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International Journal of Modern Physics B

COUPLED CLUSTER TECHNIQUES AND THE RABI HAMILTONIAN

Clive Emary

Published Nov 10, 2003• 5 citations
Publisher

Abstract

The Rabi Hamiltonian is a simple, yet non-trivial model of light-matter interactions. Here we present a brief review of the application of the normal coupled cluster method (NCCM) to this model. We concentrate on the NCCM description of the excitation spectrum and of simple time evolutions of the system, providing a link between the two that limits the accuracy of NCCM dynamical calculations in practice.

DOI
10.1142/s0217979203020600

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The Rabi Hamiltonian, which describes the interaction of a single mode of electromagnetic radiation with a two-level system, is one of the fundamental models of quantum optics. It is also of wider interest as it provides a. generic model for the interaction of bosons and fermions. To allow for a systematic analysis of the strong-coupling behaviour, we have applied the coupled cluster method (CCM) to the Rabi Hamiltonian to calculate its spectrum. We find strong evidence for the existence of a somewhat subtle quantum phase transition.
Diagrammatic and Coupled Cluster techniques are used to develop an approach to the single-particle Green's function G which concentrates on G directly rather than first approximating the irreducible self-energy and then solving Dyson's equation. As a consequence the ionization and attachment parts of the Green's function satisfy completely decoupled sets of equations. The proposed Coupled Cluster Green's Function method (CCGF) is intimately connected to both Coupled Cluster Linear Response Theory (CCLRT) and the Normal Coupled Cluster Method (NCCM). These relations are discussed in detail. © 1992 John Wiley & Sons, Inc.
The authors used the coupled cluster method (CCM) to investigate the evolution of the Rabi Hamiltonian from an initial state |0,| > composed of an empty field mode and an unexcited atom. Within the rotation-wave approxn. (RWA) the system would remain in this state indefinitely, since it is an eigenstate of the excitation no. N with corresponding eigenvalue zero. However, including of the otherwise neglected \"counter-rotating\" terms means that we allow \"energy non-conserving\" processes to occur, and their presence drives the temporal evolution of the Rabi system. The authors present results for the at. inversion and field occupation as function of time. They also show that no anti-bunching occurs, although the \"virtual\" processes do cause the field to become squeezed. [on SciFinder (R)]
What has since become known as the coupled cluster method (CCM) was invented some 35 years ago to calculate ground-state energies of closed-shell atomic nuclei.The method has since been extended in many different ways to the point where it is nowadays recognized as providing one of the most universally applicable, most powerful, and numerically most accurate of all ab initio methods in the microscopic quantum many-body theory of finite or infinite systems.We review here the applications within nuclear physics, and thereby show how the CCM provides a unifying approach of almost unique stature.The early calculations on both closed-and open-shell nuclei and on infinite nuclear matter are thus related to the recent extensions which provide both extremely accurate calculations for light nuclei and a framework for handling various problems in nuclear field theory.The latter include pion-nucleon field theory and such Hamiltonian lattice gauge field theories as the Abelian U(l) model and the non-Abelian SU(2) model.In all cases we stress the underlying concepts and the high quality of the results obtained.
In this paper we review the coupled cluster formulation of quantum many-body theory.Apart from a brief and heuristic, but essentially complete, discussion of 8 the by now rather standard tr-eatments of both ground and excited states within the 2 coupled cluster method (CeM), our main aim is to.give a rather careful critique of the various choices that have to be made in order to implement .themethod.These lS--•divide essentially into two classes.On the one hand we have the inputs to the method, 11 which amount largely to.achoice.ofstarting (or zero-order or model or uncorrelated) wayefunctions; while on the other hand we have the choice of decomposition of the ~equations into a natural hierarchy, and which amounts in practice to a particular approximation or truncati on scheme.We shall show expl tc+t ly .thatwhil e these two 13 ---choices are in principle independent of each other, in practice they are intimately 14