Zero-temperature phase diagram of binary boson-fermion mixtures

Viverit, L.; Pethick, C. J.; Smith, H.

doi:10.1103/physreva.61.053605

Cited by 233 publications

(363 citation statements)

References 17 publications

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“…The chemical potentials are to be determined by self-consistency conditions on the particles numbers, N σ = n eq σ (r)dr. On comparing the two density profiles in the limit of vanishing boson-fermion coupling, it is easily seen that the quantity (2A/3)[n eq f (r)] −1/3 may be viewed as an effective fermion-fermion coupling arising from the kinetic pressure of the Fermi gas [23]. It is also useful to introduce the radii…”

Section: Equilibrium Density Profilesmentioning

confidence: 99%

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Schematic phase diagram and collective excitations in the collisional regime for trapped boson–fermion mixtures at zero temperature

Minguzzi

Tosi

2000

Physics Letters A

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We discuss the ground state and the small-amplitude excitations of dilute bosonfermion mixtures confined in spherical harmonic traps at T = 0, assuming repulsive boson-boson interactions and with each component being in a single hyperfine state. From previous studies of the equilibrium density profiles we propose a schematic phase diagram in a plane defined by the variables a bf /a bb and a bb k (0) f , where a bb and a bf are the boson-boson and boson-fermion scattering lengths and k (0) f is the Fermi wave number at the centre of the trap. With this background we turn to the equations of motion for density fluctuations in the collisional regime and discuss some general features of the eigenmodes. We display analytic solutions for sound waves in a quasi-homogeneous mixture and for surface modes at weak fermion-boson coupling.

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Section: Equilibrium Density Profilesmentioning

confidence: 99%

“…We search for the boundary of phase separation by means of a simple condition of linear stability on the two-by-two matrix of scattering lengths a bb , a bf and a f f [23] (see also [25]). A mixed state is stable if the inequality a bb a f f −a 2 bf > 0 holds, i.e.…”

Section: Schematic Phase Diagram At Zero Temperaturementioning

confidence: 99%

Schematic phase diagram and collective excitations in the collisional regime for trapped boson–fermion mixtures at zero temperature

Minguzzi

Tosi

2000

Physics Letters A

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“…The system is thermodynamically stable if the compressibility matrix (∂ 2 e/∂n i ∂n j ), where e is the energy density, is positive. Using the mean-eld energy density [222]: 19) we obtain the stability condition:…”

Section: Molecular Physics Beyond the Scope Of This Workmentioning

confidence: 99%

Thermodynamics of Ultracold Fermi Gases

Nascimbène

Navon

Chevy

et al. 2010

Latin America Optics and Photonics Conference

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“…Using these values for eqs. (12,13), the staying probability and the transmission coefficient become D ∼ 10 8 ω and W ∼ 10 7 . As a result, we obtain τ −1 ct /ω ∼ 10 8 × exp(−10 7 ), and the life-time τ ct becomes very longer than, for example, that of clusterization by many-body collisions, ∼ (1 ∼ 10) sec.…”

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Induced instability for boson-fermion mixed condensates of alkali-metal atoms due to the attractive boson-fermion interaction

2001

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Instabilities for boson-fermion mixed condensates of trapped Alkali atoms due to the bosonfermion attractive interaction are studied using a variational method. Three regions are shown for their instabilities according to the boson-fermion interaction strength: stable, meta-stable and unstable ones. The stability condition is obtained analytically from the asymptotic expansion of the variational total energy. The life-time of metastable states is discussed for tunneling decay, and is estimated to be very long. It suggests that, except near the unstable border, meta-stable mixed condensate should be almost-stable against clusterizations. The critical border between meta-stable and unstable phases is calculated numerically and is shown to be consistent with the Mølmer scaling condition. [5][6][7], dynamical expansions after the removal of trapping potentials [8], and the instability changes of 7 Li-6 Li system with attractive boson-boson interaction [10]. Discoveries of theIn this paper, we study the instabilities and collapses of the polarized boson-fermion mixed condensates due to the attractive boson-fermion interaction. In BEC, such instabilities are observed in several systems: 1) the trapped meta-stable 7 Li BEC (observed experimentally [11]) equilibrated between the attractive boson-boson interaction and the kinetic pressure due to the finite confinement [12], 2) two-component uniform BEC (from bosons 1 and 2), whose stability condition is given by g 11 g 22 > g 2 12 (g ij : the coupling constant between bosons i and j). In the latter case, the stability condition depends only on the interaction strength, but the condition for the case 1) has also the particle number dependence [12].Let us consider the case of the trapped boson-fermion mixed condensate. In the present paper, we assume T = 0 and a spherical harmonic-oscillator for the trapping potential; extension to the deformed potential is straightforward. Using the Thomas-Fermi approximation for the fermion degree of freedom (appropriate for large N f condensate), the total energy of the system becomes a functional of the boson order-parameter Φ( r) and the fermion density distribution n f ( r): (1), the fermion-fermion interaction has been neglected; the elastic fermion-fermion s-wave scattering for a polarized gas is absent because of the Pauli blocking effects and the p-wave scattering is suppressed below 100 µK [14]. Evaluating the total energy with the variational method, we take the Gaussian ansatz for the boson order-parameter:where x = r/ξ is a radial distance scaled by the harmonic-oscillator length ξ = (h/mω) 1/2 , and N b = d 3 x|Φ(x; R)| 2 is total boson number. The variational parameter R in (2) corresponds to the root-mean-square (rms) radius of the boson density distribution. This kind of variational functions have also been used in the instability investigations of 1

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Zero-temperature phase diagram of binary boson-fermion mixtures

Cited by 233 publications

References 17 publications

Schematic phase diagram and collective excitations in the collisional regime for trapped boson–fermion mixtures at zero temperature

Schematic phase diagram and collective excitations in the collisional regime for trapped boson–fermion mixtures at zero temperature

Thermodynamics of Ultracold Fermi Gases

Induced instability for boson-fermion mixed condensates of alkali-metal atoms due to the attractive boson-fermion interaction

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