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arXiv:1009.1350 · Journal of Physics A Mathematical and Theoretical

Entanglement dynamics of two qubits under the influence of external kicks and Gaussian pulses

Ferdi Altintas, Resul Eryigit

Published Sep 15, 2011• 4 citations
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Abstract

We have investigated the dynamics of entanglement between two spin-1/2 qubits that are subject to independent kick and Gaussian pulse-type external magnetic fields analytically and numerically. We show that ‘almost-steady’ high entanglement can be created between two initially unentangled qubits by using carefully designed kick or pulse sequences.

DOI
10.1088/1751-8113/44/40/405302

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We have investigated the dynamics of entanglement between two spin-1/2 qubits that are subject to independent kick and Gaussian pulse-type external magnetic fields analytically and numerically. We show that ‘almost-steady’ high entanglement can be created between two initially unentangled qubits by using carefully designed kick or pulse sequences.
Abstract. We have investigated the analytical and numerical dynamics of entanglement for two qubits that interact with each other via Heisenberg XXX-type interaction and subject to local time-specific external kick and Gaussian pulse-type magnetic fields in x-y plane. The qubits have been assumed to be initially prepared in different pure separable and maximally entangled states and the effect of the strength and the direction of external fast pulses on concurrence has been investigated. The carefully designed kick or pulse sequences are found to enable one to obtain constant long-lasting entanglement with desired magnitude. Moreover, the time ordering effects are found to be important in the creation and manipulation of entanglement by external fields.
The entanglement of two qubits, each defined as an effective two-level, spin 1/2 system, is investigated for the case that the qubits interact via a Heisenberg XY interaction and are subject to decoherence due to population relaxation and thermal effects. For zero temperature, the time-dependent concurrence is studied analytically and numerically for some typical initial states, including a separable (unentangled) initial state. An analytical formula for non-zero steady state concurrence is found for any initial state, and optimal parameter values for maximizing steady state concurrence are given. The steady state concurrence is found analytically to remain non-zero for low, finite temperatures. We also identify the contributions of global and local coherence to the steady state entanglement.
Two charge qubits located inside a damped driven cavity is considered. The dynamical evolution of the entanglement between the two qubits is demonstrated analytically or numerically. It is found that with the cavity dissipation, the steady entanglement between the two qubits is sensitive to the initial state of the qubits, but independent of the cavity field's initial state. The two qubits initially in the separable and most mixed state can be more easily entangled. The external field can be used to enhance the steady entanglement between the two charge qubits.
In this paper, we consider two examples of an entanglement in two-qubit systems and an example of entanglement in quantum field theory (QFT). In the beginning, we study the entanglement of two spin states by a magnetic field. A nonzero entanglement appears for interacting spins. When the coupling between the spins is constant, we study the entanglement by several types of time-dependent magnetic fields. In the case of a constant difference between [Formula: see text] components of magnetic fields acting on each spin, we find several time-dependent coupling functions [Formula: see text] that also allow us to analyze analytically and numerically the entanglement measure. Considering two photons moving in an electron medium, we demonstrate that they can be entangled in a controlled way by applying an external magnetic field. The magnetic field affecting electrons of the medium affects photons and, thus, causes an entanglement of the photon beams. The third example is related to the effect of production of electron–positron pairs from the vacuum by a strong external electric field. Here, we have used a general nonperturbative expression for the density operator of the system under consideration. Applying a reduction procedure to this density operator, we construct mixed states of electron and positron subsystems. Calculating the von Neumann entropy of such states, we obtain the loss of information due to the reduction and, at the same time, the entanglement measure of electron and positron subsystems. This entanglement can be considered as an example of an entanglement in QFT.
We study the bipartite entanglement dynamics in an anisotropic two-qubit Heisenberg XYZXYZXYZ model under the influence of population relaxation and in the presence of various types of magnetic fields. We find that the maximal value of the concurrence has an intrinsic rigidity for the different external magnetic fields. Moreover, our results demonstrate that it is possible to produce entangled states and to control or to modulate the concurrence within the intrinsic maximal value with the help of external time-varying fields despite the existence of dissipation.
The transitory and steady-state entanglement of a two-qubit XY Heisenberg magnetic spin system immersed in an external magnetic field are analyzed in terms of the entanglement measure of concurrence. The dependence of the system entanglement on coupling strength, decay rate, and applied magnetic field is numerically simulated for two distinct models of system evolution involving decoherence to the environment. An applied magnetic field was found to consistently reduce the system entropy. The external magnetic field increases entanglement for small strength, and if too strong, it reduces the entanglement. The maximum entanglement is formed from a balance of external magnetic field and the decay rate. The transitory level of entanglement in the system is found to oscillate with a frequency that is proportional to the magnetic field strength before reaching steady-state entanglement. It was found that collective decay produces more entanglement than individual decay.