Pairwise entanglement

Thus far, studies of coherent optical processes in a PBG have assumed fixed (static) values of the atomic transition frequency [Quang 1997], However, in order to operate quantum logic gates, based on pairwise entanglement of atoms by field-induced dipole-dipole interactions [Brennen 1999 Petrosyan 2002 Opatrny 2003], one should be able to switch the interaction on- and off-, most conveniently by AC Stark-shifts of the transition frequency of one atom relative to the other, thereby changing its detuning from the PBG edge. 

Background. Consider that pairwise interactions between active network chains (13), commonly termed trapped entanglements, do not significantly affect the stress in a specimen deformed in simple tension or compression. Then, according to recent theory (16,17), the shear modulus for a network in which all junctions are trifunctional is given by an equation which can be written in the form (13) ... 

According to the equations derived by Miller and Macosko (24), outlined in the Appendix, the probability that a short segment selected at random in the network is part of an elastically active chain is (P /p)2 where p is the final extent of the curing reaction. If an entanglement results from pairwise interactions between chains, as proposed (13), then Te in eq 2 can be equated to (Pxi/p)4, which is the probability that two interacting chains are active. 

The pure state (113) is nonmaximally entangled state it reduces to a maximally entangled state for N l. The entangled state is analogous to the pairwise atomic state [22] or the multiatom squeezed state [23], (see also Ref. 24), predicted in the small sample model of two coupled atoms. 

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