The anti-Jaynes-Cummings model is solvable : quantum Rabi model in rotating and counter-rotating frames ; following the experiments

This article is a response to the continued assumption, cited even in reports and reviews of recent experimental breakthroughs and advances in theoretical methods, that the antiJaynes-Cummings (AJC)interaction is an intractable energy non-conserving component of the quantum Rabi model (QRM). We present three key features of QRM dynamics : (a) the AJC interaction component has a conserved excitation number operator and is exactly solvable (b) QRM dynamical space consists of a rotating frame (RF) dominated by an exactly solved Jaynes-Cummings (JC) interaction specied by a conserved JC excitation number operator which generates the U(1) symmetry of RF and a correlated counter-rotating frame (CRF) dominated by an exactly solved antiJaynes-Cummings (AJC) interaction specied by a conserved AJC excitation number operator which generates the U(1) symmetry of CRF (c) for QRM dynamical evolution in RF, the initial atom-eld state je0i is an eigenstate of the effective AJC Hamiltonian HAJC, while the effective JC Hamiltonian HJC drives this initial state je0i into a time evolving entangled state, and, in a corresponding process for QRM dynamical evolution in CRF, the initial atom-eld state jg0i is an eigenstate of the effective JC Hamiltonian, while the effective AJC Hamiltonian drives this initial state jg0i into a time evolving entangled state, thus addressing one of the long-standing challenges of theoretical and experimental QRM dynamics; consistent generalizations of the initial states je0i , jg0i to corresponding n 0 entangled eigenstates j+en i , j 􀀀g ni of the AJC in RF and JC in CRF, respectively, provides general dynamical evolution of QRM characterized by collapses and revivals in the time evolution of the atomic, eld mode, JC and AJC excitation numbers for large initial photon numbers ; the JC and AJC excitation numbers are conserved in the respective frames RF, CRF, but each evolves with time in the alternate frame.

Epidemic growth and Griffiths effects on an emergent network of excited atoms

Whether it be physical, biological or social processes, complex systems exhibit dynamics that are exceedingly difficult to understand or predict from underlying principles. Here we report a striking correspondence between the excitation dynamics of a laser driven gas of Rydberg atoms and the spreading of diseases, which in turn opens up a controllable platform for studying non-equilibrium dynamics on complex networks. The competition between facilitated excitation and spontaneous decay results in sub-exponential growth of the excitation number, which is empirically observed in real epidemics. Based on this we develop a quantitative microscopic susceptible-infected-susceptible model which links the growth and final excitation density to the dynamics of an emergent heterogeneous network and rare active region effects associated to an extended Griffiths phase. This provides physical insights into the nature of non-equilibrium criticality in driven many-body systems and the mechanisms leading to non-universal power-laws in the dynamics of complex systems.

1/n-expansion of resonant states

In this paper, we present a general analytic expansion in powers of 1/n of the resonant states of quantum mechanical systems, where n = 1, 2, 3, [Formula: see text] is the excitation number. Explicit formulas are obtained for some potential barrier models.

Jaynes–Cummings Model with Intensity Independent Interaction and Initial Field in the Binomial State

Recently, we introduced a new version of the Jaynes–Cummings model in which the interaction Hamiltonian is independent of the excitation number, or field intensity. Exact solution for this model was found allowing the study of nonclassical effects exhibited by the atom and the field, the latter initially in a coherent state. Here, we extend this study to the case of a field initially in the binomial state to investigate those nonclassical effects, as population trapping and sub-Poissonian statistics as function of the interpolating parameters of this state. The previous results are obtained from the present treatment, in the limit of a coherent state allowed by the binomial state.

JAYNES-CUMMINGS MODEL WITH INTENSITY-INDEPENDENT INTERACTION VIA THE PHASE OPERATORS

We introduce a new version of the JC-Model using the (non-Hermitian) phase operators [Formula: see text] in the interaction Hamiltonian, which becomes independent of the excitation number or the field intensity, thus being able to describe properties of the atom in the saturation regime. We employ the “dressed-states” formalism to find an exact solution for our system. As applications we investigate the occurrence of nonclassical effects in the field (squeezing and sub-Poissonian statistics) and in the atom (collapses and revivals of Rabi oscillations and population trapping).

The relativistic oscillator

This paper addresses the problem of the quantization of the relativistic simple harmonic oscillator. The oscillator consists of a pair of scalar particles of masses m 1 and m 2 moving under the influence of a potential that is linear in the squared magnitude of the spatial separation of the particles. A novel feature of the model is that the potential is an operator , this being necessary to render the notion of spatial separation for a pair of particles meaningful in the context of relativistic quantum theory. The state of the oscillator is characterized (as in the non-relativistic theory) by the excitation number n and the total spin s . The total mass M of the system is quantized, and the main result of the paper is to derive a formula for the allowable mass-levels, namely: M 2 [1— ( m 1 + m 2 ) 2 / M 2 ] [1 — ( m 1 — m 2 ) 2 / M 2 ] = 4 nΩ + γ , where Ω and γ are constants (with dimensions of mass squared) which determine the strength and zero-point energy of the oscillator, respectively. A striking feature of this formula is that when m 1 and m 2 are both small compared with M (for example, for 'light quarks’ combining to form meson states) the allowable states of the system lie on linear Regge trajectories , with M 2 = 4 nΩ + γ and s = n , n -2,....