相关论文: Heat kernel for the quantum Rabi model II: propaga…
The quantum Rabi model (QRM) is widely recognized as a particularly important model in quantum optics. It is considered to be the simplest and most fundamental system describing quantum light-matter interaction. The objective of the paper…
In this paper we derive an explicit formula for the heat kernel of the asymmetric quantum Rabi model (AQRM), a symmetry breaking generalization of the quantum Rabi model (QRM). The method described here is an extension of the recently…
The symmetric quantum Rabi model (QRM) is integrable due to a discrete $\mathbb{Z}_2$-symmetry of the Hamiltonian. This symmetry is generated by a known involution operator, measuring the parity of the eigenfunctions. An experimentally…
The heat kernel (or propagator) of the quantum harmonic oscillator (qHO) is given by the Mehler formula, and the partition function is obtained by taking its trace. In general, the spectral zeta function of the given system is obtained by…
Quantum Rabi model (QRM) is widely used for the analysis of the radiation-matter interaction at the fundamental level in cavity quantum electrodynamics. Typically the QRM Hamiltonian includes only $\boldsymbol{\mathsf{p}} \cdot…
We find explicit expressions of the special values of the Hurwitz-type spectral zeta function $\zeta(\mathrm{H};n,\lambda)$ for the Hamiltonians $\mathrm{H}$ of the one-photon quantum Rabi model (1pQRM), the two-photon quantum Rabi model…
We revisit the theoretical description of the ultrastrong light-matter interaction in terms of exactly solvable effective Hamiltonians. A perturbative approach based on polaronic and spin-dependent squeezing transformations provides an…
A generalization of the quantum Rabi model is obtained by replacing the linear (dipole) coupling between the two-level system and the radiation mode by a non-linear expression in the creation and annihilation operators, corresponding to…
Our main goal in this paper is to prove existence (and uniqueness) of the quantum propagator for time dependent quantum Hamiltonians $\hat H(t)$ when this Hamiltonian is perturbed with a quadratic white noise $\dot{\beta}\hat K$. $\beta$ is…
This work explores the non-relativistic quantum propagator $K(x,t)$ as a solution of the Schr\"odinger equation. We suppose that the propagator takes the form ${\rm exp}\left(\frac{\mathrm{i}}{\hbar}S+R\right)$, generalizing the usual WKB…
We study the solvability of the time-independent matrix Schr\"odinger differential equations of the quantum Rabi model and its 2-photon and two-mode generalizations in Bargmann Hilbert spaces of entire functions. We show that the Rabi model…
We relate Gruet formula for the heat kernel on real hyperbolic spaces to the commonly used one derived from Millson induction. The bridge between both formulas is settled by Yor result on the joint distribution of a Brownian motion and of…
In this report, we have studied exceptional spectra of the two-qubit quantum Rabi model in two situations. Firstly, an exceptional spectra is achieved in resonant condition, in which the frequencies of two qubit and photon field satisfy…
The Rabi Hamiltonian, describing the interaction between a two-level atomic system and a single cavity mode of the electromagnetic field, is one of the fundamental models in quantum optics. The model becomes exactly solvable by considering…
The precise control of light-matter interaction serves as a cornerstone for diverse quantum technologies, spanning from quantum computing to advanced atom optics. Typical experiments often feature multi-mode fields and require atoms with…
We prove that the non-commutative harmonic oscillator on $L^2(\mathbb{R})\otimes\mathbb{C}^2$ introduced by Parmeggiani and Wakayama is equivalent to the two-photon quantum Rabi model, and they are also equivalent to a holomorphic…
An ordinary unambiguous integral representation for the finite propagator of a quantum system is found by starting of a privileged skeletonization of the functional action in phase space, provided by the complete solution of the…
Heat kernel coefficients encode the short distance behavior of propagators in the presence of background fields, and are thus useful in quantum field theory. We present a Mathematica program for computing these coefficients and their…
We present a new tractable quantum Rabi model for $N$-level atoms by extending the $\mathbb Z_2$ symmetry of the two-state Rabi model. The Hamiltonian is $\mathbb Z_N$ symmetric and allows the parameters in the level separation terms to be…
The quantum Rabi model (QRM), one of the fundamental models used to describe light and matter interaction, has a deep mathematical structure revealed by the study of its spectrum. In this paper, from the explicit formulas for the partition…