# Effects of tunneling and multiphoton transitions on squeezed states generation in bistable driven systems

## TL;DR

This paper investigates how tunneling and multiphoton transitions influence the generation of squeezed states in bistable driven nonlinear oscillators, revealing enhanced squeezing and relaxation effects due to quantum phenomena.

## Contribution

It demonstrates the impact of tunneling and multiphoton transitions on squeezing and relaxation in bistable systems, linking classical and quantum descriptions through Fokker-Planck and master equations.

## Key findings

- Tunneling enhances slow relaxation rates between stable states.
- Quasienergy states in bistability regions are squeezed with uncertainty below quantum limit.
- Tunneling effects can significantly improve the generation of squeezed states.

## Abstract

Bistability of nonlinear resonantly driven oscillator in the presence of external noise is analyzed by means of classical Fokker-Planck equation in quasienergy space with account for tunneling effects and by quantum master equation in quasienergy states representation. Two time scales responsible for different stages of bistable system relaxation have been obtained. We found out that the slow relaxation rate caused by fluctuation--induced transitions between different stable states can be enhanced by several orders due to tunneling effects. It was also revealed that tunneling between nearly degenerate quasienergy states and resonant multiphoton transitions between the genuine eigenstates of the nonlinear oscillator are just the similar effects. It was demonstrated that the quasienergy states in the bistability region corresponding to higher amplitude are squeezed. The degree of squeezing is determined by the ratio between nonlinearity and detuning, so the uncertainty of one quadrature can be considerably smaller than the quantum limit. It was found out that tunneling effects can enhance the generation of output oscillator squeezed states. It is shown that 1D Fokker--Planck equation is a quasiclassical limit of a quantum master equation.