Generating and maintaining the high entangled photon pair and improving the strength of anti-correlation

Abstract

A theoretical scheme is proposed to generate a strongly entangled photon pair by a \(\Lambda \)-configured three-level atom interacting with a two-mode quantized cavity field through two strong classical fields resonating with the corresponding atomic transitions. The initial state of the two-mode cavity field is considered to be the tensor product of an arbitrary Fock state of the first mode and the vacuum and one-photon states of the second mode, while that of the three-level atom is prepared in its upper excited state. Then, the time-evolution operator in the interaction picture is used to derive two classes of continuous variable entangled displaced number squeezed states (EDNSSs) in terms of the even and odd states of the second mode, respectively. The quadrature squeezing of the EDNSSs for the first mode in the initial vacuum state is considered concerning the coherent and squeezed fields. The sub-Poissonian statistics and the photon anti-bunching effect corresponding to both the coherent and squeezed fields are investigated in terms of the excited states of the first mode, as well as the coherent and squeezed fields with the same amplitudes. Furthermore, the cross-correlation between the two bosonic modes and their two-qubit entanglement are studied; and for example, it is shown that the destructive interference (anti-correlation) corresponds to an increase in entanglement. We highlight the role of the excited states of the first mode in controlling the nonclassical properties of the even and odd EDNSSs, compared to those of the entangled coherent-squeezed states (ECSSs).