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Journal of Physics Conference Series

Diffraction effects in entanglement of two distant atoms

Z. Ficek, Sonny Natali

Published Oct 1, 2007• 0 citations
Publisher

Abstract

We investigate the process of entanglement creation between two distant atoms coupled to a single mode cavity. We consider the optical frequency regime and include a possible variation of the coupling strength of the atoms to the cavity field with the location of the atoms inside the cavity mode. We show that the degree of entanglement between the atoms is a sensitive function of the position of the atoms inside the mode. It is found that the entanglement exhibits an interesting phenomenon of diffraction when the the atoms are located between the nodes and antinodes of the cavity mode. The entanglement diffraction pattern varies with time and we explain this effect in terms of the quantum property of complementarity, which is manifested as a tradeoff between the knowledge of energy of the exchanged photon versus the evolution time of the system. Entangled states of the system are identified and the entanglement properties of the system are interpreted in terms of the coherence between the atoms.

DOI
10.1088/1742-6596/84/1/012007

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We investigate the process of entanglement creation between two distant atoms coupled to a single mode cavity. We consider the optical frequency regime and include a possible variation of the coupling strength of the atoms to the cavity field with the location of the atoms inside the cavity mode. We show that the degree of entanglement between the atoms is a sensitive function of the position of the atoms inside the mode. It is found that the entanglement exhibits an interesting phenomenon of diffraction when the the atoms are located between the nodes and antinodes of the cavity mode. The entanglement diffraction pattern varies with time and we explain this effect in terms of the quantum property of complementarity, which is manifested as a tradeoff between the knowledge of energy of the exchanged photon versus the evolution time of the system. Entangled states of the system are identified and the entanglement properties of the system are interpreted in terms of the coherence between the atoms.
A practical scheme for entanglement creation between distant atoms located inside a single-mode optical cavity is discussed. We show that the degree of entanglement and the time it takes for the entanglement to reach its optimum value is a sensitive function of the initial conditions and the position of the atoms inside the cavity mode. It is found that the entangled properties of the two atoms can readily be extracted from dynamics of a simple two-level system. Effectively, we engineer two coupled qubits whose dynamics are analogous to that of a driven single two-level system. It is found that spatial variations of the coupling constants actually help to create transient entanglement which may appear on the time scale much longer than that predicted for the case of equal coupling constants. When the atoms are initially prepared in an entangled state, they may remain entangled for all times. We also find that the entanglement exhibits an interesting phenomenon of diffraction when the atoms are located between the nodes and antinodes of the cavity mode. The diffraction pattern of the entanglement varies with time and we explain this effect in terms of the quantum property of complementarity, which is manifested as a tradeoff between the knowledge of energy of the exchanged photon versus the evolution time of the system.
The problem of the creation of entanglement exclusively from the presence of the counter-rotating terms in the interaction Hamiltonian between two atoms and a single-mode cavity field is studied. The time evolution of the concurrence between the atoms is discussed for two different initial separable states and arbitrary strengths of the coupling constants of the atoms to the cavity mode. We show that a transient entanglement can be created between the atoms only if the counter-rotating terms are taken into account in the interaction Hamiltonian. The source of the entanglement is identified, and the entanglement features are explained in terms of the properties of the reduced density operator of the atoms. In particular, we find that the main source of the entanglement is in the two-photon coherence induced by the counter-rotating terms that cause two-photon transitions through virtual states.
Spontaneous emission as a potential tool for creation of entanglement between two atoms is investigated. We assume that the atoms are coupled to the same environment and study entanglement engineering between the atoms and its transfer between different states. The role of the atomic coherence induced by spontaneous emission will be explored which, in contrast to what is generally believed, can create entanglement between initially unentangled atoms. We quantify entanglement by the concurrence and find that it exhibits threshold properties that can lead to interesting noncontinuous phenomena of sudden birth and sudden death of entanglement. In addition, we consider the mechanism involved in creation of entanglement between distant atoms coupled to a single-mode cavity field. We include a possible variation of the coupling constants between the atoms and the cavity mode with location of the atoms in a standing-wave cavity mode. Effectively, we engineer two coupled atoms whose the dynamics are analogous to that of interacting and collectively damped two nonidentical atoms. We illustrate the interesting result that spatial variations of the coupling constants can lead to a stationary entanglement between the atoms. We explain this effect in terms of the trapping phenomenon of atomic population in a non-decaying entangled state.
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By means of the quantum theory,the interaction between two-atoms located inside a dissipative cavity and single-mode coherent field was studied.The entanglement properties,between two atoms and between two-atoms and light fields,were analyzed.In addition,the reason that the decay of the cavity field and the detuning between the atom and cavity field affect the evolution of entanglement was discussed.The results show that when there is cavity loss,entanglement between the atoms and light fields may occur,however entanglement gradually disappear in the long time limit.Also,the detuning between the atom and cavity field significantly affects the entanglement.The entanglement between two atoms initially in the maximally entangled states is gradually weakened due to the decay of the light field,but the detuning between the atom and the cavity field can inhibit this decay.
The role of retardation in the entanglement dynamics of two distant atoms interacting with a multimode field of a ring cavity is discussed. The retardation is associated with a finite time required for light to travel between the atoms located at a finite distance and between the atoms and the cavity boundaries. We explore features in the concurrence indicative of retardation and show how these features evolve depending on the initial state of the system, distance between the atoms, and the number of modes to which the atoms are coupled. In particular, we consider the short-time and the long-time dynamics for both the multi- and subwavelength distances between the atoms. It is found that the retardation effects can qualitatively modify the entanglement dynamics of the atoms not only at multi- but also at subwavelength distances. We follow the temporal evolution of the concurrence and find that at short times of the evolution the retardation induces periodic sudden changes of entanglement. To analyze where the entanglement lies in the space spanned by the state vectors of the system, we introduce the collective Dicke states of the atomic system that explicitly account for the sudden changes as a periodic excitation of the atomic system to the maximally entangled symmetric state. At long times, the retardation gives rise to periodic beats in the concurrence that resemble the phenomenon of collapses and revivals in the Jaynes-Cummings model. In addition, we identify parameter values and initial conditions at which the atoms remain separable or are entangled without retardation during the entire evolution time, but exhibit the phenomena of sudden birth and sudden death of entanglement when the retardation is included.