Quantum fluctuations in the local model

In fact, it is squeezed displaced harmonic oscillator if one does not take into account the parameter 17 Introducing A does not invoke higher order nonlinearities with respect to phonon-1 coordinates. Thus (APj) = 0, like it should be for an harmonic oscillator, and the expressions for second momenta have the form  

The shape of fluctuations due to the correlation A (equation (33) closely follows the shape of the curve in Fig. 7, having its maximum close to x = 1 and /l 1. 

The similarity of the product of uncertainties of phonon coordinate and momentum displayed in Fig. 7 illustrates anharmonic source of the contribution due to the mode correlation. The correlations A manifest themselves in equations (32) and (33) as a phonon anharmonicity. It is noteworthy to emphasize its quantum origin (compare the note below equation (2)). The problem with 17 5 0 needs special consideration and will be considered elsewhere. 

A suitable choice of the variational wave functions for various electron-phonon two-level systems is a long-standing problem in solid state physics as well as in quantum optics. For two-level reflection symmetric systems with intralevel electron-phonon interaction the approach with a variational two-center squeezed coherent phonon wave function was found to yield the lowest ground state energy. The two-center wave function was constructed as a linear combination of the phonon wave functions related to both levels introducing new VP. 

In two-level models with phonon assisted tunneling, there appears coupling of both phonon modes mediated by Rabi oscillations. Therefore, also the interlevel 

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