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We describe an effective field theory for atomic lasers which reduces to the Jaynes-Cummings model in the non-relativistic, single mode limit. Our action describes a multi-mode system, with general polarizations and Lorentz invariance and…
We present a method to obtain soliton solutions to relativistic system of coupled scalar fields. This is done by examining the energy associated to static field configurations. In this case we derive a set of first-order differential…
We show theoretically that two atomic dipoles in a resonator constitute a non-linear medium, whose properties can be controlled through the relative position of the atoms inside the cavity and the detuning and intensity of the driving…
For a particle moving in a one-dimensional space an under a periodic external force, its quantization is study using the Hamiltonian (generalized linear momentum quantization) and constant of motion (velocity quantization) approaches. it is…
We investigate the ground-state properties and quantum phase transitions of an ensemble consisting of $N$ four-level atoms within an optical cavity coupled to the single cavity mode and external laser fields. The system is described by an…
We briefly report on our method [Fiore JPA 2017] of simplifying the equations of motion of charged particles in an electromagnetic field that is the sum of a plane travelling wave and a static part; it is based on changes of the dependent…
As is known, a solitary pulse in the complex cubic Ginzburg-Landau (GL) equation is unstable. We demonstrate that a system of two linearly coupled GL equations with gain and dissipation in one subsystem and pure dissipation in another…
We review our recent work leading to steady-state solutions of the semiclassical (Maxwell-Bloch) equations of a laser. These are coupled non-linear partial differential equations in space and time which have previously been solved either by…
The dynamics of a system composed of two coupled optical cavities, each containing a single two-level atom, is studied over a wide range of detuning and coupling values. A description of the field in terms of delocalized modes reveals that…
Group-theoretical approach is applied to study behavior of lossless two-level atoms in a standing-wave laser field. Due to the recoil effect, the internal and external atomic degrees of freedom become coupled. The internal dynamics is…
This paper investigates the identification of two coefficients in a coupled hyperbolic system with an observation on one component of the solution. Based on the the Carleman estimate for coupled wave equations a logarithmic type stability…
We investigate the relativistic generalization of the classical St\"{o}rmer problem, which describes the motion of charged particles in a purely magnetic dipole field. By incorporating special relativistic effects, the particle dynamics is…
In this work we investigate an optomechanical system consisting of two cavities coupled to the same mechanical resonator. We consider each cavity being weakly pumped as well as a small tunneling rate between the cavities. In such…
Quantum light-matter systems at strong coupling are notoriously challenging to analyze due to the need to include states with many excitations in every coupled mode. We propose a nonperturbative approach to analyze light-matter correlations…
We study the dynamics of a driven optomechanical cavity coupled to a charged nanomechanical resonator via Coulomb interaction. We find the tunable switch between slow-and fast- light in double-mode can be observed from the output field by…
Quantum optical systems, like trapped ions, are routinely described by master equations. The purpose of this paper is to introduce a master equation for two-sided optical cavities with spontaneous photon emission. To do so, we use the same…
A self-consistent integral equation is formulated and solved iteratively which determines the steady-state lasing modes of open multi-mode lasers. These modes are naturally decomposed in terms of frequency dependent biorthogonal modes of a…
We develop the continuum mechanics of quantum many-body systems in the linear response regime. The basic variable of the theory is the displacement field, for which we derive a closed equation of motion under the assumption that the…
We investigate the dynamics of a two-photon laser under conditions where the spatial variation of the cavity field along the cavity axis is important. Main attention is paid to linear stability analysis and numerical investigation of a…
The spectacular experimental results of the last few years in cavity quantum electrodynamics and trapped ions research has led to very high level laboratory performances. Such a stimulating situation essentially stems from two decisive…