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Acta Physica Polonica A

Lost of Bosonic Coherence Due to the Fermionic Presence Under the Synthetic Magnetic Field

T. P. Polak

Published Apr 1, 2012• 0 citations
Publisher

Abstract

We have studied eects of inter-species interaction of the bosons in a BoseFermi mixture over a large regime of particle numbers under the synthetic magnetic eld.Analytically derived formulas for the density of states for several values of the magnetic elds f = 1/2, 1/3, 1/4, 1/6, 1/8 and 3/8 allows us to calculate, with a very good accuracy, the eective interaction between bosons.The presence of the Hofstadter buttery spectrum and fermionic species induces alternating sign potential between neutral bosonic atoms.Consequently bosons can attract or repulse each other whether sign of it strongly depends on the strength of the magnetic eld applied to the sample.

DOI
10.12693/aphyspola.121.759

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We have studied eects of inter-species interaction of the bosons in a BoseFermi mixture over a large regime of particle numbers under the synthetic magnetic eld.Analytically derived formulas for the density of states for several values of the magnetic elds f = 1/2, 1/3, 1/4, 1/6, 1/8 and 3/8 allows us to calculate, with a very good accuracy, the eective interaction between bosons.The presence of the Hofstadter buttery spectrum and fermionic species induces alternating sign potential between neutral bosonic atoms.Consequently bosons can attract or repulse each other whether sign of it strongly depends on the strength of the magnetic eld applied to the sample.
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The strongly interacting bosonic and non-interacting fermionic mixtures of diluted gases are studied.An articial magnetic eld is introduced in theory by imposing a Peierls phase shift on the wave functions of the constituents.A highly nontrivial limit of the quantum-Hall limit is achieved which provides oscillations eects of the fermion mediated interaction between bosons.In consequence the eective interaction between bosons can change the magnitude and sign.This provides possible explanations of the bosonic coherence loss observed experimentally in the time of ight and peak width experiments.
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We study a confined mixture of bosons and fermions in the quantal degeneracy regime with attractive boson-fermion interaction. We discuss the effect that the presence of vortical states and the displacement of the trapping potentials may have on mixtures near collapse, and investigate the phase stability diagram of the K-Rb mixture in the mean-field approximation supposing in one case that the trapping potentials felt by bosons and fermions are shifted from each other, as it happens in the presence of a gravitational sag, and in another case, assuming that the Bose condensate sustains a vortex state. In both cases, we have obtained an analytical expression for the fermion effective potential when the Bose condensate is in the Thomas-Fermi regime, that can be used to determine the maxima of the Fermionic density. We have numerically checked that the values one obtains for the location of these maxima using the analytical formulas remain valid up to the critical boson and fermion numbers, above which the mixture collapses.
We study the phase structure of mixtures of strongly interacting bosonic atoms in a combined potential of a parabolic trap and an optical lattice. We apply a mean-field approximation and a local density approximation to the Bose-Hubbard model for the Bose-Bose mixture, and calculate the superfluid order parameter and the number of particles per site for both species. We find that the mixture is phase-separated due to the strong onsite inter-species repulsion. Considering a zero-hopping limit, we find that the coexisting phase can appear when onsite inter-species repulsion interaction is weak.
The influence of boson-boson and boson-fermion interactions on the stability of a binary mixture of bosonic and fermionic atoms is investigated. The density profiles of the trapped mixture are obtained from direct numerical solution of a modified Gross-Pitaevskii equation that is self-consistently coupled to the mean field generated by the interaction with the fermionic species, the fermions which in turn feel the mean field created by the bosons are treated in the Thomas-Fermi approximation. We study the effects of different combinations of signs of the boson-boson and the boson-fermion scattering lengths and determine explicit expressions for critical particle numbers as a function of these scattering lengths.