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Journal of Optics B Quantum and Semiclassical Optics

Quantum entanglement in a system of two spatially separated atoms driven by an external coherent laser field

Xiang-Ping Liao, Mao-Fa Fang, Xiaomei Chen, Cai Jian-Wu, Zheng Xiao-Juan

Published Sep 30, 2005• 8 citations
Publisher

Abstract

We study quantum entanglement between two spatially separated atoms driven by an external coherent laser field in the dissipative process of spontaneous emission. It is shown that the entanglement exhibits long-time oscillatory behaviour with remarkable entanglement in the peaks and the peak and period are related to the Rabi frequencies of the external coherent laser field.

DOI
10.1088/1464-4266/7/11/003

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We study quantum entanglement between two spatially separated atoms driven by an external coherent laser field in the dissipative process of spontaneous emission. It is shown that the entanglement exhibits long-time oscillatory behaviour with remarkable entanglement in the peaks and the peak and period are related to the Rabi frequencies of the external coherent laser field.
This paper studies quantum entanglement between two spatially separated atoms driven by a coherent laser field in the dissipative process of spontaneous emission. It is shown that the entanglement strongly depends on the detuning of the laser frequency from atomic transition frequency, the interatomic separation and the Rabi frequency of the coherent laser field. A considerable amount of steady state entanglement can be obtained near Δ = —α (i.e., the dipole-dipole interaction and the detuning cancel out mutually) for small atomic separation and large Rabi frequency of the coherent laser field.
Abstract. We discuss the creation of entanglement between two two-level atoms in the dissipative process of spontaneous emission. It is shown that spontaneous emission can lead to a transient entanglement between the atoms even if the atoms were prepared initially in an unentangled state. The amount of entanglement created in the system is quantified by using two different measures: concurrence and negativity. We find analytical formulas for the evolution of concurrence and negativity in the system. We also find the analytical relation between the two measures of entanglement. The system consists of two two-level atoms which are separated by an arbitrary distance r12 and interact with each other via the dipole-dipole interaction, and the antisymmetric state of the system is included throughout, even for small inter-atomic separations, in contrast to the small sample model. It is shown that for sufficiently large values of the dipole-dipole interaction initially the entanglement exhibits oscillatory behaviour with considerable entanglement in the peaks. For longer times the amount of entanglement is directly related to the population of the slowly decaying antisymmetric state.
We discuss the creation of entanglement between two two-level atoms in the dissipative process of spontaneous emission. It is shown that spontaneous emission can lead to a transient entanglement between the atoms even if the atoms were prepared initially in an unentangled state. The amount of entanglement created in the system is quantified by using two different measures: concurrence and negativity. We find analytical formulae for the evolution of concurrence and negativity in the system. We also find the analytical relation between the two measures of entanglement. The system consists of two two-level atoms which are separated by an arbitrary distance r 12 and interact with each other via the dipole–dipole interaction, and the antisymmetric state of the system is included throughout, even for small interatomic separations, in contrast to the small-sample model. It is shown that for sufficiently large values of the dipole–dipole interaction initially the entanglement exhibits oscillatory behaviour with considerable entanglement in the peaks. For longer times the amount of entanglement is directly related to the population of the slowly decaying antisymmetric state.
We study the entanglement between the internal electronic and the external vibrational degrees of freedom of a trapped atom which is driven by two lasers into electromagnetically induced transparency. It is shown that basic features of the intricate entanglement dynamics can be traced to Landau-Zener splittings (avoided crossings) in the spectrum of the atom-laser field Hamiltonian. We further construct an effective Hamiltonian that describes the behavior of entanglement under dissipation induced by spontaneous emission processes. The proposed approach is applicable to a broad range of scenarios for the control of entanglement between electronic and translational degrees of freedom of trapped atoms through suitable laser fields.
We consider two two-level atoms, interacting with two independent dissipative cavities, each of which is driven by an external source. The two cavity fields are both initially prepared in the coherent states, and the two two-level atoms are initially prepared in the singlet state |Ψ − ⟩ = (|eg⟩ – |ge⟩)/√2. We investigate the influence of the damping constant κ, the intensity of the external sources F, and the relative difference of the atomic couplings r on the entanglement between the two atoms. In the dispersive approximation, we find that the entanglement between the two atoms decreases with the time evolution, and the decreasing rate of entanglement depends on the values of F/κ, κ/ω, and r. For the given small values of F/κ and κ/ω, on the one hand, the increasing of r favors entanglement decreasing of the atomic system, on the other hand, when r → 1 the entanglement decreasing becomes slower. With the increasing of the value of κ/ω, the influence of r on the decreasing rate of entanglement becomes smaller, and gradually disappears for the big value of κ/ω.
We propose a practical physical system for creation of stationary entanglement by dissipation without employing environmental engineering techniques. The system proposed is composed of two perfectly distinguishable atoms, through their significantly different transition frequencies, with only one atom addressed by an external laser field. We show that the arrangement would easily be realized in practice by trapping the atoms at a distance equal to the quarter-wavelength of a standing-wave laser field and locating one of the atoms at a node and the other at the successive antinode of the wave. The undesirable dipole-dipole interaction between the atoms, which could be large at this small distance, is adjusted to zero by a specific initial preparation of the atoms or by a specific polarization of the atomic dipole moments. Following this arrangement, we show that the dissipative relaxation can create a stationary entanglement on demand by tuning the Rabi frequency of the laser field to the difference between the atomic transition frequencies. The laser field dresses the atom and we identify that the entangled state occurs when the frequency of one of the Rabi sidebands of the driven atom tunes to the frequency of the undriven atom. It is also found that this system behaves as a cascade open system where the fluorescence from the dressed atom drives the other atom with no feedback.