arXiv subjects

T. N. C. Mendes

Publications and source records attributed to T. N. C. Mendes.

9 recordsLinked to original sources

arXiv2010

Spontaneous emission of an atom near a wedge

It is a well known fact that non-trivial boundary conditions affect the interaction between atoms and the always present quantized electromagnetic field. In this paper, we focus on how the spontaneous emission rate of a given excited atom is altered when placed inside a perfectly conducting wedge. We begin by briefly presenting the formalism on which our calculations are founded, proceeding then to a long but straightforward calculation of the transition rate. We present results for a general atom but, for the sake of simplicity, we narrow them down to an effective two-level system in our numerical investigations. From these we conclude that the results are physically sound.

quant-ph↗

arXiv2009

Subtleties on energy calculations in the image method

In this pedagogical work we point out a subtle mistake that can be done by undergraduate or graduate students in the computation of the electrostatic energy of a system containing charges and perfect conductors if they naively use the image method. Specifically, we show that the naive expressions for the electrostatic energy for these systems obtained directly from the image method are wrong by a factor 1/2. We start our discussion with well known examples, namely, point charge-perfectly conducting wall and point charge-perfectly conducting sphere and then proceed to the demonstration of general results, valid for conductors of arbitrary shapes.

physics.class-ph↗

arXiv2009

Dispersive interaction between an atom and a conducting sphere

We calculate the van der Waals dispersive interaction between a neutral but polarizable atom and a perfectly conducting isolated sphere in the nonretarded case. We make use of two separate models, one being the semiclassical fluctuating-dipoles method, the other using ordinary quantum mechanics.

quant-ph↗

arXiv2009

Magnetic influence on classical dispersion

We discuss the Lorentz model for dispersion and absorption of radiation in dilute, linear and isotropic materials. Initially, with the purpose of making the paper as self-contained as possible, we reproduce the usual calculations concerning the interaction between the charged material oscillators and the electric field of the incident radiation, obtaining the main behavior of the reactive and dissipative electromagnetic properties of the materials. Thereafter, we also include the magnetic contribution of the Lorentz force to the equation of motion of the oscillators up to first order in $v/c$, which leads to some interesting results, like the approximately linear dependence of the refraction index with the radiation intensity and the appearance of a second region of anomalous dispersion around half the natural frequencies of the material.

physics.class-ph↗

arXiv2008

Dispersion forces between an atom and a perfectly conducting wedge

We consider the interaction between an electrically polarizable atom in its fundamental state and a wedge constituted by two semi-infinite perfectly conducting plates. Using a formalism based on a master equation, we compute the dispersion force on the atom for both retarded and non-retarded regimes.

quant-ph↗

arXiv2007

Atom-wall dispersive forces from master equation formalism

Using the general expressions for level shifts obtained from the master equation for a small system interacting with a large one considered as a reservoir, we calculate the dispersive potentials between an atom and a wall in the dipole approximation. We analyze in detail the particular case of a two-level atom in the presence of a perfectly conducting wall. We study the van der Waals as well as the resonant interactions. All distance regimes as well as the high and low temperature regimes are considered. We show that the Casimir-Polder interaction can not be considered as a direct result of the vacuum fluctuations only. Concerning the interaction between the atom and the wall at high temperature, which show that a saturation of the potential for all distances occurs. This saturated potential coincides exactly with that obtained in the London-van der Waals limit.

quant-ph↗

arXiv2006

Excited state contribution to the Casimir-Polder force at finite temperature

Using the master equation we calculate the contribution of the excited state of a two-level atom to its interacting potential with a perfectly conducting wall at finite temperature. For low temperature, $\hbar ω_0/k_B T = k_0 λ_T\gg 1$, where $ω_0 = k_0 c$ is the transition frequency of the atom and $λ_T$ is the thermal wavelength, we show that this contribution is very small $(\propto e^{-k_0λ_T})$. In the opposite limit $(k_0λ_T \ll 1)$, however, we show that the expression for the interacting potential, for all relevant distance regimes, becomes exactly the same as that for very short distances $(k_0 z \ll 1)$ and with the field in the vacuum state.

quant-ph↗

arXiv2006

A master equation approach for the interaction of an atom with a dielectric semi-infinite medium

We use the master equation approach to calculate the energy level shifts of an atom in the presence of a general dielectric semi-infinite medium characterized by a dielectric constant $ε(ω)$. Particularly, we analyze the case of a non-dispersive medium for which we obtain a general expression for the interaction as well as the asymptotic behaviors for $k_0 z \ll 1$ (non-retarded regime) and $k_0 z \gg 1$ (retarded regime), where $ω_0 = k_0 c$ is the main transition frequency of the atom. The limiting cases $ε\simeq 1$ and $ε\gg 1$ are discussed for both retarded and non-retarded limits. For the retarded limit, we compute the non-additivity contribution of van der Waals forces.

quant-ph↗

arXiv2006

Casimir-Polder forces from density matrix formalism

We use the density matrix formalism in order to calculate the energy level shifts, in second order on interaction, of an atom in the presence of a perfectly conducting wall in the dipole approximation. The thermal corrections are also examined when $\hbar ω_0/k_B T = k_0 λ_T \gg 1$, where ${$ω_0=k_0 c$}$ is the dominant transition frequency of the atom and $λ_T$ is the thermal length. When the distance $z$ between the atom and the wall is larger than $λ_T$ we find the well known result obtained from Lifshitz's formula, whose leading term is proportional to temperature and is independent of $c$, $\hbar$ and $k_0$. In the short distance limit, when $z\llλ_T$, only very small corrections to the leading vacuum term occur. We also show, for all distance regimes, that the main thermal corrections are independent of $k_0$ (dispersion is not important) and dependent of $c$, which means that there is not a non-retarded regime for the thermal contributions.

quant-ph↗