The Entanglement Of Two Identical Atoms In Single-excitation Space Inside Rectangular Waveguide By Markovian Approximation

Quantum entanglement is one of the most significant features in quantum me-chanics,also is important resources of quantum information.It is no exaggera-tion to say that there will be no quantum information if no quantum entanglemen-t.Generating,preserving and controlling entanglement are of great crucial for quan-tum communications,cryptology and computing simulator.Nevertheless,entanglement is extremely sensitive to system-environment interaction strength and the initial s-tate of the system.If we change system-environment interaction coefficient or the initial state,the evolution of entanglement will change too.In this paper,we consider two identical atoms which are modeled as two-level systems,located inside infinite long rectangular waveguide,to discuss the entangle-ment between two atoms in single-excitation space.There is TM mode and TE mode exist in the infinite long rectangular waveguide.If we assume that the moment of dipole along with z axis,will the atoms only couple to TM mode.The dispersion relationship of infinite length rectangular waveguide is nonlinear,so that existed lots of cut-off frequency Ωj(j = 1,2 …).Atoms would take place interaction with TM mode,only if the transition frequency of the atom is higher than the lowest cut-off frequency Ω1.We learn that different distances z0 between atoms would induce the variation of phases φj under the Markovian approximation.If the transition frequen-cy of the atom is inferior to the lowest cut-off frequency Ω1,the entanglement between two atoms will keep it up as an initial value.If ωa satisfies with Ω1<ωa<Ω2,the atoms will couple with only one TM transverse mode.We suppose that the first atom is the excitation state,the other one is the ground state.The entanglement between two atoms begin to increase from 0 to 50%,and not variate any more when the phase φ1=n7r,as existing dark state,which decouple with the light field.When the phase satisfies with φ1≠nπ,the entanglement enlarges from 0 and then decreas-es,what is more,the loss rate of entanglement will run-up or slow down as variation phases.We also assume that the initial state is the maximum entanglement state.The superposition state will not evolve with time,and the entanglement keeps in maxi-mum value when the phase satisfies with φ1=2n7r + π.Otherwise,if gets other phases,we would find out that the entanglement goes away from maximum value and up to 0,what’s more,various phases speed up or slow down the loss rate of entan-glement.If the transition frequency of atoms continues to increase,and satisfy withΩ2<ωa<Ω3,the atoms will couple with two TM transverse modes.Similarly,if the first atom is the excitation state,the other one is the ground state,the entangle-ment between two atoms begin to increase from 0 and reduce subsequently.As you see,variation phases φ1 and φ2 have significant influence on the loss rate of entangle-ment,therefore,the rate of entanglement changes faster than a single mode.When the phase satisfies with φ1≠nπ,the entanglement of atoms not transforms,caused by phase φ1 no longer after some time,while phase φ2 having the affect,so the loss rate of entanglement is smaller than φ1≠nπ.We consider the initial state was max-imum entanglement state,discovering that the loss of entanglement in two modes is more quickly than a single mode.Finally,we show that phase φ1 inhibits the loss of entanglement when satisfies with φ1=2nπ+π,so that the loss of entanglement is slower than other phases in this phase.In general,not only the entanglement of atoms is connected with the distance between two atoms,but also has a relation with the initial state and the mode amount of interaction.