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arXiv:1707.01168 · Physical Review A

Nonlocal bunching of composite bosons

Zakarya Lasmar, Dagomir Kaszlikowski, Paweł Kurzyński

Published Sep 14, 2017• 2 citations
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Abstract

It was suggested that two entangled fermions can behave like a single boson and that the bosonic quality is proportional to the degree of entanglement between the two particles. The relation between bosonic quality and entanglement is quite natural if one takes into account the fact that entanglement appears in bound states of interacting systems. However, entanglement can still be present in spatially separated subsystems that no longer interact. These systems are often the subject of studies on quantum nonlocality and foundations of quantum physics. Here, we ask whether an entangled spatially separated fermionic pair can exhibit bosonic properties. We show that under certain conditions the answer to this question can be positive. In particular, we propose a nonlocal bunching scenario in which two such pairs form an analog of a two-partite bosonic Fock state.

DOI
10.1103/physreva.96.032325

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It was suggested that two entangled fermions can behave like a single boson and that the bosonic quality is proportional to the degree of entanglement between the two particles. The relation between bosonic quality and entanglement is quite natural if one takes into account the fact that entanglement appears in bound states of interacting systems. However, entanglement can still be present in spatially separated subsystems that no longer interact. These systems are often the subject of studies on quantum nonlocality and foundations of quantum physics. Here, we ask whether an entangled spatially separated fermionic pair can exhibit bosonic properties. We show that under certain conditions the answer to this question can be positive. In particular, we propose a nonlocal bunching scenario in which two such pairs form an analog of a two-partite bosonic Fock state.
On the role of entanglement in the formation and stability of composite bosons by mgr.Zakarya Lasmar Composite bosons are many-body systems made of many elementary bosons, or an even number of elementary fermions.Recently, it was suggested that quantum entanglement can be understood as the origin of the bosonic character of the simplest systems of this type (bipartite composite bosons).This idea motivated a new direction of research: quantum information oriented study of composite particles.In the present work, the role of entanglement in the formation and dynamics of composite bosons is studied.We show that, in some special situations, two entangled fermions can exhibit bosonic behaviour while being specially separated.We propose a nonlocal scheme that leads two pairs of entangled fermions to form an analogue of a two-partite bosonic Fock state.Also, we show that in some situations entanglement can provide stability for a composite particle.In this case, the interaction-free dynamics of an entangled bipartite system appear to mimic the behaviour of two interacting particles.In addition, we discuss the possible reasons that can limit the influence of entanglement on the behaviour of composite particles.The no-signalling condition seems to play a crucial role, which suggests that interactions in some situations become necessary.Regarding the formation of composite bosons, I present an entanglement-based method to study the bosonic quality of fermionic multipartite systems.Using this method, I examine the bosonic quality of the ground state of the extended one-dimensional Hubbard model while tuning the strength of interactions.vii
An even number of fermions can behave in a bosonic way. The simplest scenario involves two fermions which can form a single boson, but four fermions can either behave as two bipartite bosons or further assemble into a single four-partite bosonic molecule. In general, for 2N2N2N fermions there are many possible arrangements into composite bosons. What determines which fermionic arrangement is realized in a given situation, and is it truly bosonic? This paper aims to answer the above question. We propose an entanglement-based method to assess bosonic quality of fermionic arrangements and apply it to study how the ground state of the extended one-dimensional Hubbard model changes as the strength of interparticle interactions increases.
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 indic-ator for bosonic quality is the composite boson normal-isation ratio χN+1/χN of a state of N composites. This quantity is prohibitively complicated to compute exactly for realistic two-fermion wavefunctions and large com-posite numbers N. Here, we provide an efficient char-acterisation in terms of the purity P and the largest eigenvalue λ1 of the reduced single-fermion state. We find the states that extremise χN for given P and λ1, and we provide easily evaluable, saturable upper and lower bounds for the normalisation ratio. Our results strengthen the relationship between the bosonic qual-ity of a composite particle and the entanglement of its constituents. 1
We consider an evolution of two elementary quantum particles and ask the question: under what conditions does such a system behaves as a single object? It is obvious that if the attraction between the particles is stronger than any other force acting on them the whole system behaves as one. However, recent insight from the quantum information theory suggests that in bipartite systems it is not attraction per se that is responsible for the composite nature, but the entanglement between the parts. Since entanglement can be present between the subsystems that interacted in the past, but do not interact anymore, it is natural to ask when such an entangled pair behaves as a single object. We show that there are situations when entanglement is enough to observe single-particle behavior. However, due to the no-signaling condition, in general an interaction, or a post-selective measurement, is necessary for a complex collective behavior.
Quantum correlations and entanglement in identical-particle systems have been a puzzling question which has attracted vast interest and widely different approaches. A novel approach is introduced by Kraus \emph{et al.}, [Phys. Rev. A \textbf{79}, 012306 (2009)] based on pairing correlations in fermionic systems and the use of witness formalism to detect pairing. In this contribution, this approach has been extended to bosonic systems and separability bounds based on pairing correlations for fermions and bosons have been obtained. A two-particle annihilation operator is used for constructing a two-particle observable as a candidate witness. Two different types of separability definition is introduced for bosonic systems and the separability bounds associated with each type are discussed.
We build upon work by C. K. Law [Phys. Rev. A 71, 034306 (2005)10.1103/PhysRevA.71.034306] to show in general that the entanglement between two fermions largely determines the extent to which the pair behaves like an elementary boson. Specifically, we derive upper and lower bounds on a quantity chi{N+1}/chi{N} that governs the bosonic character of a pair of fermions when N such pairs approximately share the same wave function. Our bounds depend on the purity of the single-particle density matrix, an indicator of entanglement, and demonstrate that if the entanglement is sufficiently strong, the quantity chi{N+1}/chi{N} approaches its ideal bosonic value.