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arXiv:1303.3861

Generation of quantum entanglement between three level atoms via nnn coupled cavities

Rahime Sufiani, Ahad Darkhosh

Published Mar 15, 2013• 0 citations
arXivHTMLPDF

Abstract

Based on two-photon exchange interaction between $n$ coupled optical cavities each of them containing a single three level atom, the $n$-qubit and $n$-photonic state transfer is investigated. In fact, following the approach of Ref.\cite{Alex1}, we consider $n$ coupled cavities instead of two cavities and generalize the discussions about quantum state transfer, photon transition between cavities and entanglement generations between $n$ atoms. More clearly, by employing the consistency of number of photons (the symmetry of Hamiltonian), the hamiltonian of the system is reduced from $3^n$ dimensional space into 2n dimensional one. Moreover, by introducing suitable basis for the atom-cavity state space based on Fourier transform, the reduced Hamiltonian is block-diagonalized, with 2 dimensional blocks. Then, the initial state of the system is evolved under the corresponding Hamiltonian and the suitable times $T$ at which the initially unentangled atoms, become maximally entangled, are determined in terms of the hopping strength $ξ$ between cavities.

DOI
10.48550/arxiv.1303.3861

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Based on two-photon exchange interaction between nnn coupled optical cavities each of them containing a single three level atom, the nnn-qubit and nnn-photonic state transfer is investigated. In fact, following the approach of Ref.\cite{Alex1}, we consider nnn coupled cavities instead of two cavities and generalize the discussions about quantum state transfer, photon transition between cavities and entanglement generations between nnn atoms. More clearly, by employing the consistency of number of photons (the symmetry of Hamiltonian), the hamiltonian of the system is reduced from 3n3^n3n dimensional space into 2n dimensional one. Moreover, by introducing suitable basis for the atom-cavity state space based on Fourier transform, the reduced Hamiltonian is block-diagonalized, with 2 dimensional blocks. Then, the initial state of the system is evolved under the corresponding Hamiltonian and the suitable times TTT at which the initially unentangled atoms, become maximally entangled, are determined in terms of the hopping strength ξξξ between cavities.
The generation of entanglement between two identical coupled cavities, each containing a single three-level atom, is studied when the cavities exchange two coherent photons and are in the N=2,4N=2,4N=2,4 manifolds, where NNN represents the maximum number of photons possible in either cavity. The atom-photon state of each cavity is described by a qutrit for N=2N=2N=2 and a five-dimensional qudit for N=4N=4N=4. However, the conservation of the total value of NNN for the interacting two-cavity system limits the total number of states to only 4 states for N=2N=2N=2 and 8 states for N=4N=4N=4, rather than the usual 9 for two qutrits and 25 for two five-dimensional qudits. In the N=2N=2N=2 manifold, two-qutrit states dynamically generate four maximally entangled Bell states from initially unentangled states. In the N=4N=4N=4 manifold, two-qudit states dynamically generate maximally entangled states involving three or four states. The generation of these maximally entangled states occurs rather rapidly for large hopping strengths. The cavities function as a storage of periodically generated maximally entangled states.
The generation of entanglement between three identical coupled cavities, each containing a single three-level atom, is studied when the cavities exchange two coherent photons and are in the N=2, 4, and 6 manifolds, where NNN represents the maximum number of photons possible in any one cavity. The combined states of the atom and the photon in a cavity is given by a qutrit for N=2, a five-dimensional qudit for N=4, and a seven-dimensional qudit for N=6. The conservation of the operator N^\hat{N}N^ for the interacting three-cavity system limits the total number of tripartite states to only 6, 18, and 38, rather than the usual 33=273^3=2733=27, 53=1255^3=12553=125, and 73=3437^3 =34373=343 states for N=2, 4, and 6, respectively. The deterministic generation of entanglement from general initially unentangled tripartite states is studied in the limit of large hopping strength, where all the solutions are analytic and given in terms of exponential functions. Several types of resulting tripartite entanglement are analyzed in order to obtain maximally entangled states.
The generation of entanglement between three identical coupled cavities, eachcontaining a single three-level atom, is studied when the cavities exchange two coherent photonsand are in the N =2, 4, and 6 manifolds, where N represents the maximum number of photonspossible in any one cavity. The combined states of the atom and the photon in a cavity is given bya qutrit for N = 2, a five-dimensional qudit for N = 4, and a seven-dimensional qudit for N = 6. Theconservation of the operator Nˆ for the interacting three-cavity system limits the total number oftripartite states to only 6, 18, and 38, rather than the usual 33 = 27, 53 = 125, and 73 = 343 states for N =2, 4, and 6, respectively. The deterministic generation of entanglement from general initiallyunentangled tripartite states is studied in the limit of large hopping strength, where all the solutionsare analytic and given in terms of exponential functions. Several types of resulting tripartiteentanglement are analyzed in order to obtain maximally entangled states.
The temporal evolution of two coupled cavities, each containing a single three-level atom, is studied when the cavities exchange two coherent photons. The general state of the system is a linear superposition of symmetric and antisymmetric states with the symmetric states controlled by two of the four eigenfrequencies and the antisymmetric states by the other two. The system undergoes Rabi oscillations between the two symmetric (antisymmetric) states. There is state transfer between the cavities when both atoms are in the ground state and two photons are exchanged. In addition, there is also Rabi ``flopping'' whereby one atom is in the excited state and the other in the ground state and the roles are reversed in a periodic fashion by the exchange of two photons. The generation of entanglement can be explicitly given as a function of time. Models of coupled cavities are of interest in distributed quantum information and computation.
The problem of the complete transfer of quantum states and entanglement in a four-qubit system composed of two single-mode cavities and two two-level atoms is investigated. The transfer of single and double excitation states is discussed for two different coupling configurations between the qubits. In the first, the coupling is mediated by the atoms that simultaneously couple to the cavity modes. In the second configuration, each atom resides inside one of the cavities and the coupling between the cavities is mediated by the overlapping field modes. A proper choice of basis states makes it possible to identify states that could be completely transferred between themselves. Simple expressions are derived for the conditions for the complete transfer of quantum states and entanglement. These conditions impose severe constraints on the evolution of the system in the form of constants of motion. The constrains on the evolution of the system imply that not all states can evolve in time, and we find that the evolution of the entire system can be confined into that occurring among two states only. Detailed analysis show that in the case where the interaction is mediated by the atoms, only symmetric superposition states can be completely and reversibly transferred between the atoms and the cavity modes. In the case where the interaction is mediated by the overlapping field modes, both symmetric and antisymmetric superposition states can be completely transferred. We also show that the system is capable of generating purely photonic NOON states, but only if the coupling is mediated by the atoms, and demonstrate that the ability to generate the NOON states relies on perfect transfer of an entanglement from the atoms to the cavity modes.
We study quantum state transfer and multipartite entanglement generation in the ensembles of qubits enclosed by a one-dimensional system of coupled optical cavities. Each cavity contains N qubits whose interaction with the quantum field of their respective cavity is governed by the Dicke Lipkin–Meshkov–Glick model. An excitation initially seeded in the ensemble at the end of the one-dimensional chain of coupled cavities transfers to the corresponding ensemble of the last cavity with success that depends on the mode-ensemble coupling χ , ensemble-mode detuning δ , photon hopping rate λ , and size of a given ensemble N . Suitable choices of such parameters enable overcoming the freezing effect induced by the choice of a far-off detuning regime. We identify working points at which three-ensemble W states and two-ensemble maximally entangled states emerge in the multipartite entanglement dynamics. This study provides a basis for manipulation of quantum states in a multipartite coupled cavity arrangement that may be useful in understanding very complex systems in the field of quantum information processing.