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Modern Physics Letters B

MUTUAL TRANSFER OF SQUEEZING EFFECT IN COUPLED TWO-PHOTON LASERS

Adalto R. Gomes, B. Baseia, Gil C. Marques

Published Jul 10, 1995• 5 citations
Publisher

Abstract

We investigate the mutual influence of two interacting 2-photon lasers, each subsystem being modelled as a quadratic oscillator in terms of the ladder operators âi, [Formula: see text] owing to the generation and transfer of squeezing effect. We find an exact solution for this coupled system which allows us to obtain the variances in the conjugate operators ẑi, [Formula: see text]. The results are exhibited in several plots showing the influence of the involved parameters. The second oscillator exhibits squeezing even if its nonlinear term is absent, due to the transference of the effect originated in the first (nonlinear) oscillator. Concerning this effect, the oscillators compete or cooperate depending on the parameters range; for some parameter range the system becomes unstable, as shown in numerical plots.

DOI
10.1142/s0217984995000978

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A quantum system described by a two-dimensional harmonic oscillator with a varying mass parameter plus the projection of the angular momentum in the z direction with a time-dependent mode coupling constant is considered to study the two-mode squeezing and photon generation phenomena. For some specific time dependences of the oscillator mass and an arbitrary function of time for the coupling constant exact results on the time evolution of the density matrix and the Wigner function are presented. An analytical expression of the photon distribution is obtained explicitly in terms of Hermite polynomials of two variables, and it shows the effect of oscillations characteristic of squeezing and correlation of the photon quadratures.
With the help of second-order nonlinear interactions and hence Hamiltonian, we construct the equations of motion corresponding to pump and signal (second harmonic) fields in a second harmonic generation. The corresponding coupled differential equations involving the non-commuting field operators are not solvable in closed analytical forms. With the help of a perturbation method, we obtain analytical solutions of these field operators up to cubic orders in the interaction constant. In an appropriate limit (truncating the solution up to the second order in the interaction constant), these solutions lead to the existing solutions under the short-time approximation. The present analytical solutions are exploited to investigate the squeezing and the antibunching of photons of the input coherent light coupled to the said second-order nonlinear medium. We report the squeezing and antibunching effects of the pump field even for solutions up to the second order and hence the present results are consistent with earlier results. However, for the second harmonic mode, we report the squeezing involving the leading cubic term in the interaction constant.
We investigate in detail the role of a reservoir concerning the squeezing effect in a driven coupled-oscillator system. In our model, a harmonic oscillator (single cavity mode) is coupled to a two-state oscillator (two-level atom) driven by a classical field. The oscillators are coupled to their respective reservoirs, by which the oscillators are damped. The degree of squeezing in the short-time limit is found to be independent of the damping rate of the harmonic oscillator in a perturbative regime. More remarkably, the harmonic oscillator, which is in a coherent state in the absence of its reservoir, gets squeezed in the steady state when it is coupled to the reservoir. The reservoir assumes two competing roles of assisting and suppressing the squeezing effect induced by the nonlinear interaction of the coupled oscillators. As a result, the squeezing effect is increased to some extent with the damping rate of the harmonic oscillator. In addition, the ``matching condition'' for the optimal squeezing is obtained such that the pumping field intensity should be inversely proportional to the damping rate.