Squeezing and bunching of photons of coherent light interacting with two quantum anharmonic oscillators coupled through the angular momentum

The Hamiltonian and hence the equations of motion involving the field operators of two quantum anharmonic oscillators coupled through the angular momentum are constructed. The anharmonic terms are such that the conservative nature of the Hamiltonian is retained. The coupled differential equations involving the field operators are nonlinear and are noncommuting as well. The exact closed form analytical solutions of the field operators are certainly a challenging task to address. The numerical solutions for the field operators are also unlikely because of the presence of nonlinearity and the noncommuting nature of the field operators. We provide the solutions of the field operators by using the short time approximation. The solutions are used to investigate the squeezing and the antibunching of photons for composite coherent light interacting with two oscillators coupled through the angular momentum. The second order variances for the canonically conjugate quadrature of both modes are exhibited as a function of dimensionless coupling and anharmonic terms. By considering the phase angles of composite coherent light as zero, we obtain the squeezing in one of the quadrature components \(X_{1}\) at the cost of other quadrature \(P_{1}\) when the frequency of the first oscillator is less than the second one. The squeezing pattern gets reversed when the frequency of the first oscillator is less than the frequency of the second oscillator. The squeezing is increased with the increase of dimensionless coupling time. The monotonic increase of the squeezing with the increase of the dimensionless coupling time is attributed to the shortcomings of short time approximation. However, the dimensionless nonlinear constant causes a decrease in the squeezing effects. The identical behaviour is exhibited for the second mode. The antibunching of photons for both modes is found improbable. Rather, we end up with the bunching of photons for both modes.