On the N-exciton normalization factor

Combescot, Monique; Leyronas, X.; Tanguy, Christian

doi:10.1140/epjb/e2003-00003-1

Cited by 39 publications

(55 citation statements)

References 2 publications

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“…In this paper we will examine the case with M = N , which is the number of atoms of one of the spin components in the gas. In the case of fermions and if N ≫ 1, Combescot et al [9] have shown that…”

Section: Bosonic Testsmentioning

confidence: 99%

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Bosonic characters of atomic Cooper pairs across resonance

Pong

Law

2007

Phys. Rev. A

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We study the two-particle wave function of paired atoms in a Fermi gas with tunable interaction strengths controlled by Feshbach resonance. The Cooper pair wave function is examined for its bosonic characters, which is quantified by the correction of Bose enhancement factor associated with the creation and annihilation composite particle operators. An example is given for a threedimensional uniform gas. Two definitions of Cooper pair wave function are examined. One of which is chosen to reflect the off-diagonal long range order (ODLRO). Another one corresponds to a pair projection of a BCS state. On the side with negative scattering length, we found that paired atoms described by ODLRO are more bosonic than the pair projected definition. It is also found that at (kF a) −1 ≥ 1, both definitions give similar results, where more than 90% of the atoms occupy the corresponding molecular condensates.

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Section: Bosonic Testsmentioning

confidence: 99%

“…The value of χ M reflects the correction of Bose enhancement factor, and was used to study ground state excitons statistics [8,9] and the connection to quantum entanglement [10]. The key quantity was shown to be the ratio χ M+1 /χ M which goes to one for a perfect boson.…”

Section: Introductionmentioning

confidence: 99%

Bosonic characters of atomic Cooper pairs across resonance

Pong

Law

2007

Phys. Rev. A

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“…The statistics of composites was recently re-considered from the perspective of quantum information [4]. Both, in the many-body properties of Bose-Einstein-Condensates (BECs) [8][9][10][11][12][13][14][15][16] and in dynamical processes [17][18][19][20], entanglement between two fermionic constituents turns out to be the crucial ingredient to ensure bosonic behavior [4].While for atoms and molecules, the impact of the Pauli principle that acts on the constituent electrons is typically small [9], the question of the effective compositional hierarchy and the impact of bosonic and fermionic effects on a higher level remains open, e.g., for molecules made of two bosonic atoms, and it is lively debated for α-particles in nuclear physics [21][22][23]. For a composite boson made of two bound bosonic constituents, no Pauliblocking jeopardizes the multiple occupation of singleparticle states.…”

mentioning

confidence: 99%

“…However, as we show below, the behavior of two-boson composites can heavily deviate from the ideal, because the single-particle states of the constituents tend to be unusually often multiply populated, leading to a super -bosonic compound. Although all matter is ultimately made of fermions, any high-level composite that is made of two bosonic constituents will face such super-bosonic effects.The quantitative indicator for bosonic features in the many-body theory of composites is the composite-boson normalization ratio χ N +1 /χ N [4,[8][9][10][11]. However, even when the two-boson wavefunction is known, the complexity of the algebraic expression for χ N +1 /χ N renders an evaluation for large N unfeasible [4].…”

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Two-boson composites

2013

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Composite bosons made of two bosonic constituents exhibit deviations from ideal bosonic behavior due to their substructure. This deviation is reflected by the normalization ratio of the quantum state of N composites. We find a set of saturable, efficiently evaluable bounds for this indicator, which quantifies the bosonic behavior of composites via the entanglement of their constituents. We predict an abrupt transition between ordinary and exaggerated bosonic behavior in a condensate of two-boson composites.PACS numbers: 05.30.Jp, 03.65.Ud Introduction. The (fermionic) bosonic behavior of any elementary or composite particle is ultimately implied by the spin-statistics theorem [1, 2], which can be derived under many different assumptions [3]. For composite bosons made of two fermions, the Pauli principle that acts on the constituents modifies the ideally expected bunching behavior [5][6][7], and changes the bosonic commutation relation [4]. The statistics of composites was recently re-considered from the perspective of quantum information [4]. Both, in the many-body properties of Bose-Einstein-Condensates (BECs) [8][9][10][11][12][13][14][15][16] and in dynamical processes [17][18][19][20], entanglement between two fermionic constituents turns out to be the crucial ingredient to ensure bosonic behavior [4].While for atoms and molecules, the impact of the Pauli principle that acts on the constituent electrons is typically small [9], the question of the effective compositional hierarchy and the impact of bosonic and fermionic effects on a higher level remains open, e.g., for molecules made of two bosonic atoms, and it is lively debated for α-particles in nuclear physics [21][22][23]. For a composite boson made of two bound bosonic constituents, no Pauliblocking jeopardizes the multiple occupation of singleparticle states. One could therefore expect such compound to simply inherit the bosonic nature of its own constituents. However, as we show below, the behavior of two-boson composites can heavily deviate from the ideal, because the single-particle states of the constituents tend to be unusually often multiply populated, leading to a super -bosonic compound. Although all matter is ultimately made of fermions, any high-level composite that is made of two bosonic constituents will face such super-bosonic effects.The quantitative indicator for bosonic features in the many-body theory of composites is the composite-boson normalization ratio χ N +1 /χ N [4,[8][9][10][11]. However, even when the two-boson wavefunction is known, the complexity of the algebraic expression for χ N +1 /χ N renders an evaluation for large N unfeasible [4].Here, we solve this problem by providing tight, saturable bounds for the normalization ratio, which allow us to efficiently characterize two-boson composites via three easily accessible quantities: the number of composites N , and the purity P and the largest eigenvalue λ 1 of the reduced density matrix of one constituent boson, which can be obtained from the two-boson wavefunction. This...

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How bosonic is a pair of fermions?

2014

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Composite particles made of two fermions can be treated as ideal elementary bosons as long as the constituent fermions are sufficiently entangled. In that case, the Pauli principle acting on the parts does not jeopardise the bosonic behaviour of the whole. An indicator for bosonic quality is the composite boson normalisation ratio $\chi_{N+1}/\chi_{N}$ of a state of $N$ composites. This quantity is prohibitively complicated to compute exactly for realistic two-fermion wavefunctions and large composite numbers $N$. Here, we provide an efficient characterisation in terms of the purity $P$ and the largest eigenvalue $\lambda_1$ of the reduced single-fermion state. We find the states that extremise $\chi_N$ for given $P$ and $\lambda_1$, and we provide easily evaluable, saturable upper and lower bounds for the normalisation ratio. Our results strengthen the relationship between the bosonic quality of a composite particle and the entanglement of its constituents.Comment: minor changes, accepted by Applied Physics B, 11 pages, 5 figure

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On the N-exciton normalization factor

Cited by 39 publications

References 2 publications

Bosonic characters of atomic Cooper pairs across resonance

Bosonic characters of atomic Cooper pairs across resonance

Two-boson composites

How bosonic is a pair of fermions?

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