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Register a new userQuasimomentum distribution and expansion of an anyonic gas
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We point out that the momentum distribution is not a proper observable for a system of anyons in two-dimensions. In view of anyons as Wilczeks composite charged flux-tubes, this is a consequence of the fact that the orthogonal components of the kinetic momentum operator do not commute at the position of a flux tube, and thus cannot be diagonalized in the same basis. As a substitute for the momentum distribution of an anyonic (spatially localized) state, we propose to use the asymptotic single-particle density after expansion of anyons in free space from the state. This definition is identical with the standard one when the statistical parameter approaches that for bosons or fermions. Exact examples of expansion dynamics, which underpin our proposal, and observables that can be used to measure anyonic statistics, are shown.
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We analyze free expansion of a trapped one-dimensional Bose gas after a sudden release from the confining trap potential. By using the stationary phase and local density approximations, we show that the long-time asymptotic density profile and the momentum distribution of the gas are determined by the initial distribution of Bethe rapidities (quasimomenta) and hence can be obtained from the solutions to the Lieb-Liniger equations in the thermodynamic limit. For expansion from a harmonic trap, and in the limits of very weak and very strong interactions, we recover the self-similar scaling solutions known from the hydrodynamic approach. For all other power-law traps and arbitrary interaction strengths, the expansion is not self-similar and shows strong dependence of the density profile evolution on the trap anharmonicity. We also characterize dynamical fermionization of the expanding cloud in terms of correlation functions describing phase and density fluctuations.
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The recent experimental advancement to realise ultracold gases scattering off an eight-fold optical potential [Phys. Rev. Lett. 122, 110404 (2019)] heralds the beginning of a new technique to study the properties of quasicrystalline structures. Quasicrystals possess long-range order but are not periodic, and are still little studied in comparison to their periodic counterparts. Here, we consider an ultracold bosonic gas in an eight-fold symmetric lattice and assume a toy model where the atoms occupy the ground states of the local minima of the potential. The ground state phases of the system are studied, with particular interest in the local nature of the phases. The usual Mott-insulator, density wave, and supersolid phases of the standard and extended Bose-Hubbard model are observed. For non-zero long-range interactions, we find that density wave states can spontaneously break the eight-fold symmetry, and may even possess no rotational symmetry. We find the local variation in the number of nearest neighbours to play a vital role in the phase transitions, local structure, and global symmetries of the ground states. This variation in the number of nearest neighbours is not a unique property of the considered eight-fold lattice, and we expect our results to be generalisable to any quasicrystalline potential where there are only small position dependent variations in the site energy, tunnelling and interactions.
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