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Modern Physics Letters B

Correlated Squeezed State Approach for Complex Phonon Coupling in a Tunnelling System

Sotirios Baskoutas, P. Papanikolaou

Published May 10, 1997• 0 citations
Publisher

Abstract

In the present paper we propose a method of studying a two-state system coupled linearly to a boson field with complex coupling in a correlated squeezed state approach. The complex coupling leads to the initiation of complex probability density with complex statistical averages. Exploiting the biorthonormal formalism we obtain the analytical forms of the complex expectation value E of H as well as the complex tunneling reduction factor. As it is seen from our results the localization–delocalization transition of the tunneling particle is modified for small values of the real part of the coupling constant in comparison with the conventional (g real) correlated squeezed state approach.

DOI
10.1142/s0217984997000591

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In the present paper we propose a method of studying a two-state system coupled linearly to a boson field with complex coupling in a correlated squeezed state approach. The complex coupling leads to the initiation of complex probability density with complex statistical averages. Exploiting the biorthonormal formalism we obtain the analytical forms of the complex expectation value E of H as well as the complex tunneling reduction factor. As it is seen from our results the localization–delocalization transition of the tunneling particle is modified for small values of the real part of the coupling constant in comparison with the conventional (g real) correlated squeezed state approach.
We propose a correlated squeezed-state approach to study the dissipative two-state system at zero temperature. We have found that the ground state of this system can be better described by the correlated squeezed-state ansatz than those given in earlier variational treatments. In this new ground state the suppression effect of the phonon overlapping integral on the renormalized tunneling parameter is much more alleviated. Thus, the condition for the localization-delocalization transition of the two-state system is significantly modified in this correlated squeezed state, when compared with previous studies.
The sequential to correlated-tunneling transition of two identical bosons confined in a symmetrical double well potential is studied using a time-dependent variational formalism. Increasing the strength of the short-range boson-boson interaction, the probability of finding both bosons in the same well allow to identify three regimes. For small values of the boson- boson coupling constante, this probability display beatings. Then, the probability of finding both bosons in the same well becomes quasi-periodical in time, for almost all values of the coupling constant; however, there is a zero-measure set, which contains an infinity of points, for which this probability is time-periodic. Finally, for larger values of the coupling constant, this probability changes periodically. Based on the dynamics of the probability of finding one boson on each well and increasing the boson-boson interaction, we find that tunnelling changes from a regime where one boson tunnels after the other to a regime in which they tunnel together.
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.