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arXiv:1902.08157 · Physical Review A

Assembly of 2N entangled fermions into multipartite composite bosons

Zakarya Lasmar, Peter Alexander Bouvrie, Adam S. Sajna, Malte C. Tichy, Paweł Kurzyński

Published Sep 5, 2019• 5 citations
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Abstract

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 $2N$ 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.

DOI
10.1103/physreva.100.032105

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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.
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
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.
We assess whether a confined Wigner molecule constituted by 2N2N2N fermions behaves as NNN bosons or 2N2N2N fermions. Following the work by Law [Phys. Rev. A 71, 034306 (2005)] and Chudzicki et al. [Phys. Rev. Lett. 104, 070402 (2010)] we discuss the physical meaning and the reason why a large amount of entanglement is needed in order to ensure a bosonic composite behavior. By applying a composite boson ansatz, we found that a Wigner molecule confined in a two-dimensional trap presents a bosonic behavior induced by symmetry. The two-particle Wigner molecule ground state required by the composite boson ansatz was obtained within the harmonic approximation in the strong interacting regime. Our approach allows us to address few-particle states (widely studied within a variety of theoretical and numerical techniques) as well as a large number of particles (difficult to address due to computational costs). For a large number of particles, we found strong fermionic correlations exposed by the suppression of particle fluctuations. For a small number of particles, we show that the wave function calculated within the composite boson ansatz captures the Friedel-Wigner transition. The latter is shown in a regime in which strong correlations due to the Pauli exclusion principle arise; therefore, we conclude that the coboson ansatz reproduces the many-particle physics of a confined Wigner molecule, even in the presence of strong deviations of the ideal bosonic behavior due to fermionic correlations.
We consider composite bosons (cobosons) comprised two elementary particles, fermions or bosons, in an entangled state. First, we show that the effective number of cobosons implies the level of correlation between the two constituent particles. For the maximum level of correlation, the effective number of cobosons is the same as the total number of cobosons, which can exhibit the original Bose–Einstein condensation (BEC). In this context, we study a model of BEC for indistinguishable cobosons with a controllable parameter, i.e., entanglement between the two constituent particles. We find that bi-fermions behave in a predictable way, i.e., the effective number of the ground state coboson is an increasing function of entanglement between a pair of constituent fermions. Interestingly, bi-bosons exhibit the opposite behavior—the effective number of the ground state coboson is a decreasing function of entanglement between a pair of constituent bosons.
We reveal a quantum coherent state characterized by composite bosonic trions, wherein paired fermions further bind with bosons, in one-dimensional Bose-Fermi mixtures.This phase emerges in two separate models, both featuring onsite boson-fermion attraction that induces negative binding energy for the composite trions. The first is the pair-hopping model, in which spinless fermions undergo pair hopping to form preformed pairs. The second is the extended Bose-Fermi Hubbard model, describing dipolar bosons and fermions with density-density interactions. Notably, the formation of composite trions is independent of the specific pairing interactions of fermions. Extensive density matrix renormalization group calculations demonstrate the quasi-condensation of the composite trions, evidenced by algebraically decaying correlations of trions, gapped single-particle excitations, and suppressed fermion pair correlations. Our findings provide valuable insights into the three-body pairing mechanism in mixed-particle systems.
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.