Single-mode quantum properties of the codirectional Kerr nonlinear coupler: frequency mismatch and exact solution

Abstract

In this paper, we investigate the single mode quantum properties of the codirectional Kerr nonlinear coupler when the frequency mismatch is involved and a condition for an exact solution of equations of motion is fulfilled. Particularly, we investigate quadrature and principal squeezing, Wigner function, quadrature distribution, phase distribution and phase variance. We show that the quadrature squeezing and the phase variance can exhibit collapse-revival and collapse-revivalsubrevival phenomena, respectively, based on the values of the detuning parameter.Furthermore, we analytically demonstrate that the system can generate cat states, in particular, Yurke-Stoler states.

Quantum properties of the codirectional three-mode Kerr nonlinear coupler

“…The linear coupling between the waveguides are represented by λ 1 and λ 2 , which we assume to be real. Hamiltonian (1) gives a generalization to several models discussed in the literatures earlier by controlling the values of the interaction parameters such as anhramonic oscillator [27], up-conversion process [28] and two-mode KNC [21]. The scheme describing Hamiltonian (1) is shown in Fig.…”

“…the switching of energy between waveguides, manifests itself by periodic functions in (5), whereas the Kerr nonlinearities in the waveguides are described by the nonlinear (quadratic) phase, which plays an essential role in generating the nonclassical effects. On the other hand, the fundamental modeâ 1 can provide richer nonclassical effects than those produced by the second and third modes as well as the conventional coupler [21,22] (see Fig. 1).…”

“…In conclusion, when λ 1 and λ 2 are large or λ 1 >> λ 2 the squeezing factors for the fundamental and second modes provide RCP. On the other hand, the occurrence of the RCP in the squeezing factors of the fundamental mode can be explained in the following sense [21]. The squeezing factors (16) include two forms of periodic functions: one is coming from the self-cross-nonlinear interaction part of (1), in particular, the exponential function whose period is π/χ, and the other is arising from the linear-interaction part whose period is π/µ.…”

“…Furthermore, we extend the investigation to include the purity for the single-mode case, which can be evaluated by means of the symmetric characteristic function. Now the jth mode symmetric characteristic function is [21] FIG. 4: The W function for the single-mode case for χ = 0.5s −1 , t = πs and for α j = 0.9, λ 1 = λ 2 = 1/(2 √ 2s −1 ) (a) (fundamental mode), (b) (second mode); and α 1 = 2, α 2 = α 3 = 0 and…”

“…In these cases it has been shown that there is a possibility to control the switching characteristics and principal squeezing effect by adjusting the shape of the waveguides. Quite recently, we have investigated the single-mode quantum properties of the codirectional Kerr nonlinear coupler when the frequency mismatch is involved and a condition for obtaining an exact solution for the equations of motion is fulfilled [21,22]. For this case we have shown that the mean-photon numbers exhibit oscillatory behaviour rather than revivals and collapses.…”