Bistability of a nonlinear resonantly-driven oscillator in the presence of external noise is analyzed using the classical Fokker-Planck equation in the quasienergy space with account for tunneling effects and by quantum master equation in quasienergy states representation. Two timescales responsible for different stages of this bistable system relaxation have been obtained. We found that the slow relaxation rate caused by fluctuation-induced transitions between different stable states can be enhanced by several orders of magnitude due to the 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 that the uncertainty of one quadrature can be considerably smaller than the quantum limit. We found that tunneling effects can enhance the generation of output oscillator squeezed states. It was demonstrated that 1D Fokker-Planck equation is a quasiclassical limit of a quantum master equation.arXiv:1901.05243v2 [cond-mat.mes-hall]

The non-equilibrium statistics and kinetics of a simple bistable system (resonantly driven nonlinear oscillator coupled to reservoir) have been investigated by means of master equation for the density matrix and quasiclassical Fokker-Planck equation in quasienergy space. We found out that the system's statistical and kinetic properties drastically change when the quasienergy states become nearly degenerate and the occupation of the most excited state is strongly enhanced. It has been revealed that in nearly degenerate case a new critical quasienergy parameter emerges. Below the critical quasienergy value the eigenstates are superpositions of the quasiclassical states from different phase space regions, while above this value the eigenstates correspond to only one particular region of the phase space. We have also generalized Keldysh theory for ionization of atoms in the electromagnetic field for bistable systems. It has been demonstrated that Keldysh parameter in bistability region is large when pumping intensity is smaller than the critical value. It has been shown by direct calculations that multi-photon transition amplitude coincides with the tunneling amplitude. So, multi-photon transitions and tunneling between the regions of the phase space are just the same effects. We also demonstrated that for bistable systems the Keldysh parameter logarithmically depends on the external field amplitude.

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We theoretically study Dyakonov surface waveguide modes that propagate along the planar strip interfacial waveguide between two uniaxial dielectrics. We demonstrate that owing to the one-dimensional electromagnetic confinement, Dyakonov surface waveguide modes can propagate in the directions that are forbidden for the classical Dyakonov surface waves at the infinite interface. We show that this situation is similar to a waveguide effect and formulate the resonance conditions at which Dyakonov surface waveguide modes exist. We demonstrate that the propagation of such modes without losses is possible. We also consider a case of two-dimensional confinement, where the interface between two anisotropic dielectrics is bounded in both orthogonal directions. We show that such a structure supports Dyakonov surface cavity modes. Analytical results are confirmed by comparing with full-wave solutions of Maxwell’s equations. We believe that our work paves the way toward new insights in the field of surface waves in anisotropic media.