Abstract
In this paper, the finite-size Dicke model of arbitrary number of qubits is solved analytically in a unified way within extended coherent states. For the or Dicke models (k is an integer), the G-function, which is only an energy dependent determinant, is derived in a transparent manner. The regular spectrum is completely and uniquely given by stable zeros of the G-function. The closed-form exceptional eigenvalues are also derived. The level distribution controlled by the pole structure of the G-functions suggests non-integrability for model at any finite coupling in the sense of recent criteria found in the literature. A preliminary application to the exact dynamics of genuine multipartite entanglement in the finite-N Dicke model is presented using the obtained exact solutions.
Highlights
The Dicke model [1] describes the interaction of a number (N > 1) of two-level atoms with a single bosonic mode and has been a paradigmatic example of collective quantum behavior
Using the exact eigensolutions, we study the dynamics of the genuine multipartite entanglement (GME) from the maximum entangled states, such as Bell states for N = 2 and GHZ states for N = 3 and 4
This work is to extend the methodology of G-function in the Rabi model to the identical multi-qubit cases, thereby allowing in-depth studies in some fundamental issues and practically feasible treatment to energy spectra and eigenstates
Summary
The Dicke model [1] describes the interaction of a number (N > 1) of two-level atoms (qubits) with a single bosonic mode and has been a paradigmatic example of collective quantum behavior. Chen et al [24] have presented numerical exact solutions to this model using extended coherent states (ECS) [25], where the truncation of the Hilbert space can be alleviated systematically. It has been extensively shown in Refs. Non-integrability, and genuine multipartite entanglement dynamics of the Dicke model of bosonic creation and annihilation operators in the Bargmann space of analytical functions [30]. We will propose an analytic scheme to the exact solution for the finite N Dicke model
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