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Non-Markovian Entanglement Dynamics of Two Qubits Interacting Through a Quantum Field


Two necessary requirements on the physical conditions of a system suitable for quantum information processing are the sustenance of a sufficient degree of quantum coherence and the preservation of quantum entanglement.  Interaction of a quantum system with its environment has a tendency to diminish or destroy its quantum coherence and entanglement.  Our research has focused on these two issues.  Working with simple systems but with more probing analysis, we aim to provide results in regimes physically relevant but often glossed over in textbook treatments.  In particular we focus on the non-Markovian (processes involving memory) regimes which correspond usually to short time, low temperature conditions or for strongly coupled or correlated systems.  These are also the conditions more conducive to quantum information processing.  In this talk I present results [1] from studies of the non-equilibrium dynamics of a pair of qubits made of two-level atoms at a finite distance apart and interacting with one common electromagnetic field but not directly with each other.  The case of two qubits each interacting with its own field has been studied by Yu and Eberly [2] earlier who reported the appearance of 'sudden death' of quantum entanglement in time.  With two qubits in the same field, where the field mediates the qubits through induced interaction, the behavior is much more complex [3].  This is also a more commonly encountered situation such as in the construction of quantum gates.  We obtain analytic expressions for the dependence of quantum entanglement on time and on the spatial separation between the two qubits, the latter is an effect which has never been obtained, or even conjured, in entanglement studies.  Our investigation also brings out a new perspective on some basic issues such as nonlocality in quantum entanglement understood in the EPR sense.  We assert that the quantum mechanical interpretation of entanglement is incomplete because the causal propagation of the interceding field is left out completely in prior studies.  Inclusion of this key element from relativistic quantum field theory considerations may paint alter our view and understanding of these basic issues at the foundation of quantum mechanics.

[1] C. Anastopoulos, S. Shresta and B. L. Hu, Quantum Entanglement under Non-Markovian Dynamics of Two Qubits Interacting with a Common Electromagnetic Field , under consideration by Phys. Rev. A  [quant-ph/0610007].

[2] T. Yu and J. H. Eberly, Phys. Rev. Lett. 93 , 140404 (2004).

[3] Z. Ficek and R. Tanas, Phys. Rev. A 74 , 024304 (2006).