Generation of Entangled Tripartite States in Three Identical Cavities

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 $N$ 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 $\hat{N}$ for the interacting three-cavity system limits the total number of tripartite states to only 6, 18, and 38, rather than the usual $3^3=27$ , $5^3=125$ , and $7^3 =343$ 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, 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 $N$ 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 $\hat{N}$ for the interacting three-cavity system limits the total number of tripartite states to only 6, 18, and 38, rather than the usual $3^3=27$, $5^3=125$, and $7^3 =343$ 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.

arXiv:1203.4173Mar 19, 20120 citations

Dynamical generation of maximally entangled states in two identical cavities

Moorad Alexanian

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 $N=2,4$ manifolds, where $N$ represents the maximum number of photons possible in either cavity. The atom-photon state of each cavity is described by a qutrit for $N=2$ and a five-dimensional qudit for $N=4$ . However, the conservation of the total value of $N$ for the interacting two-cavity system limits the total number of states to only 4 states for $N=2$ and 8 states for $N=4$ , rather than the usual 9 for two qutrits and 25 for two five-dimensional qudits. In the $N=2$ manifold, two-qutrit states dynamically generate four maximally entangled Bell states from initially unentangled states. In the $N=4$ 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 two identical coupled cavities, each containing a single three-level atom, is studied when the cavities exchange two coherent photons and are in the $N=2,4$ manifolds, where $N$ represents the maximum number of photons possible in either cavity. The atom-photon state of each cavity is described by a qutrit for $N=2$ and a five-dimensional qudit for $N=4$. However, the conservation of the total value of $N$ for the interacting two-cavity system limits the total number of states to only 4 states for $N=2$ and 8 states for $N=4$, rather than the usual 9 for two qutrits and 25 for two five-dimensional qudits. In the $N=2$ manifold, two-qutrit states dynamically generate four maximally entangled Bell states from initially unentangled states. In the $N=4$ 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.

Physical Review ANov 3, 20117 citations

Generation of quantum entanglement between three level atoms via $n$ coupled cavities

Rahime Sufiani, Ahad Darkhosh

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.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.

arXiv:1303.3861Mar 15, 20130 citations

Tripartite entanglement in multimode cavity quantum electrodynamics

Nishan Amgain, Mostafijur Rahman, Umar Arshad +3 more

We numerically investigate the generation and dynamics of tripartite entanglement among qubits (quantum emitters or atoms) in multimode cavity quantum electrodynamics (cQED). Our cQED architecture features three initially unentangled excited two-level quantum emitters confined within a triangle-shaped multimode optical cavity, which later become entangled due to a Jaynes-Cummings-like interaction. Using the tripartite negativity measure of entanglement and fidelity with respect to the genuine tripartite entangled state (Greenberger-Horne-Zeilinger state, to be precise), we analyze the impact of the number of cavity modes, qubit locations, and losses (spontaneous emission from qubits and photon leakage from the cavity mirrors) on the generated entanglement. Our key results include the presence of two kinds of retardation effects: one resulting from the time it takes for photons to propagate from one qubit to another, and the other to complete one round trip in the cavity. We observed these retardation effects only in multimode cavities, with the exciting possibility of controlling the collapse and revival patterns of tripartite entanglement by altering the qubit locations in the cavity. Furthermore, the impact of losses on the generated entanglement and the dependence of maximum entanglement on the total number of modes yield results that surpass those reported for single and two excitations. With recent advances in circuit quantum electrodynamics, these findings hold promise for the development of entanglement-based quantum networking protocols and quantum memories.We numerically investigate the generation and dynamics of tripartite entanglement among qubits (quantum emitters or atoms) in multimode cavity quantum electrodynamics (cQED). Our cQED architecture features three initially unentangled excited two-level quantum emitters confined within a triangle-shaped multimode optical cavity, which later become entangled due to a Jaynes-Cummings-like interaction. Using the tripartite negativity measure of entanglement and fidelity with respect to the genuine tripartite entangled state (Greenberger-Horne-Zeilinger state, to be precise), we analyze the impact of the number of cavity modes, qubit locations, and losses (spontaneous emission from qubits and photon leakage from the cavity mirrors) on the generated entanglement. Our key results include the presence of two kinds of retardation effects: one resulting from the time it takes for photons to propagate from one qubit to another, and the other to complete one round trip in the cavity. We observed these retardation effects only in multimode cavities, with the exciting possibility of controlling the collapse and revival patterns of tripartite entanglement by altering the qubit locations in the cavity. Furthermore, the impact of losses on the generated entanglement and the dependence of maximum entanglement on the total number of modes yield results that surpass those reported for single and two excitations. With recent advances in circuit quantum electrodynamics, these findings hold promise for the development of entanglement-based quantum networking protocols and quantum memories.

arXiv:2507.11885Physical Review ASep 26, 20250 citations

Generation of entangled states of two atoms inside a leaky cavity

T. W. Chen, C. K. Law, P. T. Leung

An in-depth theoretical study is carried out to examine the quasideterministic entanglement of two atoms inside a leaky cavity. Two $\ensuremath{\Lambda}$-type three-level atoms, initially in their ground states, may become maximally entangled through the interaction with a single photon. By working out an exact analytic solution, we show that the probability of success depends crucially on the spectral function of the injected photon. With a cavity photon, one can generate a maximally entangled state with a certain probability that is always less than $50%.$ However, for an injected photon with a narrower spectral width, this probability can be significantly increased. In particular, we discover situations in which entanglement can be achieved in a single trial with an almost unit probability.An in-depth theoretical study is carried out to examine the quasideterministic entanglement of two atoms inside a leaky cavity. Two $\ensuremath{\Lambda}$-type three-level atoms, initially in their ground states, may become maximally entangled through the interaction with a single photon. By working out an exact analytic solution, we show that the probability of success depends crucially on the spectral function of the injected photon. With a cavity photon, one can generate a maximally entangled state with a certain probability that is always less than $50%.$ However, for an injected photon with a narrower spectral width, this probability can be significantly increased. In particular, we discover situations in which entanglement can be achieved in a single trial with an almost unit probability.

arXiv:quant-ph/0309182Physical Review ANov 19, 200311 citations

Two-photon exchange between two three-level atoms in separate cavities

Moorad Alexanian

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 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.

Physical Review AFeb 22, 201117 citations

N

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

\hat{N}

for the interacting three-cavity system limits the total number of tripartite states to only 6, 18, and 38, rather than the usual

3^3=27

5^3=125

, and

7^3 =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 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=2,4

manifolds, where

N

represents the maximum number of photons possible in either cavity. The atom-photon state of each cavity is described by a qutrit for

N=2

and a five-dimensional qudit for

N=4

. However, the conservation of the total value of

N

for the interacting two-cavity system limits the total number of states to only 4 states for

N=2

and 8 states for

N=4

, rather than the usual 9 for two qutrits and 25 for two five-dimensional qudits. In the

N=2

manifold, two-qutrit states dynamically generate four maximally entangled Bell states from initially unentangled states. In the

N=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.

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.

50%.

However, for an injected photon with a narrower spectral width, this probability can be significantly increased. In particular, we discover situations in which entanglement can be achieved in a single trial with an almost unit probability.