Depletion of the Bose-Einstein condensate in Bose-Fermi mixtures (original) (raw)
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Quantum phase transition in Bose-Fermi mixtures
2011
We study a quantum Bose-Fermi mixture near a broad Feshbach resonance at zero temperature. Within a quantum field theoretical model a two-step Gaussian approximation allows to capture the main features of the quantum phase diagram. We show that a repulsive boson-boson interaction is necessary for thermodynamic stability. The quantum phase diagram is mapped in chemical potential and density space, and both first and second order quantum phase transitions are found. We discuss typical characteristics of the first order transition, such as hysteresis or a droplet formation of the condensate which may be searched for experimentally.
Finite-temperature effects on the collapse of trapped Bose-Fermi mixtures
Physical Review A, 2003
By using the self-consistent Hartree-Fock-Bogoliubov-Popov theory, we present a detailed study of the mean-field stability of spherically trapped Bose-Fermi mixtures at finite temperature. We find that, by increasing the temperature, the critical particle number of bosons (or fermions) and the critical attractive Bose-Fermi scattering length increase, leading to a significant stabilization of the mixture. PACS numbers: 03.75.Ss, 32.80.Pj
2005
The bosonic atoms used in present day experiments on Bose-Einstein condensation are made up of fermionic electrons and nucleons. In this Letter we demonstrate how the Pauli exclusion principle for these constituents puts an upper limit on the Bose-Einstein-condensed fraction. Detailed numerical results are presented for hydrogen atoms in a cubic volume and for excitons in semiconductors and semiconductor bilayer systems. The resulting condensate depletion scales differently from what one expects for bosons with a repulsive hard-core interaction. At high densities, Pauli exclusion results in significantly more condensate depletion. These results also shed a new light on the low condensed fraction in liquid helium II. PACS numbers: 05.30.Jp, 74.20.Fg, 71.35.Lk Recent experiments with ultracold fermionic gases have demonstrated the gradual crossover between a Bose-Einstein condensate of two-fermion molecules and a BCS-like condensate of fermion pairs . Turning this picture around, one might ask to what extent subatomic degrees of freedom play a role in Bose-Einstein condensates of bosonic atoms, because these atoms are made up of fermions: electrons and nucleons. From the energetic point of view there is no effect: subatomic excitation energies greatly exceed the thermal energy scale of Bose-Einstein condensation. Therefore one can safely assume that the subatomic degrees of freedom are completely frozen [4]. However, even for a frozen internal structure one has to take into account the correct symmetries: at the level of the many-electron wave function, quantum mechanics dictates antisymmetry, which makes that electrons can not overlap. As a consequence, the Pauli principle for the electrons limits the available phase space for the bosonic atoms, which can have an influence on the properties of the condensate . It has been demonstrated before that a condensate of bosons made up of fermions has a maximum occupation number . For hydrogen atoms, that number corresponds to a condensate density of the order of 1/(4πa 3 0 ), with a 0 the Bohr radius. Such high densities are not reached in present day experiments on Bose-Einstein condensates . Still, the Pauli principle can have an effect also at lower densities, where it leads to condensate depletion. It is generally believed that it is sufficient to model this effect through an effective interaction for the bosons which is strongly repulsive at short distances, like a hard-sphere potential or e.g. the (unphysical) r −12 term in the Lennard-Jones potential. The condensate will be depleted, simply because of the excluded volume. However, the only physical parameter which determines the low-density properties of the condensate is the scattering length. It is demonstrated below that any bosonic interaction with the right scattering length fails to reproduce the Pauli exclusion effect at high densities. We show how Pauli exclusion puts an upper bound on the Bose-Einstein condensed fraction of ultracold atomic gases. The bound is made quantitative for hydrogen atoms, through the use of an exactly solvable pair-ing model. The consequences for ultracold alkali gases, exciton condensates in semiconductors and liquid helium II are discussed.
Critical temperature of Bose Einstein condensation in trapped atomic Bose Fermi mixtures
Journal of Physics B: Atomic, Molecular and Optical Physics, 2002
We determine the critical temperature of a 3D homogeneous system of hard-sphere bosons by pathintegral Monte Carlo simulations and finite-size scaling. In the low density limit, we find that the critical temperature is increased by the repulsive interactions, as DT C ͞T 0 ϳ ͑na 3 ͒ g , where g 0.34 6 0.03. At high densities the result for liquid helium, namely, a lower critical temperature than in the noninteracting case, is recovered. We give a microscopic explanation for the observed behavior.
Quantum phase transitions in Bose–Fermi systems
Annals of Physics, 2011
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We unravel the nonequilibrium dynamics of two fermionic impurities immersed in a one-dimensional bosonic gas following an interspecies interaction quench. Monitoring the temporal evolution of the single-particle density of each species we reveal the existence of four distinct dy-namical regimes. For weak interspecies repulsions both species either perform a breathing motion or the impurity density splits into two parts which interact and disperse within the bosonic cloud. Turning to strong interactions we observe the formation of dark-bright states within the mean-field approximation. However, the correlated dynamics shows that the fermionic density splits into two repelling density peaks which either travel towards the edges of the bosonic cloud where they equi-librate or they approach an almost steady state propagating robustly within the bosonic gas which forms density dips at the same location. For these strong interspecies interactions an energy transfer process from the impurities to their environment occurs at the many-body level, while a periodic energy exchange from the bright states (impurities) to the bosonic species is identified in the absence of correlations. Finally, inspecting the one-body coherence function for strong interactions enables us to conclude on the spatial localization of the quench-induced fermionic density humps.
Molecular transitions in Fermi condensates
Eprint Arxiv Cond Mat 0404301, 2004
We discuss the transition of fermion systems to a condensate of Bose dimers, when the interaction is varied by use of a Feshbach resonance. We argue that there is an intermediate phase between the superfluid Fermi gas and the Bose condensate of molecules, consisting of extended dimers.