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Physical Review A

Time evolution of entangled Bell states in coupled quantum dots in the presence of fluctuations

N. S. Maslova, Vladimir N. Mantsevich, Igor Michailovitsch Sokolov, P. I. Arseyev

Published Mar 25, 2024• 1 citation
Publisher

Abstract

We analyze the dynamics of two-qubit entangled Bell states in coupled quantum dots (QDs) in the presence of both fluctuations and coherent electron hopping between the dots. The explicit expression for time-dependent probability to find the system in the different Bell states was obtained for various initial conditions by means of Keldysh diagram technique. It was revealed that time evolution of one pair of Bell states and its decay rate strongly differs from another one. It was demonstrated that one pair of Bell states is more robust against fluctuations than another one. The stationary occupation of Bell states for different initial conditions was also analyzed. Obtained results are important for the problems where long-living Bell states are needed such as the security of quantum communication and quantum information processing.

DOI
10.1103/physreva.109.032430

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We analyze the dynamics of two-qubit entangled Bell states in coupled quantum dots (QDs) in the presence of both fluctuations and coherent electron hopping between the dots. The explicit expression for time-dependent probability to find the system in the different Bell states was obtained for various initial conditions by means of Keldysh diagram technique. It was revealed that time evolution of one pair of Bell states and its decay rate strongly differs from another one. It was demonstrated that one pair of Bell states is more robust against fluctuations than another one. The stationary occupation of Bell states for different initial conditions was also analyzed. Obtained results are important for the problems where long-living Bell states are needed such as the security of quantum communication and quantum information processing.
The time evolution of an initially prepared entangled state in the system of coupled quantum dots has been analyzed by means of two different theoretical approaches: equations of motion for all orders localized electron correlation functions, considering interference effects, and kinetic equations for the pseudoparticle occupation numbers with constraint on the possible physical states. Results obtained by means of different approaches were carefully analyzed and compared to each other. Revealing a direct link between concurrence (degree of entanglement) and quantum dots pair correlation functions allowed us to follow the changes of entanglement during the time evolution of the coupled quantum dots system. It was demonstrated that the degree of entanglement can be controllably tuned during the time evolution of quantum dots system.
We investigate the entanglement dynamics of two electron-spin qubits in the quantum-dot (QD)–microcavity system in the large-detuning limit and subjected to two different noise sources: electron-spin dephasing and relaxation. We show that when one of the two dots is prepared initially in the excited state, the created entanglement exhibits oscillatory behavior at the beginning of evolution and then completely disappears over time. For two QDs that are initially in either the Einstein–Podolsky–Rosen-Bell states or the Werner states, their entanglement evolution exhibits the same behavior in the presence of pure dephasing, but is completely different under the relaxation process. We also show that the interdot interaction induced by a single-mode cavity field does not contribute to the dynamics of entanglement for these Bell states and Werner states.
Background. The study of entangled states in Jaynes–Cummings models and its multiqubit generalizations and extensions remains an important and relevant topic in modern quantum optics, quantum information science and solid state physics. This is due to the fact that such models naturally describe the dynamics of interaction of logical elements of quantum devices, such as quantum computers or quantum networks (qubits) with microwave fields of resonators used to control the states of qubits. In this regard, it is very important to search for the most efficient schemes of generation, control and monitoring of entangled qubit states within the framework of Jaynes–Cummings type models. Aim. To investigate the entanglement dynamics of a pair of qubits, each of which is locked in a single-mode resonator and interacts non-resonantly with the vacuum field mode, in the presence of detuning between frequencies of transitions in the qubits and frequencies of resonator modes and dipole-dipole interaction of the qubits. Methods. To analyze the dynamics of the considered system, the solution of the time-dependent quantum Schrödinger equation is investigated. The exact solution of the above equation in the case of entangled Bell-type initial qubits states is found. This is used to calculate the criterion of entanglement of a pair of qubits – negativity. Numerical modeling of the time dependence of negativity for different values of the parameters of the considered model has been carried out. Results. It is shown that the presence of detuning, the difference in the qubit-photon couplings and the intensity of the dipole-dipole interaction significantly affect the maximum degree of entanglement of the qubit subsystem during its evolution. It is found that for certain parameters of the model under consideration, the initial Bell entangled states of qubits can be considered as long-lived stable states. Conclusion. The possibility of realization of long-lived and robust two-qubit entangled states in the system under consideration has been established. The obtained results can be used for effective control and manipulation of the degree of entanglement of qubits interacting with microwave fields of resonators.
The time-evolution of the atom′s occupancy in the system of two-mode entangled coherent fields interacting with two atoms in Bell states via two-photon process is investigated by means of quantum theory.The results show that the atom′s occupancy is zero if the two atoms are initially in Bell state |β11.If the two atoms are initially in the other three Bell states,the oscillation frequency of the atom′s occupancy accelerates and the amplitude decreases apparently with the increase of mean photon numbers of field.The degree of the entanglement for the entangled coherent fields can′t influence the oscillation frequency and the position of the atom′s occupancy curve.If the two atoms are initially in Bell state |β01,the Rabi oscillation frequency of the atom′s occupancy accelerates apparently with the increase of the coupling strength of interaction between atoms.While the two atoms are initially in Bell state |β10 or |β00,the collapse-revival phenomenon of the atom′s occupancy disappears gradually.
The generation of entanglement between two identical, interacting quantum dots---initially in ground states---by a coherent field and the subsequent time evolution of the entanglement are studied by calculating the concurrence between the two dots. The results predict that while it is possible to generate entanglement (or entanglement of formation, as defined for a mixed state) between the two dots, at no time do the dots become fully entangled to each other or is a maximally entangled Bell state ever achieved. We also observe that the degree of entanglement increases with an increase in the photon number inside the cavity and a decrease in the dot-photon coupling. The behavior of the two-dot system, initially prepared in an entangled state and interacting with thermal light, is also studied.