Nonclassical ground state for Fröhlich palaron

Abstract

Based on the variational approach proposed by Huybrecht , using the two-mode squeezed coherent state as the second-step canonical transformation, we have investigated the nonclassical ground state for the Fröhlich polaron through considering the dynamical correlation bewteen the phonon wave vectors q and q' . Due to the correlation effect between the phonon coherent state and the phonon squcezed state, caused by the two-mode squeezing effect of the phonon coherent state, the coherent parameter fq and the two-mode squeezing angle φqq' also have a big correction correspondingly. As a result , this effect has greatly enhanced the coherent effect and the squeezing angle effect . The calculation and the analysis based on the ground state energy of the polaron have shown that 1) for the weakly coupled region ,the correction ΔE(1)c due to the effect of the displaced-phonon squcezed state is comparable to the Feynma n' s path integral calculation (ΔEf) and the coherent state correetion by Huybrechts (ΔE0), while the correction (ΔE(2)c) due to the squeezing effect of the phonon coherent state has an essential contribution , i.e. ΔE(2)c«(ΔEf,ΔE0); 2) for the strongly-coupled region ,the contribution from the displaced-phonon squcezed state has a greatly reduction , ΔE(1)c≥(ΔEf,ΔE0) .Althougth, at the same time ,the contribution due to the squeezing effect of the phonon coherent state also has a greatly reduction ,we still have ΔE(2)c«(ΔEf,ΔE0).