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arXiv:cond-mat/0411686 · Physical Review A

Density waves in a quasi-one-dimensional atomic gas mixture of bosons and two-component fermions

E. Nakano, Hiroyuki Yabu

Published Oct 6, 2005• 7 citations
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Abstract

Density-wave structures are studied in a quasi-one-dimensional atomic gas mixture of one-component bosons and two-component fermions using the mean-field approximation at zero temperature. Owing to the Peierls instability in the fermion system, the ground state of the system shows a fermion density wave and periodic Bose-Einstein condensation induced by the boson-fermion interatomic interaction. For the two-component fermions, two density waves appear in each component, and their phase difference distinguishes two types of ground states, the in-phase and the out-phase density waves. In this paper, a self-consistent method is presented to treat the density-wave states in a boson-fermion mixture with two-component fermions. The analysis of the effective potential and the interaction energies shows that the density waves appearing in the ground state are in phase or out of phase depending on the strength of the interfermion interaction. It is also shown that the periodic Bose-Einstein condensate coexists with the in-phase density wave of fermions, but, in the case of out of phase, only the uniform condensate appears. The phase diagram of the system is given for the effective coupling constants.

DOI
10.1103/physreva.72.043602

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Density-wave structures are studied in a quasi-one-dimensional atomic gas mixture of one-component bosons and two-component fermions using the mean-field approximation at zero temperature. Owing to the Peierls instability in the fermion system, the ground state of the system shows a fermion density wave and periodic Bose-Einstein condensation induced by the boson-fermion interatomic interaction. For the two-component fermions, two density waves appear in each component, and their phase difference distinguishes two types of ground states, the in-phase and the out-phase density waves. In this paper, a self-consistent method is presented to treat the density-wave states in a boson-fermion mixture with two-component fermions. The analysis of the effective potential and the interaction energies shows that the density waves appearing in the ground state are in phase or out of phase depending on the strength of the interfermion interaction. It is also shown that the periodic Bose-Einstein condensate coexists with the in-phase density wave of fermions, but, in the case of out of phase, only the uniform condensate appears. The phase diagram of the system is given for the effective coupling constants.
We study the quasi-one-dimensional (Q1D) spin-polarized Bose-Fermi mixture of atomic gases at zero temperature. Bosonic excitation spectra are calculated in the random phase approximation on the ground state with uniform Bose-Einstein condensates (BEC's) and the Peierls instabilities are shown to appear in bosonic collective excitation modes with wave number 2kF2{k}_{F}2kF​ by the coupling between the Bogoliubov-phonon mode of bosonic atoms and the fermion particle-hole excitations. The ground-state properties are calculated in the variational method, and, corresponding to the Peierls instability, the state with a periodic BEC and fermionic density waves with the period $\ensuremath{\pi}∕{k}_{F}$ are shown to have a lower energy than the uniform one. We also briefly discuss the Q1D system confined in a harmonic oscillator potential and derive the Peierls instability condition for it.
We consider a system of repulsively interacting Bose-Fermi mixtures of spin-polarized uniform atomic gases at zero temperature. We examine possible realization of ppp-wave superfluidity of fermions due to an effective attractive interaction via density fluctuations of Bose-Einstein condensate within mean-field approximation. We find the ground state of the system by direct energy comparison of the ppp-wave superfluid state in a single uniform mixed phase and normal Fermi gas state in a phase-separated phase, and suggest an occurrence of the ppp-wave superfluidity for a strong boson-fermion interaction regime. We study some signatures of the ppp-wave superfluid, such as anisotropic energy gap and quasiparticle energy in the axial state, that have not been observed in spin-unpolarized superfluid of atomic fermions. We also show that a Cooper pair is a tightly bound state, such as a diatomic molecule in the strong boson-fermion coupling regime, and suggest an observable indication of the ppp-wave superfluid in the real experiment.
We study a mixture of fermionic and bosonic cold atoms on a two-dimensional optical lattice, where the fermions are prepared in two isospin states and the bosons have Bose-Einstein condensed. Number density fluctuations of the condensate form delocalized bosonic modes which couple to the fermionic atoms similarly to the electron-phonon coupling in crystals. We study the phase diagram for this system at fixed fermion density of one per site. We find that tuning of the lattice parameters and interaction strengths drives the system to undergo antiferromagnetic ordering, s-wave and d-wave pairing superconductivity, or a charge density-wave phase. We use functional renormalization group analysis where retardation effects are fully taken into account. We calculate response functions and also provide estimates of the energy gap associated with the dominant order, and how it depends on different parameters of the problem.
We investigate the mechanical instability toward density collapse and the transition temperature of Bose-Einstein condensation (BEC) in the weakly coupled boson-fermion many-body mixture of single-component boson and fermion gases, in the case of the repulsive boson-boson and attractive boson-fermion interactions; no fermion-fermion interaction is assumed to be originated from the Pauli exclusion because of the diluteness of the mixture. The mechanical instability occurs in the bosonic gas where the induced boson-boson attraction mediated by the fermion polarization overcomes the boson-boson repulsive interaction at low temperatures. We calculate the onset temperature of the mechanical instability and the BEC transition temperature for the interaction strength and the boson-fermion number ratio. We also discuss the relation between the mechanical instability and the BEC transition using a diagrammatic method.
The structure of trapped binary mixtures of bosonic and fermionic atoms at zero temperature is studied using a modified Gross-Pitaevskii equation for the bosons which self-consistently includes the mean-field interaction generated by the fermionic cloud. The density of the fermionic component is described within the Thomas-Fermi approximation. The influence of the boson-boson and the boson-fermion s-wave interaction on the density profiles and the stability of the mixture is investigated systematically. Critical particle numbers for the mean-field collapse caused either by attractive boson-boson or by attractive boson-fermion interactions and for the onset of spatial component separation are discussed. It is shown that the interplay between the boson-boson and the boson-fermion interaction generates a rich and complex phase diagram. Finally, the specific properties and prospects of the boson-fermion mixtures available in present experiments are addressed.