Daniel Braak

It is shown that a semiclassical Rabi model with parity-time ( PT ) symmetry possesses quasiexact solutions, which can be found using the Lie-algebraic approach. These solutions are located precisely at the exceptional points of the spectrum, the boundaries of the PT -symmetric phase. The corresponding constraints on the model parameters can be interpreted as a resonance relationship between the constant and periodic driving terms. For sufficiently large resonance ratio and judiciously chosen parameters, we find that the time evolution of the complete qubit can be described exactly.

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).

The asymmetric quantum Rabi model (AQRM) is a fundamental model in quantum optics describing the interaction of light and matter. Besides its immediate physical interest, the AQRM possesses an intriguing mathematical structure which is far from being completely understood. In this paper, we focus on the distribution of the level spacing, the difference between consecutive eigenvalues of the AQRM in the limit of high energies, i.e. large quantum numbers. In the symmetric case, that is the quantum Rabi model (QRM), the spacing distribution for each parity (given by the Z 2 -symmetry) is fully clarified by an asymptotic expression derived by de Monvel and Zielinski, though some questions remain for the full spectrum spacing. However, in the general AQRM case, there is no parity decomposition for the eigenvalues. In connection with numerically exact studies and recent theoretical results, we describe the spacing distribution for the AQRM which is characterized by a new type of periodicity and symmetric behavior of the distribution with respect to the bias parameter, reflecting the hidden symmetry of the AQRM. In addition, we observe in the AQRM the excited state quantum phase transition for large values of the bias parameter, analogous to the QRM with large qubit energy, and an internal symmetry of the level spacing distribution for fixed bias. This novel symmetry is independent from the symmetry for half-integer bias and not explained by current theoretical knowledge.

The Rabi–Stark model is a nonlinear generalization of the quantum Rabi model including the dynamical Stark shift as a tunable term, which can be realized via quantum simulation on a cavity QED platform. When the Stark coupling becomes equal to the mode frequency, the spectrum changes drastically, a transition usually termed “spectral collapse” because numerical studies indicate an infinitely degenerate ground state. We show that the spectrum extends continuously from a threshold value up to infinity. A set of normalizable states is embedded in the continuum, which furnishes an unexpected analogy to the atomic Stark effect. Bound states and continuum can be obtained analytically through two equally justified but different confluence processes of the associated differential equation in Bargmann space. Moreover, these results are obtained independently using a method based on adiabatic elimination of the spin degree of freedom and corroborated through large-scale numerical checks.

Contrary to the statement made in Section 2.2. and a paper by Ng et al., the Hamiltonian of the two‐photon quantum Rabi model is self‐adjoint for all . Other results of the article are not affected.

The asymmetric quantum Rabi model (AQRM) is a fundamental model in quantum optics describing the interaction of light and matter. Besides its immediate physical interest, the AQRM possesses an intriguing mathematical structure which is far from being completely understood. In this paper, we focus on the distribution of the level spacing, the difference between consecutive eigenvalues of the AQRM in the limit of high energies, i.e. large quantum numbers. In the symmetric case, that is the quantum Rabi model (QRM), the spacing distribution for each parity (given by the $\mathbb{Z}_2$-symmetry) is fully clarified by an asymptotic expression derived by de Monvel and Zielinski, though some questions remain for the full spectrum spacing. However, in the general AQRM case, there is no parity decomposition for the eigenvalues. In connection with numerically exact studies for the first 40,000 eigenstates we describe the spacing distribution for the AQRM which is characterized by a new type of periodicity and symmetric behavior of the distribution with respect to the bias parameter. The results reflects the hidden symmetry of the AQRM known to appear for half-integer bias. In addition, we observe in the AQRM the excited state quantum phase transition for large values of the bias parameter, analogous to the QRM with large qubit energy, and an internal symmetry of the level spacing distribution for fixed bias. This novel symmetry is independent from the symmetry for half-integer bias and not explained by current theoretical knowledge.

The various generalized spectral determinants (G‐functions) of the two‐photon quantum Rabi model are analyzed with emphasis on the qualitative aspects of the regular spectrum. Whereas all of them yield at least a subset of the exact regular eigenvalues, only theG‐function proposed by Chen et al. in 2012 exhibits an explicitly known pole structure which dictates the approach to the collapse point. This function is derived rigorously employing the ‐symmetry of the model and shown that its zeros correspond to the complete regular spectrum.

The quantum Rabi model (QRM) with linear coupling between light mode and qubit exhibits the analog of a second-order phase transition for vanishing mode frequency which allows for criticality-enhanced quantum metrology in a few-body system. We show that the QRM including a nonlinear coupling term exhibits much higher measurement precisions due to its first-order-like phase transition at finite frequency, avoiding the detrimental slowing-down effect close to the critical point of the linear QRM. When a bias term is added to the Hamiltonian, the system can be used as a fluxmeter or magnetometer if implemented in circuit QED platforms.