2n±1), a quantitative signature of the lifting of particle-hole symmetry due to Landau-level mixing.

No abstract

No abstract