On the spectrum of a class of quantum models

Abstract

The spectrum of any quantum model which eigenvalue equation reduces to a three-term recurrence, such as a displaced harmonic oscillator, the Jaynes-Cummings (JC) model, the Rabi model, and a generalized Rabi model, can be determined as zeros of a corresponding transcendental function F(x). The latter can be analytically determined as an infinite series defined solely in terms of the recurrence coefficients. The ease in obtaining the spectrum is of importance regarding recent experimental advances in preparing ultrastrongly interacting quantum systems, which can no longer be reliably described by the exactly solvable JC model. The relevant computer code has been made freely available online.

Kreuser's generalization of Perron's theorem enabled (i) to straightforwardly broaden the definition of the class of quantum models and (ii) to provide a general proof that ${\varphi }_m(z)\in \mathcal{B}$ (6 pages comprising 3 figures; to appear in Europhys. Lett.)

References in corpus (3)

• Beyond the Jaynes-Cummings model: circuit QED in the ultrastrong coupling regime
• Observation of the Bloch-Siegert Shift in a Qubit-Oscillator System in the Ultrastrong Coupling Regime
• Ultrastrong coupling regime of cavity QED with phase-biased flux qubits

Cited by in corpus (1)

• Continued Fractions and the Rabi Model