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Quantum degeneracy and interaction effects in spin-polarized Fermi-Bose mixtures

L. VICHI, M. INGUSCIO, S. Stringari, TINO, GUGLIELMO MARIA

Published Jan 1, 1998• 8 citations
OpenAlex

Abstract

Various features of spin-polarized Fermi gases confined in harmonic traps are\ndiscussed, taking into account possible perspectives of experimental measurements. The\nmechanism of the expansion of the gas is explicitly investigated and compared with that of an\ninteracting Bose gas. The role of interactions in the equilibrium and non-equilibrium behaviour\nof the fermionic component in Fermi–Bose mixtures is discussed. Special emphasis is given to\nthe case of potassium isotope mixtures.

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Quantum degeneracy and interaction effects in spin-polarized Fermi - Bose mixtures

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Various features of spin-polarized Fermi gases confined in harmonic traps are discussed, taking into account possible perspectives of experimental measurements. The mechanism of the expansion of the gas is explicitly investigated and compared with that of an interacting Bose gas. The role of interactions in the equilibrium and non-equilibrium behaviour of the fermionic component in Fermi - Bose mixtures is discussed. Special emphasis is given to the case of potassium isotope mixtures.

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Bess Fang, Patrizia Vignolo, Christian Miniatura +1 more

We consider a strongly interacting one-dimensional (1D) Bose-Fermi mixture confined in a harmonic trap. It consists of a Tonks-Girardeau (TG) gas (1D Bose gas with repulsive hard-core interactions) and of a noninteracting Fermi gas (1D spin-aligned Fermi gas), both species interacting through hard-core repulsive interactions. Using a generalized Bose-Fermi mapping, we determine the one-body density matrices, exact particle density profiles, momentum distributions, and behavior of the mixture under 1D expansion when opening the trap. In real space, bosons and fermions do not display any phase separation: the respective density profiles extend over the same region and they both present a number of peaks equal to the total number of particles in the trap. In momentum space the bosonic component has the typical narrow TG profile, while the fermionic component shows a broad distribution with fermionic oscillations at small momenta. Due to the large boson-fermion repulsive interactions, both the bosonic and the fermionic momentum distributions decay as $C{p}^{\ensuremath{-}4}$ at large momenta, like in the case of a pure bosonic TG gas. The coefficient $C$ is related to the two-body density matrix and to the bosonic concentration in the mixture. When opening the trap, both momentum distributions ``fermionize'' under expansion and turn into that of a Fermi gas with a particle number equal to the total number of particles in the mixture.

arXiv:0809.4419•Physical Review A•Feb 26, 2009•20 citations
Various features of spin-polarized Fermi gases confined in harmonic traps are\ndiscussed, taking into account possible perspectives of experimental measurements. The\nmechanism of the expansion of the gas is explicitly investigated and compared with that of an\ninteracting Bose gas. The role of interactions in the equilibrium and non-equilibrium behaviour\nof the fermionic component in Fermi–Bose mixtures is discussed. Special emphasis is given to\nthe case of potassium isotope mixtures.
The main topic of these lectures is the physics of quantum degenerate atomic Fermi gases both under uniform confinement and in harmonic traps. To begin with, a general introduction on ideal Fermi gases is proposed. This "academic" limit is relevant in experiments where ultracold fermionic atoms are all polarized in a single spin state: the low atom momenta together with the fermionic nature of the atoms forbid atomic s-wave scattering and the atoms can be considered as free. Interactions are then introduced for the case of a gas with two spin components. Interactions can be tuned via Feshbach resonances and control the microscopic features of the superfluid phase, ranging from the BCS limit (formation of Cooper pairs) to the BEC limit (Bose-Einstein condensation of dimers). Various theoretical approaches for the description of the BCS-BEC crossover and their predictions in comparison with the experimental results are discussed.
Recent theoretical and experimental progress on studying one-dimensional systems of bosonic, fermionic, and Bose-Fermi mixtures of a few ultracold atoms confined in traps is reviewed in the broad context of mesoscopic quantum physics. We pay special attention to limiting cases of very strong or very weak interactions and transitions between them. For bosonic mixtures, we describe the developments in systems of three and four atoms as well as different extensions to larger numbers of particles. We also briefly review progress in the case of spinor Bose gases of a few atoms. For fermionic mixtures, we discuss a special role of spin and present a detailed discussion of the two- and three-atom cases. We discuss the advantages and disadvantages of different computation methods applied to systems with intermediate interactions. In the case of very strong repulsion, close to the infinite limit, we discuss approaches based on effective spin chain descriptions. We also report on recent studies on higher-spin mixtures and inter-component attractive forces. For both statistics, we pay particular attention to impurity problems and mass imbalance cases. Finally, we describe the recent advances on trapped Bose-Fermi mixtures, which allow for a theoretical combination of previous concepts, well illustrating the importance of quantum statistics and inter-particle interactions. Lastly, we report on fundamental questions related to the subject which we believe will inspire further theoretical developments and experimental verification.
Abstract We discuss an equilibrium mean-field properties of mixtures consisting of bosons and spin-polarized fermionic atoms with a point-like interaction in an arbitrary dimension 2 < d < 4 . Particularly, besides the standard weak-coupling limit of the system with slightly depleted Bose condensate and almost ideal Fermi gas, we discuss the (meta)stable phase with dimers composed exactly of one boson and one fermion. The peculiarities of the fermion-dimer and the boson-dimer three-body effective interactions and their impact on the thermodynamic stability of the dilute Bose-Fermi mixtures are elucidated.
We consider a strongly interacting one-dimensional (1D) Bose-Fermi mixture confined in a harmonic trap. It consists of a Tonks-Girardeau (TG) gas (1D Bose gas with repulsive hard-core interactions) and of a noninteracting Fermi gas (1D spin-aligned Fermi gas), both species interacting through hard-core repulsive interactions. Using a generalized Bose-Fermi mapping, we determine the one-body density matrices, exact particle density profiles, momentum distributions, and behavior of the mixture under 1D expansion when opening the trap. In real space, bosons and fermions do not display any phase separation: the respective density profiles extend over the same region and they both present a number of peaks equal to the total number of particles in the trap. In momentum space the bosonic component has the typical narrow TG profile, while the fermionic component shows a broad distribution with fermionic oscillations at small momenta. Due to the large boson-fermion repulsive interactions, both the bosonic and the fermionic momentum distributions decay as $C{p}^{\ensuremath{-}4}$ at large momenta, like in the case of a pure bosonic TG gas. The coefficient CCC is related to the two-body density matrix and to the bosonic concentration in the mixture. When opening the trap, both momentum distributions ``fermionize'' under expansion and turn into that of a Fermi gas with a particle number equal to the total number of particles in the mixture.