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Journal of Physics Conference Series

Quantum dynamics of a two-atom-qubit system

Nguyen Van Hieu, Bich Ha Nguyen, Le Thi Ha Linh

Published Sep 1, 2009• 1 citation
Publisher

Abstract

A physical model of the quantum information exchange between two qubits is studied theoretically. The qubits are two identical two-level atoms, the physical mechanism of the quantum information exchange is the mutual dependence of the reduced density matrices of two qubits generated by their couplings with a multimode radiation field. The Lehmberg-Agarwal master equation is exactly solved. The explicit form of the mutual dependence of two reduced density matrices is established. The application to study the entanglement of two qubits is discussed.

DOI
10.1088/1742-6596/187/1/012010

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A physical model of the quantum information exchange between two qubits is studied theoretically. The qubits are two identical two-level atoms, the physical mechanism of the quantum information exchange is the mutual dependence of the reduced density matrices of two qubits generated by their couplings with a multimode radiation field. The Lehmberg-Agarwal master equation is exactly solved. The explicit form of the mutual dependence of two reduced density matrices is established. The application to study the entanglement of two qubits is discussed.
The aim of this topical review is a systematic and concise presentation of the results of a series of theoretical works on the quantum dynamics of two-spin-qubit systems towards the elaboration of a physical mechanism of the quantum information transfer between two spin-qubits. For this purpose the main attention is paid to exactly solvable models of two-spin-qubit systems, since the analytical expressions of the elements of their reduced density matrices explicitly exhibit the mutual dependence of the quantum information encoded into the spin-qubits. The treatment of their decoherence due to the interaction with the environment is performed in the Markovian approximation. Rate equations for axially symmetric systems of two coupled spin-qubits non-interacting, as well as interacting, with the environment are exactly solved. It is shown how the solutions of rate equations demonstrate the physical mechanism of the quantum information exchange between the spin-qubits. This mechanism holds also in all two-spin-qubit systems whose rate equations can be solved only by means of numerical calculations. Exact solutions of rate equations for two uncoupled spin-qubits interacting with two separate environments reveal an interesting physical phenomenon in the time evolution of the qubit-qubit entanglement generated by their interaction with the environments: the entanglement sudden death and revival. A two-spin-qubit system with an asymptotically decoherence free subspace was also explicitly constructed. The presented calculations and reasonings can be extended for application to the study of spin-qubit chains or networks.
The theory of the quantum information transmission between two semiconductor two-level quantum dots as two qubits through an intermediary photon gas in a cavity is presented. The reduced density matrix of each two-level quantum dot is the quantum information encoded into this qubit. The quantum information exchange between two distant qubits imbedded in the photon gas is performed in the form of the mutual dependence of their reduced density matrices due to the interaction between the electrons in the qubits and the photon gas. The system of rate equations for the reduced density matrix of the two-qubit system is derived. From the solution of this system of equations it follows the mutual dependence of the reduced density matrices of two distant qubits.
The quantum dynamics of a system of two interacting spin-qubits is studied for elaborating the physical mechanism of the quantum information transfer between them. A simple model with their Heisenberg XY exchange interaction is investigated. The rate equations are established. The analytical expressions of their solution are exactly derived. They explicitly demonstrate, how the quantum information encoded into a spin-qubit at the initial time t = 0 is transfered to other one at any time t > 0.
We study the non-equilibrium dynamics of a pair of qubits made of two-level atoms separated in space with distance r and interacting with one common electromagnetic field but not directly with each other. Our calculation makes a weak coupling assumption, but no Born or Markov approximation. We derived a non-Markovian master equation for the evolution of the reduced density matrix of the two-qubit system after integrating out the electromagnetic field modes. It contains a Markovian part with a Lindblad type operator and a nonMarkovian contribution, the physics of which is the main focus of this study. We use the concurrence function as a measure of quantum entanglement between the two qubits. Two classes of states are studied in detail: Class A is a one parameter family of states which are the superposition of the highest energy |I〉 ≡ |11〉 and lowest energy |O〉 ≡ |00〉 states, υiz, |A〉≡p|I〉+(1−p)|O〉, with 0 ≤ p ≤ 1; and Class B states |B〉 are linear combinations of the symmetric |+〉=12(|01〉+|10〉) and the antisymmetric |−〉=12(|01〉−|10〉) Bell states.
In the consideration of Milburn model of intrinsic decoherence,we investigate the entanglement between two two-level atoms interacting with a Fock state of single-mode quantized radiation field.The reduced density matrix of the atom system is given explicitly.Due to the intrinsic decoherence,the entanglement of the atoms will decrease as the evolution of the system.And finally,the atoms system will approach a stationary state which the stationary entanglement depends on the initial states of the field and the atoms.Here,the entanglement is calculated by making use of the concurrence.