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arXiv:1206.2769 · New Journal of Physics

Dynamics of atom–atom correlations in the Fermi problem

Massimo Borrelli, Carlos Sabín, Gerardo Adesso, Francesco Plastina, Sabrina Maniscalco

Published Oct 3, 2012• 13 citations
arXivHTMLPDF

Abstract

We present a detailed perturbative study of the dynamics of several types of atom–atom correlations in the famous Fermi problem. This is an archetypal model to study micro-causality in the quantum domain, where two atoms, one initially excited and the other prepared in its ground state, interact with the vacuum electromagnetic field. The excitation can be transferred to the second atom via a flying photon, and various kinds of quantum correlations between the two are generated during this process. Among these, prominent examples are given by entanglement, quantum discord and non-local correlations. The aim of this paper is to analyze the role of the light cone in the emergence of such correlations.

DOI
10.1088/1367-2630/14/10/103010

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We present a detailed perturbative study of the dynamics of several types of atom–atom correlations in the famous Fermi problem. This is an archetypal model to study micro-causality in the quantum domain, where two atoms, one initially excited and the other prepared in its ground state, interact with the vacuum electromagnetic field. The excitation can be transferred to the second atom via a flying photon, and various kinds of quantum correlations between the two are generated during this process. Among these, prominent examples are given by entanglement, quantum discord and non-local correlations. The aim of this paper is to analyze the role of the light cone in the emergence of such correlations.
We analyze whether a pair of neutral two level atoms can become entangled in a finite time while they remain causally disconnected. The interaction with the electromagnetic field is treated perturbatively in the electric dipole approximation. We start from an initial vacuum state and obtain the final atomic correlations for the cases where n=0n=0n=0, 1, or 2 photons are produced in a time ttt, and also when the final field state is unknown. Our results show that correlations are sizable inside and outside the mutual light cone for n=1n=1n=1 and 2, and also that quantum correlations become classical by tracing over the field state. For n=0n=0n=0 we obtain entanglement generation by photon propagation between the atoms, the correlations come from the indistinguishability of the source for n=1n=1n=1, and may give rise to entanglement swapping for n=2n=2n=2.
We analyze the entanglement dynamics of a system composed by a pair of neutral two-level atoms that are initially entangled, and the electromagnetic field, initially in the vacuum state, within the formalism of perturbative quantum field theory up to the second order. We show that entanglement sudden death and revival can occur while the atoms remain spacelike separated and therefore cannot be related with photon exchange between the atoms. We interpret these phenomena as the consequence of a transfer of atom-atom entanglement to atom-field entanglement and vice versa. We also consider the different bipartitions of the system, finding similar relationships between their entanglement evolutions.
Quantum correlation without entanglement in a two-atom-vacuum field system is investigated. The influence of the atomic dipole-dipole interaction on quantum correlation is also examined. We find that, when both atoms are initially in separable excited states, the quantum discord of two atoms appears while their entanglement wholly vanishes throughout the evolution. We explain our results in detail. Our results provide a novel method of achieving a quantum correlation resource without entanglement in the real system.
We analyze entanglement generation between a pair of neutral two level atoms that are initially excited in a common electromagnetic vacuum. The nonlocal correlations that appear due to the interaction with the field can become entanglement when the field state is known. We distinguish two different situations: in the first, the field remains in the vacuum state, and second two photons are present in the final state. In both cases we study the dependence of the entanglement with time and interatomic distance, at ranges related with locality issues.
We investigate (non-relativistic) atomic systems interacting with quantum electromagnetic field (QEF). The resulting model describes spontaneous emission of light from a two-level atom surrounded by various initial states of the QEF. We assume that the quantum field interacts with the atom via the standard, minimal-coupling Hamiltonian, with the A2 term neglected. We also assume that there will appear at most single excitations (photons). By conducting the analysis on a general level we allow for an arbitrary initial state of the QEF (which can be for instance: the vacuum, the ground state in a cavity, or the squeezed state). We derive a Volterra-type equation which governs the time evolution of the amplitude of the excited state. The two-point function of the initial state of the QEF, integrated with a combination of atomic wavefunctions, forms the kernel of this equation.
Abstract The dynamics of entanglement and quantum discord (QD) between two two-level atoms interacting with two dissipative coupled cavities in the presence of initial atom-cavity correlations is investigated. In comparison with the result of the initial factorized state, we show that the initial state contained quantum correlation of atom-cavity is most robust against the dissipative environment, and the initial atom-cavity correlations, especially the quantum correlation, play a constructive role in the generation of atomic entanglement and QD. Simultaneously, the comparison between Markovian and non-Markovian dynamics, and the influences of inter-cavity hopping rate are also taken into account and analyzed.