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Journal of Physics B Atomic Molecular and Optical Physics

Position-dependent dynamics of two qubits in a leakage cavity

Jun Jing, Zhiguo Lü, Hongru Ma, Hang Zheng

Published Jun 23, 2008• 5 citations
Publisher

Abstract

The position-dependent entanglement dynamics of two qubits embedded in a leakage cavity is investigated. The two qubits are initialled in Bell states and the cavity mode is taken as a standing wave. It is found that (i) the dynamics of the Bell states can be divided into two groups according to one-photon entangled states and two-photon entangled states; (ii) the entanglement life of the one-photon entangled states can be kept as long as possible if we put the two qubits at certain positions; (iii) at larger detuning, the entanglement dynamics manifests more robustly.

DOI
10.1088/0953-4075/41/13/135502

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The position-dependent entanglement dynamics of two qubits embedded in a leakage cavity is investigated. The two qubits are initialled in Bell states and the cavity mode is taken as a standing wave. It is found that (i) the dynamics of the Bell states can be divided into two groups according to one-photon entangled states and two-photon entangled states; (ii) the entanglement life of the one-photon entangled states can be kept as long as possible if we put the two qubits at certain positions; (iii) at larger detuning, the entanglement dynamics manifests more robustly.
The dynamics of entanglement and fidelity for a subsystem of two separate spin-1∕21∕21∕2 qubits prepared in Bell states is investigated. One of the subsystem qubit labeled AAA is under the influence of a Heisenberg XYXYXY spin bath, while another one labeled BBB is uncoupled with that. We discuss two cases: (i) the number of bath spins is infinite, $N\ensuremath{\rightarrow}\ensuremath{\infty}$, and (ii) NNN is finite, N=40N=40N=40. In both cases, the bath is initially prepared in a thermal equilibrium state. It is shown that the time dependence of the concurrence and the fidelity of the two subsystem qubits can be controlled by tuning the parameters of the spin bath, such as the anisotropic parameter, the temperature, and the coupling strength with qubit AAA. It is interesting to find that the dynamics of the concurrence is independent of four different initial Bell states and that of the fidelity is divided into two groups.
The dynamics of quantum discord for two identical qubits in two independent single-mode cavities and a common single-mode cavity are discussed. For the initial Bell state with correlated spins, while the entanglement sudden death can occur, the quantum discord vanishes only at discrete moments in the independent cavities and never vanishes in the common cavity. Interestingly, quantum discord and entanglement show opposite behavior in the common cavity, unlike in the independent cavities. For the initial Bell state with anti-correlated spins, quantum discord and entanglement behave in the same way for both independent cavities and a common cavity. It is found that the detunings always stabilize the quantum discord.
In this paper, we investigate the entanglement dynamics of two entangled two-level atoms interacting with a single-mode field in a dissipative cavity. The results show that the evolution properties of the entanglement degree of two entangled atoms depend on the initial atomic entanglement degree and form, the average photon number of the cavity field, and the cavity leakage rate. When the atoms are initially in a particular entangled state, the degree of entanglement can be amplified and not influenced by the dissipation of the cavity field.
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.
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 propose a scheme to generate entanglement between two distant qubits (two-level atom) which are separately trapped in their own (in general) non-Markovian dissipative cavities by utilizing entangling swapping, considering the case in which the qubits can move along their cavity axes rather than a static state of motion. We first examine the role of movement of the qubit by studying the entropy evolution for each subsystem. The average entropy over the initial states of the qubit is calculated. Then by performing a Bell state measurement on the fields leaving the cavities, we swap the entanglement between qubit-field in each cavity into qubit-qubit and field-field subsystems. The entangling power is used to measure the average amount of swapped entanglement over all possible pure initial states. Our results are presented in two weak and strong coupling regimes, illustrating the positive role of movement of the qubits on the swapped entanglement. It is revealed that by considering certain conditions for the initial state of qubits, it is possible to achieve a maximally long-leaving stationary entanglement (Bell state) which is entirely independent of the environmental variables as well as the velocity of qubits. This happens when the two qubits have the same velocities.