How bosonic is a pair of fermions?

Abstract

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.

minor changes, accepted by Applied Physics B, 11 pages, 5 figures

References in corpus (9)

• Observation of Bose-Einstein Condensation of Molecules
• Stability of a Bose-Einstein condensate revisited for composite bosons
• Bosonic behavior of entangled fermions
• Collective interference of composite two-fermion bosons
• Energy dependence of the entanglement entropy of composite boson (quasiboson) systems
• Nuclear alpha-particle condensates: Definitions, occurrence conditions, and consequences
• Compositeness effects, Pauli's principle and entanglement
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Cited by in corpus (11)

• Entanglement between two spatially separated ultracold interacting Fermi gases
• Composite-boson approach to molecular Bose-Einstein condensates in mixtures of ultracold Fermi gases
• Fermionic versus bosonic behavior of confined Wigner molecules
• Quantum information approach to Bose-Einstein condensation of composite bosons
• Statistical signatures of states orthogonal to the Fock-state ladder of composite bosons
• On the description of composite bosons in discrete models
• Bosonic Particle-Correlated States: A Nonperturbative Treatment Beyond Mean Field
• Assembly of 2N entangled fermions into multipartite composite bosons
• On dynamical stability of composite quantum particles: when entanglement is enough and when interaction is needed
• Nonlocal bunching of composite bosons
• Partition function of N composite bosons