Light Squeezing at the Transition to Quantum Chaos

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We investigate theoretically the dynamics of squeezed state generation in nonlinear systems possessing a transition from regular to chaotic dynamics in the limit of a large number of photons. As an example, the model of a kicked Kerr oscillator is considered. We show that at the transition to quantum chaos the maximum possible degree of squeezing increases exponentially in time, in contrast to the regular dynamics, where the degree of squeezing increases in time only power-wise. We demonstrate the one-to-one correspondence of the degree of squeezing and the value of the local Lyapunov instability rate in corresponding classical chaotic system.