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انجمن اپتیک و فوتونیک ایران

Dynamics of Entanglement of a Collective of Qubits Interacting with a Dissipative Cavity

Alireza Nourmandipour, Morteza Rafiee, Mohammad Kazem Tavassoly

Published Feb 10, 2016• 0 citations
OpenAlex

Abstract

In this paper, the pairwise entanglement of two qubits in a system consists of a dissipative cavity with an arbitrary number of qubitsis investigated. To model the dissipation in this cavity, the Gardiner-Collett approach has been utilized.Theanalytical expression of the wave function of the system is obtainedby solving the time-dependent Schrodinger equation with the initial state as a superposition of single-excitation of two arbitrary qubits. Entanglement dynamics of any two qubitsfor different number of qubits and various coupling regimeshas been investigated.

Related papers

Dynamics and protecting of entanglement in two-level systems interacting with a dissipative cavity: the Gardiner–Collett approach

Alireza Nourmandipour, M K Tavassoly

Abstract In this paper, we study the exact entanglement dynamics of two two-level atoms in a dissipative cavity. We use the Gardiner–Collett Hamiltonian to model the dissipative cavity, in which we assume that the two atoms resonantly interact with the cavity field and the cavity field itself interacts with the surrounding medium. Then, with the help of the Fano’s technique we show that this system can be regarded as two atoms interacting with a heat bath. In such a case, we find that there exists a decoherence-free state that does not evolve in time. At this time there exists a so-called super-radiant state which decays in time due to dissipation. At last, we use the quantum Zeno effect to preserve the entanglement which already has been stored in the system.

arXiv:1607.00126•Journal of Physics B Atomic Molecular and Optical Physics•Jul 8, 2015•30 citations

Dynamics and protection of entanglement in n -qubit systems within Markovian and non-Markovian environments

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We provide an analytical investigation of the pairwise entanglement dynamics for a system, consisting of an arbitrary number of qubits dissipating into a common and non-Markovian environment for both weak- and strong-coupling regimes. In the latter case, a revival of pairwise entanglement due to the memory depth of the environment is observed. The leakage of photons into a continuum state is assumed to be the source of dissipation. We show that for an initially Werner state, the environment washes out the pairwise entanglement, but a series of nonselective measurements can protect the relevant entanglement. On the other hand, by limiting the number of qubits initially in the superposition of single excitation, a stationary entanglement can be created between qubits initially in the excited and ground states. Finally, we determine the stationary distribution of the entanglement versus the total number of qubits in the system.

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Entanglement dynamic of arbitrary number qubit in the open quantum systems

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We study the entanglement dynamics of multi-qubit systems coupled to a common dissipative environment, focusing on systems with one or two initially excited qubits. Using the Lindblad master equation, we derive the time evolution of the density matrix and analyze the entanglement between qubit pairs via the concurrence measure. The solution method involves applying the Lindblad super-operator to the initial density matrix, generating a subspace of non-duplicate states. We extend our analysis to $n$-qubit systems, including three-qubit and four-qubit configurations, and explore the effects of thermal noise on entanglement dynamics. Our results demonstrate how initial conditions, system size, and environmental interactions shape entanglement, providing valuable insights for quantum information processing applications.

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The effect of the classical driving field on the dynamics of entanglement of two qubits interacting with two dissipative cavities

Alireza Nourmandipour

In this article, we first introduce a system consisting of two dissipative cavities, in each of which there is a two-level atom. Each of the atoms is under the influence of a classical laser field, which causes the displacement of their energy levels. The correlation between two cavities is given by the field-field interaction term. We use the Gardiner-Collet model to describe the dissipation in this research. After introducing the Hamiltonian of the system, we simplify the Hamiltonian by using the Fano technique and introducing two sets of new operators. Also, with introducing the atomic bare bases, the Hamiltonian of the system will become a solvable form. Then, by using the technique of Laplace transforms, we solve the time-dependent Schrödinger equation and find the explicit form of the system's wave function at every moment of time. Having the wave function of the atom-atom system and using the concurrence criterion, we investigate the entanglement dynamics of the system in two strong and weak interaction regimes corresponding to the non-Markovian and Markovian regimes. The results show that there will be no stable state of entanglement in this system. We will also show that the classical laser field will play a constructive role in maintaining the initial entanglement as well as the generated entanglement.

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Entanglement in a driven two-qubit system coupled to common cavity

Amit Dey

A system, comprised of a qubit pair coupled to a common cavity, is studied with the aim of establishing qubit entanglement. This study is the sequel of the paper Phys. Rev. A 111, 043705 (2025), where similar model was investigated for an initially vacuum cavity. In the present manuscript the cavity with finite initial occupancy is considered and the effect of asymmetric qubit cavity couplings is investigated. For a closed system scenario, the ratio of the qubit-cavity couplings shows a threshold beyond which no maximally-entangled qubit state is available. The threshold value is shown to depend on the excitation level of the cavity. For a driven-dissipative case steady state entanglement is shown to depend non-monotonically on the qubit drive. Intricate interplay of drive, dissipation, and coupling asymmetry is shown to be pivotal for steady-state entanglement generation.

quant-pharXiv:2603.20866•Mar 24, 2026•0 citations
In this paper, the pairwise entanglement of two qubits in a system consists of a dissipative cavity with an arbitrary number of qubitsis investigated. To model the dissipation in this cavity, the Gardiner-Collett approach has been utilized.Theanalytical expression of the wave function of the system is obtainedby solving the time-dependent Schrodinger equation with the initial state as a superposition of single-excitation of two arbitrary qubits. Entanglement dynamics of any two qubitsfor different number of qubits and various coupling regimeshas been investigated.
Abstract In this paper, we study the exact entanglement dynamics of two two-level atoms in a dissipative cavity. We use the Gardiner–Collett Hamiltonian to model the dissipative cavity, in which we assume that the two atoms resonantly interact with the cavity field and the cavity field itself interacts with the surrounding medium. Then, with the help of the Fano’s technique we show that this system can be regarded as two atoms interacting with a heat bath. In such a case, we find that there exists a decoherence-free state that does not evolve in time. At this time there exists a so-called super-radiant state which decays in time due to dissipation. At last, we use the quantum Zeno effect to preserve the entanglement which already has been stored in the system.
We provide an analytical investigation of the pairwise entanglement dynamics for a system, consisting of an arbitrary number of qubits dissipating into a common and non-Markovian environment for both weak- and strong-coupling regimes. In the latter case, a revival of pairwise entanglement due to the memory depth of the environment is observed. The leakage of photons into a continuum state is assumed to be the source of dissipation. We show that for an initially Werner state, the environment washes out the pairwise entanglement, but a series of nonselective measurements can protect the relevant entanglement. On the other hand, by limiting the number of qubits initially in the superposition of single excitation, a stationary entanglement can be created between qubits initially in the excited and ground states. Finally, we determine the stationary distribution of the entanglement versus the total number of qubits in the system.
The article studies the dynamics of pairwise entanglement of three qubits, two of which are trapped in a resonator and interact with a single-mode ideal resonator through single-photon transitions, and the third qubit is outside the resonator. This takes into account the dipole-dipole coupling between the isolated qubit and the qubit in the resonator. We have found a solution to the quantum nonstationary Schrodinger equation for the total wave function of the system for the initial separable and biseparable states of qubits and the thermal initial state of the resonator field. Using these solutions, the criterion of entanglement of qubit pairs - negativity is calculated. The results of numerical simulation of the negativity criterion have shown that the including of a small dipole-dipole coupling between an isolated and one of the trapped qubits can lead to significant entanglement of qubit pairs for all initial states. There is a transition of entanglement from one pair of atoms to other pairs of atoms during the evolution of the system. It is also shown that for some separable and biseparable states, the dipole-dipole interaction can suppress the effect of sudden death of entanglement.
We study the entanglement dynamics of multi-qubit systems coupled to a common dissipative environment, focusing on systems with one or two initially excited qubits. Using the Lindblad master equation, we derive the time evolution of the density matrix and analyze the entanglement between qubit pairs via the concurrence measure. The solution method involves applying the Lindblad super-operator to the initial density matrix, generating a subspace of non-duplicate states. We extend our analysis to nnn-qubit systems, including three-qubit and four-qubit configurations, and explore the effects of thermal noise on entanglement dynamics. Our results demonstrate how initial conditions, system size, and environmental interactions shape entanglement, providing valuable insights for quantum information processing applications.
In this article, we first introduce a system consisting of two dissipative cavities, in each of which there is a two-level atom. Each of the atoms is under the influence of a classical laser field, which causes the displacement of their energy levels. The correlation between two cavities is given by the field-field interaction term. We use the Gardiner-Collet model to describe the dissipation in this research. After introducing the Hamiltonian of the system, we simplify the Hamiltonian by using the Fano technique and introducing two sets of new operators. Also, with introducing the atomic bare bases, the Hamiltonian of the system will become a solvable form. Then, by using the technique of Laplace transforms, we solve the time-dependent Schrödinger equation and find the explicit form of the system's wave function at every moment of time. Having the wave function of the atom-atom system and using the concurrence criterion, we investigate the entanglement dynamics of the system in two strong and weak interaction regimes corresponding to the non-Markovian and Markovian regimes. The results show that there will be no stable state of entanglement in this system. We will also show that the classical laser field will play a constructive role in maintaining the initial entanglement as well as the generated entanglement.
A system, comprised of a qubit pair coupled to a common cavity, is studied with the aim of establishing qubit entanglement. This study is the sequel of the paper Phys. Rev. A 111, 043705 (2025), where similar model was investigated for an initially vacuum cavity. In the present manuscript the cavity with finite initial occupancy is considered and the effect of asymmetric qubit cavity couplings is investigated. For a closed system scenario, the ratio of the qubit-cavity couplings shows a threshold beyond which no maximally-entangled qubit state is available. The threshold value is shown to depend on the excitation level of the cavity. For a driven-dissipative case steady state entanglement is shown to depend non-monotonically on the qubit drive. Intricate interplay of drive, dissipation, and coupling asymmetry is shown to be pivotal for steady-state entanglement generation.