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Acta Physica Sinica

TWO-PHONON COHERENT STATES IN A DISSIPATIVE QUANTUM TUNNELING SYSTEM

Y Hang

Published Jan 1, 1990• 0 citations
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Abstract

In this paper, a two-phonon coherent state has been introduced to investigate the influence of coupling with a quantum tunneling system on phonon states. Comparing with usual one-phonon coherent state, this new phonon slate has the following properties: (1) Its energy is renormalized by the quantum tunneling system; (2) Its suppression effect on the renormalized tunneling parameter is reduced; (3) It makes the whole system in a more stable ground state.

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Acta Physica Sinica•Jan 1, 1989•0 citations
In this paper, a two-phonon coherent state has been introduced to investigate the influence of coupling with a quantum tunneling system on phonon states. Comparing with usual one-phonon coherent state, this new phonon slate has the following properties: (1) Its energy is renormalized by the quantum tunneling system; (2) Its suppression effect on the renormalized tunneling parameter is reduced; (3) It makes the whole system in a more stable ground state.
The variational approach is applied to the study of the ground state of quantum tunneling system interacting with two phonons by use of a correlated-squeezed transformation. We fine: 1) For the two phonons bath, the ground state energy of the phonons with correlation effect is lower than that without correlation effect; 2) The effect of correlation varies with the mode parameters: In the resonant regime of the phonons and two-state system, the correlation effect is more significant and will be strengthened together with the increase of coupling coefficient.
The ground states of phonons in a dissipative quantum tunneling system and their influences on the localiza ion-delocalization transtion are investigated by a variational approach. We find that: 1. There are two kind of influences, displacement and deformation, on phonon states due to coupling with a tunneling particle, and displaced -squeezed states are proposed to describe both these influences. 2. The localization-delocahzation transition depends on the choice of phonon ground state. The transition will occur at strong coupling as the energy of the ground state decreases.
We present a systematic analysis of the ground state properties of a tunneling system coupled to an Ohmic bath. The nonadiabatic effects induced by coupling with tunneling particle, on the ground state properties of phonons are taken into account. For this we have considered both displacement and deformation of phonons via a variational treatment. The symmetry breaking transition, or the delocalization-localization transition, of the tunneling particle is presented and is compared with earlier known results. We also show that in the critical regime a gap will be opened near the zero momentum in the spectrum of the phonons. The modified phonon spectrum along with the phonon displacement field correlation functions have been calculated. It is shown that in the critical regime the tunneling system stabilizes the lattice against long wavelength fluctuations.