Abstract
We study the Two Photon Quantum Rabi Model by way of its spectral functions and survival probabilities. This approach allows numerical precision with large truncation numbers, and thus exploration of the spectral collapse. We provide independent checks and calibration of the numerical results by studying an exactly solvable case and comparing the essential qualitative structure of the spectral functions. We stress that the large time limit of the survival probability provides us with an indicator of spectral collapse, and propose a technique for the detection of this signal in the current and upcoming quantum simulations of the model.
Highlights
The Quantum Rabi Model (QRM) and the Two-Photon Quantum Rabi Model (2γQRM) represent two basic models for the description of the interaction of light and matter
The paper is organized as follows: we present the model and apply a unitary transformation such that the eigenstates factorize in a bosonic and a spin part[39]; we exploit the connection between the resolvent of a tridiagonal matrix and continued fractions to obtain a numerical determination for the spectral function of factorized states|n, σ〉; we use the previous results to study the survival probability of the vacuum state of the system
In the factorized states basis|n, σ〉, the resolvent of the QRM and 2γQRM can readily be expressed in continued fraction form, which makes a numerical calculation of the spectral function ρ(E, |n, σ〉) accessible
Summary
Elena Lupo[1,2], Anna Napoli[1,3], Antonino Messina[3,4], Enrique Solano5,6,7 & Íñigo L. In this paper we put forward the spectral analysis of a factorized state|n, σ〉 ≡ |n〉|σ〉 of the 2γQRM, n being the eigenvalue of the number operator a†a and σ being the eigenvalue of the spin operator σz This approach, valid in each point of the parameter space, is an alternative to the Bargman solution of the model. The paper is organized as follows: we present the model and apply a unitary transformation such that the eigenstates factorize in a bosonic and a spin part[39]; we exploit the connection between the resolvent of a tridiagonal matrix and continued fractions to obtain a numerical determination for the spectral function of factorized states|n, σ〉; we use the previous results to study the survival probability of the vacuum state of the system. Each effective Hamiltonian ∼Hw is explicitly tridiagonal in the Fock basis
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