Spectral collapse in mixed Rabi model

Chi‐Fai Lo

Vittorio Penna, Francesco Antonino Raffa, Roberto Franzosi

Abstract We investigate the origin of spectral collapse occurring in nonlinear Rabi Hamiltonians with an su(1,1) coupling scheme, showing how the collapse can be triggered by the competition between the Rabi parameter g and the field frequency W . The collapse already appears in the model Hamiltonian where the atomic-energy term is absent. After showing that su(1,1) is the dynamical algebra of the Hamiltonian, we demonstrate how the occurrence of spectral collapse can be directly related to the three types of equivalence classes characterizing the structure of this algebra. We highlight how the dramatic change of the spectrum significantly affects the structure of eigenstates represented in a suitable momentum–coordinate picture.

Román J. Armenta‐Rico, F. H. Maldonado-Villamizar, B. M. Rodríguez-Lara

Spectral collapse, the transition from a discrete to a continuous spectrum, is a characteristic in quantum Rabi models. We explore this phenomenon in the two-photon quantum Rabi model using optical phase space, and we find that, in the so-called degenerate qubit regime, the collapse is similar to the transition from a harmonic to an inverted oscillator with the free-particle potential as a critical transition point. In the degenerate qubit regime, we construct Dirac-normalizable eigenfunctions with well-defined parity for the model. In the general model, we use parity to diagonalize the system in the qubit basis and numerically find that the qubit frequency does not change the critical point where spectral collapse occurs. We numerically confirm the existence of an exceptional state at the critical coupling, and we argue its analytic provenance from both a Born-Oppenheimer and a variational approximation.

Anne Boutet de Monvel, Lech Zieliński

Zu‐Jian Ying, Hang‐Hang Han, Bo‐Jian Li +2 more

Abstract Applications of quantum systems with non‐linear light–matter interaction have to deal with a peculiar instability in the ultra‐ and deep strong coupling regime, the so‐called “spectral collapse.” To solve this problem, the present work investigates a generalized quantum Rabi model (QRM) with two‐ and four‐photon terms in view of applications for critical quantum metrology. In the introduced model, the spectral collapse occurring in the standard two‐photon QRM is stabilized by the presence of the quartic potential. The collapse is then transformed into a quantum phase transition, which occurs in the low‐frequency limit of the light mode, whose remnant at finite ratio between qubit and mode frequencies can be applied to critically enhanced quantum metrology. It is found that the four‐photon term entails a much higher measurement precision compared to the standard two‐photon QRM. The mechanism behind the higher precision can be traced to the different behavior of the ground state wave function as the system is tuned through the transition. As the standard two‐photon QRM, despite the absence of the spectral collapse, the proposed model allows for a finite preparation time for the probe state (PTPS).

Andrzej J. Maciejewski, Maria Przybylska, Tomasz Stachowiak