Dimer-dimer scattering length for fermions with different masses: Analytical study for large mass ratio

Alzetto, Florent; Combescot, R.; Leyronas, X.

doi:10.1103/physreva.87.022704

Cited by 12 publications

(22 citation statements)

References 18 publications

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“…By contrast, for large mass ratios, the a s curve, which essentially scales as ln(m β /m α ), coincides with that of Ref. 8 (pink dash-dotted curve). The small discrepancy we find near equal fermion masses comes from the missing excited relative-motion states ν = ν 0 .…”

Section: B Cold-atom Potentialmentioning

confidence: 82%

“…The resulting scattering length a s , shown as a black solid curve in Fig. 1, yields a s ≃ 0.64a for equal fermion masses, instead of ≃ 0.60a as obtained by previous procedures [5,6,8], all of which are numerically far more demanding. By contrast, for large mass ratios, the a s curve, which essentially scales as ln(m β /m α ), coincides with that of Ref.…”

Section: B Cold-atom Potentialmentioning

confidence: 91%

“…This study first focused on semiconductor excitons made of oppositely charged carriers [1][2][3]. However, the achievement, in the 90's, of cold-atom Bose-Einstein condensates has triggered its study [4][5][6][7][8] for dimers made of two fermionic atoms that differ by their hyperfine levels. More recently, the scattering of positronium atoms [9][10][11][12][13][14][15][16] and dark-matter particles [17,18] has attracted considerable attention due to their possible Bose-Einstein condensation.…”

Section: Introductionmentioning

confidence: 99%

“…Depending on the complexity of these fermion-fermion interactions, various approaches have been proposed: standard field theoretical or diagrammatic approach [1,2,4,6,8], quantum Monte Carlo method [3], stochastic variational method [10], coupled-channel approach [11,12], adiabatic hyperspherical method [13], renormalization group approach [7], and brute-force resolution of the four-body Schrödinger equation [5]. All, except the coupled-channel approach, rely on a free-fermion formulation of the problem.…”

Section: Introductionmentioning

confidence: 99%

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Correlated-pair approach to composite-boson scattering lengths

2016

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We derive the scattering length of composite bosons (cobosons) within the framework of the composite boson many-body formalism that uses correlated-pair states as a basis, instead of free fermion states. The integral equation constructed from this physically relevant basis makes transparent the role of fermion exchange in the coboson-coboson effective scattering. Three potentials used for Cooper pairs, fermionic-atom dimers, and semiconductor excitons are considered. While the s-wave scattering length for the BCS-like potential is just equal to its Born value, the other two are substantially smaller. For fermionic-atom dimers and semiconductor excitons, our results, calculated within a restricted correlated-pair basis, are in good agreement with those obtained from procedures numerically more demanding. We also propose model coboson-coboson scatterings that are separable and thus easily workable, and that produce scattering lengths which match quantitatively well with the numerically-obtained values for all fermion mass ratios. These separable model scatterings can facilitate future works on many-body effects in coboson gases.

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Section: B Cold-atom Potentialmentioning

confidence: 82%

Section: B Cold-atom Potentialmentioning

confidence: 91%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Correlated-pair approach to composite-boson scattering lengths

2016

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“…However, the long-range character of Coulomb potential, and mostly the lack of appropriate procedure to handle carrier exchanges that occur along with repeated fermion-fermion interactions, have impeded significant progress. The realization, two decades ago, of Bose-Einstein condensates in ultracold atomic gases brought a new impetus, prompting scattering length studies for fermionic-atom dimers [16][17][18][19][20], and more recently for positronium atoms [21][22][23][24][25][26][27][28]. These studies commonly use fermions as elementary quantum objects.…”

mentioning

confidence: 99%

Scattering amplitudes for dark and bright excitons

Shiau¹,

Combescot²,

Combescot³

et al. 2017

EPL

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Using the composite boson many-body formalism that takes single-exciton states rather than free carrier states as a basis, we derive the integral equation fulfilled by the exciton-exciton effective scattering from which the role of fermion exchanges can be unraveled. For excitons made of (±1/2)-spin electrons and (±3/2)-spin holes, as in GaAs heterostructures, one major result is that most spin configurations lead to brightness-conserving scatterings with equal amplitude ∆, in spite of the fact that they involve different carrier exchanges. A brightness-changing channel also exists when two opposite-spin excitons scatter: dark excitons (2, −2) can end either in the same dark states with an amplitude ∆e, or in opposite-spin bright states (1, −1), with a different amplitude ∆o, the number of carrier exchanges being even or odd respectively. Another major result is that these amplitudes are linked by a striking relation, ∆e + ∆o = ∆, which has decisive consequence for exciton Bose-Einstein condensation. Indeed, this relation leads to the conclusion that the exciton condensate can be optically observed through a bright part only when excitons have a large dipole, that is, when the electrons and holes are well separated in two adjacent layers. In contrast to the structureless 4 He, a number of bosonic condensates have more than one component inherited from the internal spin and orbital degrees of freedom of their constituents, the superfluid then being multi-component. Dipolar Bose gases [1] and superfluid phases of 3 He [2] are prime examples. This also occurs to excitons, which are composite bosons (cobosons for short) made of one conduction electron and one valence hole. Since electrons and holes carry spins, so do excitons, their condensate depending on these internal degrees of freedom. Recently, it has been shown that signatures of exciton condensates were long held back by the missed fact that the lowest-energy states are dark [3, 4], that is, not coupled to light. This fact precludes a direct photoluminescence observation of exciton condensate in a very dilute regime. Unambiguous optical evidences for Bose-Einstein condensation are bound to the density regime where dark and bright components coexist coherently [5]. The expected darkening[6-10] of the exciton gas upon cooling has been recently seen. Macroscopic spatial coherence of the bright component has also been revealed [7,10], in this way providing the most unambiguous evidence for the coexistence of dark and bright exciton condensates.As a rule, the energy of a condensate depends weakly on its internal degrees of freedom, all possible "spin" phases being essentially degenerate. These degeneracies are lifted once interactions are taken into account. One then has to determine which combination of the competing phases produces the lowest energy that rules the macroscopic properties of the condensate. In this Letter, we show that the relation between brightness-conserving and brightness-changing scattering amplitudes constitutes a crucial element to charact...

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Correlation energy for elementary bosons: Physics of the singularity

Shiau¹,

Combescot²,

Chang³

2016

Annals of Physics

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We propose a compact perturbative approach that reveals the physical origin of the singularity occurring in the density dependence of correlation energy: like fermions, elementary bosons have a singular correlation energy which comes from the accumulation, through Feynman "bubble" diagrams, of the same non-zero momentum transfer excitations from the free particle ground state, that is, the Fermi sea for fermions and the Bose-Einstein condensate for bosons. This understanding paves the way toward deriving the correlation energy of composite bosons like atomic dimers and semiconductor excitons, by suggesting Shiva diagrams that have similarity with Feynman "bubble" diagrams, the previous elementary boson approaches, which hide this physics, being difficult to do so.

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Dimer-dimer scattering length for fermions with different masses: Analytical study for large mass ratio

Cited by 12 publications

References 18 publications

Correlated-pair approach to composite-boson scattering lengths

Correlated-pair approach to composite-boson scattering lengths

Scattering amplitudes for dark and bright excitons

Correlation energy for elementary bosons: Physics of the singularity

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