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arXiv:1108.2998 · New Journal of Physics

Particle addition and subtraction channels and the behavior of composite particles

Paweł Kurzyński, Ravishankar Ramanathan, Akihito Soeda, Tan Kok Chuan, Dagomir Kaszlikowski

Published Sep 26, 2012• 22 citations
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Abstract

Composite particles made of elementary fermions can exhibit a wide range of behavior ranging from fermionic to bosonic depending on the quantum state of the fermions and the experimental situation considered. This behavior is captured by the fundamental operations of single-particle addition and subtraction and two-particle interference. We analyze the quantum channels that implement the physical operations of addition and subtraction of indistinguishable particles. In particular, we construct optimal Kraus operators to implement these probabilistic operations for systems of a finite number of particles. We then use these to measure the quality of bosonic and fermionic behavior in terms of single-particle addition and subtraction and two-particle interference. For the specific case of composite particles made of two distinguishable fermions, we find a transition from fermionic to bosonic behavior as a function of the entanglement between the two constituents. We also apply these considerations to composite particles of two distinguishable bosons and identify the relation between entanglement and bosonic behavior for these systems.

DOI
10.1088/1367-2630/14/9/093047

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Composite particles made of elementary fermions can exhibit a wide range of behavior ranging from fermionic to bosonic depending on the quantum state of the fermions and the experimental situation considered. This behavior is captured by the fundamental operations of single-particle addition and subtraction and two-particle interference. We analyze the quantum channels that implement the physical operations of addition and subtraction of indistinguishable particles. In particular, we construct optimal Kraus operators to implement these probabilistic operations for systems of a finite number of particles. We then use these to measure the quality of bosonic and fermionic behavior in terms of single-particle addition and subtraction and two-particle interference. For the specific case of composite particles made of two distinguishable fermions, we find a transition from fermionic to bosonic behavior as a function of the entanglement between the two constituents. We also apply these considerations to composite particles of two distinguishable bosons and identify the relation between entanglement and bosonic behavior for these systems.
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 study the necessary conditions for systems composed of two distinguishable fermions to exhibit bosonic behavior. We base our analysis on tools of quantum information theory such as entanglement, local operations and classical communication and the majorization criterion for probability distributions. Introduction of these tools yields new insights into the old and important problem of identifying the conditions for existence of composite bosons. We precisely identify the role entanglement plays in the formation and behavior of such composite particles.
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
The composite character of two-fermion bosons manifests itself in the interference of many composites as a deviation from the ideal bosonic behavior. A state of many composite bosons can be represented as a superposition of different numbers of perfect bosons and fermions, which allows us to provide the full Hong-Ou-Mandel-like counting statistics of interfering composites. Our theory quantitatively relates the deviation from the ideal bosonic interference pattern to the entanglement of the fermions within a single composite boson.