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Chinese Physics

Stationary entanglement between two spatially separated atoms driven by a coherent laser field

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

Published May 1, 2007• 5 citations
Publisher

Abstract

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.

DOI
10.1088/1009-1963/16/5/032

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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.
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.
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.
The pairwise entanglement of an arbitrary atomic pair randomly extracted from a laser-driven dense multiqubit sample in the presence of quantum dissipation due to spontaneous emission is considered. The dipole–dipole interaction between the particles shifts the laser-qubit resonance frequency and consequently modifies the quantum entanglement. By means of an appropriate tuning of the laser frequency, one can optimize the entanglement in this system. For large ensembles, the maximum entanglement occurs near the laser parameters where the steady-state sample exhibits phase transition phenomena.
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.
In this paper we propose a scheme in which two-mode entanglement in a steady state is produced by using two lasers to resonantly drive a single four-level atom embedded inside a two-mode optical cavity. In this scheme, atomic coherence induced by a classical laser plays an important role in the process of preparing the entangled state. With the coupling of a strong control field, direct two-photon transition is generated and the relatively weak pump field induces the parametric interaction between two photons, which makes them entangle with each other. By numerical calculation, we find that the degree of entanglement depends strongly on the Rabi frequencies of the classical laser fields and the cavity losses.