Amplitude squared squeezing and the photon antibunching of thermal light interacting with two oscillators coupled through the angular momentum

The problem of two oscillators coupled through the angular momentum and the corresponding Hamiltonian is investigated analytically. The equations of motion of the coupled oscillators lead to a system of coupled differential equations involving the non-commuting operators. Interestingly, these coupled differential equations are found decoupled at the cost of the fourth-order differential equations involving the parameters (c-number) of the individual oscillator. Despite the complex nature, the analytical solutions of these fourth-order differential equations and hence the dynamical behaviour involving the oscillators are obtained in closed analytical forms. These solutions are used to investigate the amplitude squared squeezing (ASS) and the second order correlation function for zero time delay and hence the antibunching of photons for the input thermal light interacting with the two oscillators coupled through the angular momentum. The exact analytical expressions for the ASS and the antibunching of photons are exhibited. Despite the usefulness of these analytical expressions, it is extremely difficult to draw physics out of these solutions. To provide some flavour of the analytical expressions of the ASS and the second-order correlation function for zero time delay, we provide some interesting symbolic calculations. For example, the antibunching of photons is favoured for a particular mode if the number of photons is less in the said mode. The data used for these symbolic calculations are theoretical, however, they are chosen in such a way as to be close to the real experimental situation.