Enhanced excitation of a driven bistable system induced by spectrum degeneracy

Abstract

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.

Multiphoton resonance in a driven Kerr oscillator in presence of high-order nonlinearities

“…The magnitude of the splitting turns out to be proportional to high-order nonlinearity coefficients. In addition, we extend the analysis of previous works [12] [13] to the case of finite damping having the order or being larger than tunneling and multiphoton splitting between the Hamiltonian eigenstates from different regions of the phase portrait.…”

“…2 in Ref. [13]. Also, the presence of small higher-order nonlinearities doesn't change the qualitative structure of the classical phase portrait.…”

“…Because of that, the trajectories form superpositions only when a certain resonance condition for the system parameters is fulfiled. In absence of high-order nonlinearities, it was shown [13] that this happens when the detuning ∆ is an integer or halfinteger multiple of α independently of f . This manifests as the anticrossings of the Hamiltonian quasienergy levels dependence on ∆ at constant driving field.…”

“…One of the most pronounced quantum effects is related with tunneling between different regions of the phase portrait of the classical oscillator. Tunneling transitions modify the occupation probabilities of the classical stable states and the transition rates, namely, they increase the occupation of the high-amplitude stable state and thus lead to enhanced excitation of the mode [12] [13]. In fact, tunneling between different regions of the phase portrait corresponds to the quasiclassical treatment of multiphoton transitions, namely, the excitation of the oscillator with simultaneous absorption of many external field quanta.…”

“…If no higher nonlinearities are present, this occurs when the detuning between the driving field and the oscillator mode is an integer or half-integer multiple of the Kerr frequency shift per quantum. This property follows from a special symmetry of the model Hamiltonian [13], and because of this, the eigenstates of the quantum Hamiltonian correspond to superpositions of quasiclassical states belonging to different regions of the phase portrait. Because of that, the dependence of the higher-amplitude and lower-amplitude states populations on detuning has pronounced peaks and drops at integer and half-integer detuning-nonlinearity ratio.…”