Entanglement in bosonic systems

We discuss entanglement generation in a closed system of one or two atomic quantum dots (qubits) coupled via Raman transitions to a pool of cold interacting bosons. The system exhibits rich entanglement dynamics, which we analyze in detail in an exact quantum mechanical treatment of the problem. The bipartite setup of only one atomic quantum dot coupled to a pool of bosons turns out to be equivalent to two qubits which easily get entangled from an initial product state. We show that both the number of bosons in the pool and the boson-boson interaction crucially affect the entanglement characteristics of the system. The tripartite system of two atomic quantum dots and a pool of bosons reduces to a qubit-qutrit-qubit realization. We consider entanglement possibilities of the pure system as well as of reduced ones by tracing out one of the constituents, and show how the entanglement can be controlled by varying system parameters. We demonstrate that the qutrit, as expected, plays a leading role in entangling the two qubits and the maximum entanglement depends in a nontrivial way on the pool characteristics.We discuss entanglement generation in a closed system of one or two atomic quantum dots (qubits) coupled via Raman transitions to a pool of cold interacting bosons. The system exhibits rich entanglement dynamics, which we analyze in detail in an exact quantum mechanical treatment of the problem. The bipartite setup of only one atomic quantum dot coupled to a pool of bosons turns out to be equivalent to two qubits which easily get entangled from an initial product state. We show that both the number of bosons in the pool and the boson-boson interaction crucially affect the entanglement characteristics of the system. The tripartite system of two atomic quantum dots and a pool of bosons reduces to a qubit-qutrit-qubit realization. We consider entanglement possibilities of the pure system as well as of reduced ones by tracing out one of the constituents, and show how the entanglement can be controlled by varying system parameters. We demonstrate that the qutrit, as expected, plays a leading role in entangling the two qubits and the maximum entanglement depends in a nontrivial way on the pool characteristics.

arXiv:1212.2909Physical Review AOct 3, 20138 citations

On the role of entanglement in the formation and stability of composite bosons

Zakarya Lasmar

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.viiOn 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

Jan 1, 20190 citations

Entanglement in Open Quantum Systems

Diplomarbeit von Marc Busse

Jan 1, 20060 citations

Universal Entanglers for Bosonic and Fermionic Systems

Joel Klassen, Jianxin Chen, Bei Zeng

A universal entangler (UE) is a unitary operation which maps all pure product states to entangled states. It is known that for a bipartite system of particles $1,2$ with a Hilbert space $\mathbb{C}^{d_1}\otimes\mathbb{C}^{d_2}$ , a UE exists when $\min{(d_1,d_2)}\geq 3$ and $(d_1,d_2)\neq (3,3)$ . It is also known that whenever a UE exists, almost all unitaries are UEs; however to verify whether a given unitary is a UE is very difficult since solving a quadratic system of equations is NP-hard in general. This work examines the existence and construction of UEs of bipartite bosonic/fermionic systems whose wave functions sit in the symmetric/antisymmetric subspace of $\mathbb{C}^{d}\otimes\mathbb{C}^{d}$ . The development of a theory of UEs for these types of systems needs considerably different approaches from that used for UEs of distinguishable systems. This is because the general entanglement of identical particle systems cannot be discussed in the usual way due to the effect of (anti)-symmetrization which introduces "pseudo entanglement" that is inaccessible in practice. We show that, unlike the distinguishable particle case, UEs exist for bosonic/fermionic systems with Hilbert spaces which are symmetric (resp. antisymmetric) subspaces of $\mathbb{C}^{d}\otimes\mathbb{C}^{d}$ if and only if $d\geq 3$ (resp. $d\geq 8$ ). To prove this we employ algebraic geometry to reason about the different algebraic structures of the bosonic/fermionic systems. Additionally, due to the relatively simple coherent state form of unentangled bosonic states, we are able to give the explicit constructions of two bosonic UEs. Our investigation provides insight into the entanglement properties of systems of indisitinguishable particles, and in particular underscores the difference between the entanglement structures of bosonic, fermionic and distinguishable particle systems.A universal entangler (UE) is a unitary operation which maps all pure product states to entangled states. It is known that for a bipartite system of particles $1,2$ with a Hilbert space $\mathbb{C}^{d_1}\otimes\mathbb{C}^{d_2}$, a UE exists when $\min{(d_1,d_2)}\geq 3$ and $(d_1,d_2)\neq (3,3)$. It is also known that whenever a UE exists, almost all unitaries are UEs; however to verify whether a given unitary is a UE is very difficult since solving a quadratic system of equations is NP-hard in general. This work examines the existence and construction of UEs of bipartite bosonic/fermionic systems whose wave functions sit in the symmetric/antisymmetric subspace of $\mathbb{C}^{d}\otimes\mathbb{C}^{d}$. The development of a theory of UEs for these types of systems needs considerably different approaches from that used for UEs of distinguishable systems. This is because the general entanglement of identical particle systems cannot be discussed in the usual way due to the effect of (anti)-symmetrization which introduces "pseudo entanglement" that is inaccessible in practice. We show that, unlike the distinguishable particle case, UEs exist for bosonic/fermionic systems with Hilbert spaces which are symmetric (resp. antisymmetric) subspaces of $\mathbb{C}^{d}\otimes\mathbb{C}^{d}$ if and only if $d\geq 3$ (resp. $d\geq 8$). To prove this we employ algebraic geometry to reason about the different algebraic structures of the bosonic/fermionic systems. Additionally, due to the relatively simple coherent state form of unentangled bosonic states, we are able to give the explicit constructions of two bosonic UEs. Our investigation provides insight into the entanglement properties of systems of indisitinguishable particles, and in particular underscores the difference between the entanglement structures of bosonic, fermionic and distinguishable particle systems.

arXiv:1305.7489Leibniz international proceedings in informaticsJan 1, 20131 citation

Decoherence and entanglement in quantum systems

Journal of Russian Laser ResearchSep 1, 20070 citations

A universal entangler (UE) is a unitary operation which maps all pure product states to entangled states. It is known that for a bipartite system of particles

1,2

with a Hilbert space

\mathbb{C}^{d_1}\otimes\mathbb{C}^{d_2}

, a UE exists when

\min{(d_1,d_2)}\geq 3

and

(d_1,d_2)\neq (3,3)

. It is also known that whenever a UE exists, almost all unitaries are UEs; however to verify whether a given unitary is a UE is very difficult since solving a quadratic system of equations is NP-hard in general. This work examines the existence and construction of UEs of bipartite bosonic/fermionic systems whose wave functions sit in the symmetric/antisymmetric subspace of

\mathbb{C}^{d}\otimes\mathbb{C}^{d}

. The development of a theory of UEs for these types of systems needs considerably different approaches from that used for UEs of distinguishable systems. This is because the general entanglement of identical particle systems cannot be discussed in the usual way due to the effect of (anti)-symmetrization which introduces "pseudo entanglement" that is inaccessible in practice. We show that, unlike the distinguishable particle case, UEs exist for bosonic/fermionic systems with Hilbert spaces which are symmetric (resp. antisymmetric) subspaces of

\mathbb{C}^{d}\otimes\mathbb{C}^{d}

if and only if

d\geq 3

(resp.

d\geq 8

). To prove this we employ algebraic geometry to reason about the different algebraic structures of the bosonic/fermionic systems. Additionally, due to the relatively simple coherent state form of unentangled bosonic states, we are able to give the explicit constructions of two bosonic UEs. Our investigation provides insight into the entanglement properties of systems of indisitinguishable particles, and in particular underscores the difference between the entanglement structures of bosonic, fermionic and distinguishable particle systems.