Rabi Model Research Articles

Study of fractional order rabies transmission model via Atangana–Baleanu derivative

In this work, we aim at disentangling the theoretical contribution through mathematical modeling approach to advance the understanding of rabies dynamics and control in livestock population. A fractional order model of rabies, using Atangana–Baleanu fractional operator is created. The analysis of suggested system and its application are both conducted. The capacity of proposed model to forecast the disease can help researchers and livestock health care agencies to take preventive actions.

Approximate analytic solution of the dissipative semiclassical Rabi model under parametric multi-tone modulations

Abstract We present an analytic method for obtaining the dynamics of the dissipative time-modulated
semiclassical Rabi model, which describes a two-level system (qubit) with time-dependent parameters, 
coupled to a single-mode bosonic field via the dipole-interaction and to
a thermal reservoir. We consider the simultaneous harmonic
modulations of the qubit transition frequency and the qubit-field coupling strength,
with arbitrary frequencies, and obtain closed analytic expressions for the
density operator under the coarse-graining approximation. Our
approximate results are in excellent ageement with exact numerical data, and
illustrate how the qubit state can be controlled in the dispersive regime by properly
adjusting the system parameters.

Experimental Quantum Simulation of Multicriticality in Closed and Open Rabi Model

Experimental Quantum Simulation of Multicriticality in Closed and Open Rabi Model

Quantum Entanglement in the Rabi Model with the Presence of the $$A^{2}$$ Term

Quantum Entanglement in the Rabi Model with the Presence of the $$A^{2}$$ Term

Three-Term Asymptotic Formula for Large Eigenvalues of the Quantum Rabi Model with a Resonant Bias

Three-Term Asymptotic Formula for Large Eigenvalues of the Quantum Rabi Model with a Resonant Bias

Three-term asymptotic formula for large eigenvalues of the two-photon quantum Rabi model

We prove that the spectrum of the two-photon quantum Rabi Hamiltonian consists of two eigenvalue sequences (E_{m}^{+})_{m=0}^{\infty} , (E_{m}^{-})_{m=0}^{\infty} satisfying a three-term asymptotic formula with the remainder estimate O(m^{-1}\ln m) when m tends to infinity. Our asymptotic formula can be written so that the third term is given by an explicit oscillatory integral and an explicit remainder estimate.

Quantum Fisher information and polaron picture for the identification of transition coupling in the quantum Rabi model

Quantum Fisher information and polaron picture for the identification of transition coupling in the quantum Rabi model

Anisotropic qubit-photon interactions inducing multiple antibunching-to-bunching transitions of photons

We investigate photon correlations in the open anisotropic quantum Rabi model via quantum dressed master equation. Multiple antibunching-to-bunching transitions are generally exhibited at deep-strong qubit-photon coupling, which becomes vanishing in the standard open quantum Rabi model. The observed two-photon statistics can be well described analytically within a few lowest eigenstates at low temperatures. It is revealed that the additional photon antibunching effect mainly originates from the selection rule of the correlation-measurement-induced eigenstate transitions. Furthermore, we also unravel the phenomena that higher-order correlation function lifts up dramatically once passing the crossing point of excited states, which is attributed to the on-off switch of dominant cooperative transition with level crossing. We hope these results may fertilize the analysis of the nonclassical photon statistics in anisotropic coupled qubit-photon systems.

Dark-state solution and symmetries of the two-qubit multimode asymmetric quantum Rabi model

We study the two-qubit asymmetric quantum Rabi model (AQRM) and find its dark-state solution. Such solutions have at most one photon and constant eigenenergy in the whole coupling regime, causing level crossings in the spectrum, although there is no explicit conserved quantity except for energy. We find an operator in the eigenenergy basis to label all the degeneracies with its eigenvalues, and compare it with the well-known hidden symmetry which exists when bias parameter ϵ is a multiple of half of the resonator frequency ω. Extended to the multimode case, we find symmetries related with conserved bosonic number operators, which also cause level crossings. This paves the way for further symmetry studies on generalized Rabi models.

Zeta limits for the spectrum of quantum Rabi models

Zeta limits for the spectrum of quantum Rabi models

Unified diagrammatic approach to quantum transport in few-level junctions for bosonic and fermionic reservoirs: Application to the quantum Rabi model

Unified diagrammatic approach to quantum transport in few-level junctions for bosonic and fermionic reservoirs: Application to the quantum Rabi model

Anisotropic Rabi model with two-photon relaxation

Anisotropic Rabi model with two-photon relaxation

Error-Tolerant Amplification and Simulation of the Ultrastrong-Coupling Quantum Rabi Model.

Cat-state qubits formed by photonic cat states have a biased noise channel, i.e., one type of error dominates over all the others. We demonstrate that such biased-noise qubits are also promising for error-tolerant simulations of the quantum Rabi model (and its varieties) by coupling a cat-state qubit to an optical cavity. Using the cat-state qubit can effectively enhance the counterrotating coupling, allowing us to explore several fascinating quantum phenomena relying on the counterrotating interaction. Moreover, another benefit from biased-noise cat qubits is that the two main error channels (frequency and amplitude mismatches) are both exponentially suppressed. Therefore, the simulation protocols are robust against parameter errors of the parametric drive that determines the projection subspace. We analyze three examples: (i)collapse and revivals of quantum states; (ii)hidden symmetry and tunneling dynamics; and (iii)pair-cat-code computation.

Floquet systems with continuous dynamical symmetries: characterization, time-dependent noether charge, and solvability

We study quantum Floquet (periodically-driven) systems having continuous dynamical symmetry (CDS) consisting of a time translation and a unitary transformation on the Hilbert space. Unlike the discrete ones, the CDS strongly constrains the possible Hamiltonians H(t) and allows us to obtain all the Floquet states by solving a finite-dimensional eigenvalue problem. Besides, Noether’s theorem leads to a time-dependent conservation charge, whose expectation value is time-independent throughout evolution. We exemplify these consequences of CDS in the seminal Rabi model, an effective model of a nitrogen-vacancy center in diamonds without strain terms, and Heisenberg spin models in rotating fields. Our results provide a systematic way of solving for Floquet states and explain how they avoid hybridization in quasienergy diagrams.

Multicritical dissipative phase transitions in the anisotropic open quantum Rabi model

We investigate the nonequilibrium steady state of the anisotropic open quantum Rabi model, which exhibits first-order and second-order dissipative phase transitions upon varying the degree of anisotropy between the coupling strengths of rotating and counter-rotating terms. Using both semiclassical and quantum approaches, we find a rich phase diagram resulting from the interplay between the anisotropy and the dissipation. First, there exists a bistable phase where both the normal and superradiant phases are stable. Second, there are multicritical points where the phase boundaries for the first- and second-order phase transitions meet. We show that a new set of critical exponents governs the scaling of the multicritical points. Finally, we discuss the feasibility of observing the multicritical transitions and bistability using a pair of trapped ions where the anisotropy can be tuned by controlling the intensity of the Raman transitions. Our study enlarges the scope of critical phenomena that may occur in finite-component quantum systems, which could be useful for applications in critical quantum sensing. Published by the American Physical Society 2024

Spacing distribution for quantum Rabi models * *Dedicated to Mr. Hiromichi Shinohara, who was instrumental in establishing NTT-IFM, on his 70th birthday.

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 Z2 -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.

Periodic quantum Rabi model with cold atoms at deep strong coupling

The quantum Rabi model describes the coupling of a two-state system to a bosonic field mode. Recent theoretical work has pointed out that a generalized periodic version of this model, which maps onto Hamiltonians applicable in superconducting qubit settings, can be quantum simulated with cold trapped atoms. Here, we experimentally demonstrate atomic dynamics predicted by the periodic quantum Rabi model far in the deep strong-coupling regime. The two-state system is represented by two Bloch bands of cold atoms in an optical lattice, and the bosonic mode by oscillations in a superimposed optical dipole trap potential. The observed dynamics beyond the usual quantum Rabi physics becomes relevant when the edge of the Brillouin zone is reached, and evidence for collapse and revival of the initial state is revealed at extreme coupling conditions. Published by the American Physical Society 2024

Tutorial on nonperturbative cavity quantum electrodynamics: is the Jaynes–Cummings model still relevant?

In this tutorial review, we briefly discuss the role that the Jaynes–Cummings model occupies in present-day research in cavity quantum electrodynamics with a particular focus on the so-called ultrastrong-coupling regime. We start by critically analyzing the various approximations required to distill such a simple model from standard quantum electrodynamics. We then discuss how many of those approximations can be, and often have been, broken in recent experiments. The consequence of these failures has been the need to abandon the Jaynes–Cummings model for more complex models. In this, the quantum Rabi model has the most prominent role, and we will rapidly survey its rich and peculiar phenomenology. We conclude the paper by showing how the Jaynes–Cummings model still plays a crucial role even in nonperturbative light–matter coupling regimes.

Can quantum Rabi model with A2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\varvec{A}}^\ extbf{2}$$\\end{document}-term avoid no-go theorem and make quantum simulation of mass-enhancement in SUSY breaking?

We study the model of a mass enhancement in the supersymmetric quantum mechanics. This model is so simple that it may be implemented as a quantum simulation of the mass enhancement taking place when supersymmetry (SUSY) is spontaneously broken. It is evolved from a prototype based on the quantum Rabi model. Here, our quantum simulation means the realization of the target quantum phenomenon as a physical entity with some quantum-information devices. The original prototype is given as a mathematical model, and has the transition from the N=2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {N}}=2$$\\end{document} SUSY to its spontaneous breaking, though it has no mass enhancement. It is recently reported that the transition is observed for this prototype in a trapped-ion experiment with devising a method experimentally to realize the transition. The model proposed in this paper describes how the mass enhancement takes place in the fermionic states by the excitation of the 1-mode light boson in the SUSY breaking. In this model, the bosonic and fermionic states are graded by qubits. Although our model’s interaction does not have the Higgs potential, the mass enhancement in the fermionic states is caused by the radiative enhancement with the help of the X-gate’s swap between the fermionic and bosonic states.

The quantum Rabi model: towards Braak’s conjecture

We establish a density one version of Braak’s conjecture on the fine structure of the spectrum of the quantum Rabi model, as well as a recent conjecture of Braak, Nguyen, Reyes-Bustos and Wakayama on the nearest neighbor spacings of the spectrum. The proof uses a three-term asymptotic expansion for large eigenvalues due to Boutet de Monvel and Zielinski, and a number theoretic argument from uniform distribution theory.