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Physical Review A

Atom dynamics between conducting plates

S. Al‐Awfi, M. Babiker

Published Sep 1, 1998• 21 citations
Publisher

Abstract

The dynamics of atoms subject to laser light propagating between perfectly conducting parallel plates is investigated. In the semiclassical approximation the motion of atoms in this context is governed by a van der Waals--type potential, together with a dynamic dipole potential that comes into play as soon as a cavity mode is excited. In addition, the atoms become subject to an average dissipative (spontaneous) force associated with the cavity mode that always acts parallel to the plates. We show that, by a suitable choice of field intensity and detuning, the total transverse potential can be used to confine atoms in transverse vibrational states, while their motion in the parallel direction is controlled by the dissipative force. Significant variations of the characteristics of the system with atom velocity, dipole orientation, and type of excited cavity mode are emphasized. These features are illustrated using typical parameters for the case of sodium atoms between parallel plates with subwavelength separations.

DOI
10.1103/physreva.58.2274

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Physica Scripta•Jul 1, 2009•2 citations
The dynamics of atoms subject to laser light propagating between perfectly conducting parallel plates is investigated. In the semiclassical approximation the motion of atoms in this context is governed by a van der Waals--type potential, together with a dynamic dipole potential that comes into play as soon as a cavity mode is excited. In addition, the atoms become subject to an average dissipative (spontaneous) force associated with the cavity mode that always acts parallel to the plates. We show that, by a suitable choice of field intensity and detuning, the total transverse potential can be used to confine atoms in transverse vibrational states, while their motion in the parallel direction is controlled by the dissipative force. Significant variations of the characteristics of the system with atom velocity, dipole orientation, and type of excited cavity mode are emphasized. These features are illustrated using typical parameters for the case of sodium atoms between parallel plates with subwavelength separations.
This thesis is concerned with the theory of spontaneous emission in the context of cavity QED and the guiding of atoms by laser light in confined geometries. We focus on three different geometrical shapes of waveguide, namely the parallel plate guide and two kinds of cylindrical waveguide: one with a rectangular cross section and another with a circular cross section. These waveguides are assumed to be characterised by two distinct properties. Firstly, all three types of guide have perfect conductor boundary conditions, which means that the guide walls are infinitely conducting and, consequently, lossless. Secondly, the guides are assumed to have subwavelength dimensions (less than the atom electric dipole transition wavelength #lambda#). The first consequence of this is that the spontaneous emission process is possible only via a few cavity modes. For each type of structure, we examine the confinement of electromagnetic fields within it and proceed to quantise these fields by following the standard procedure, incorporating the boundary conditions at the guide walls. This allows the position-dependent spontaneous emission rate to be evaluated for an electric dipole located at an arbitrary point within the guide. Asymptotic limits of the spontaneous emission rate are then derived which serve as useful checks of the calculations. For the rectangular guide, we are able to recover the results appropriate for the parallel-plate case when side a of the rectangular cross section becomes large, while side b is kept fixed. For the circular guide, we are able to recover the results appropriate for the free space case when the radius of the guide becomes large. The second part of the thesis deals with the theory of the motion of atoms in the spatially varying light fields inside the three different shapes of waveguide. In each structure we examine the forces that act on the atom and solve the equation of motion leading to the atom dynamics when an electric dipole within the guide is subject to an excited p-polarised cavity mode. The characteristics of the atomic motion in the guide in the presence of a cavity mode are then explored. We show that under these conditions the atom becomes subject to a transverse dipole potential and a dissipative force, both of which vary across the guide and are also functions of the atom velocity along the mode propagation direction. The dipole potential is responsible for the transverse trapping (and hence the channelling) of atoms at specific regions of the cross section, while the dissipative force controls the longitudinal motion of the channelled atoms. The conditions facilitating atom guiding are explored using typical parameters for sodium atoms in guides of subwavelength dimensions. The roles of the van der Waals and Casimir-Polder potentials on the atomic motion in waveguides is clarified theoretically in the context of the parallel-plate guide and we show that such potentials are effective only at relatively short distances from the guide walls. Finally, we show that atomic motion in a hollow circular guide is subject to a quantised torque arising from the orbital angular momentum effects associated with any excited waveguide mode of order l > 0. We find that an appropriately detuned atom immersed in such a mode may be trapped radially in a vibrational state and be made to exhibit novel rotational effects associated with the light torque, including a rotational frequency shift. (author)
We study the effects of phase fluctuations of a laser on the dynamics of a two-level atom. We assume that the atom is in a cavity and consider two cases in which the atom is either sandwiched between two parallel metal plates or placed inside a rectangular metallic waveguide. We use the well-known master equation and utilize the phase diffusion model for our analysis. We derive expressions for the dipolar and dissipative forces acting on the atom. We then show that the laser fluctuations produce an increase in the magnitude of the dissipative force and a reduction in the dipolar force. We illustrate that the atom-laser interaction gives rise to a potential, which binds the atom to the central part of the cavity. We also show that the atomic velocity produces significant changes on the potential and on the force acting on the atom. The combined effects of the velocity and laser fluctuations on the atomic motion are discussed.
We investigate the vibrational energy eigenvalues and eigenfunctions of the neutral sodium atom trapped by the optical dipole potential due to a cavity mode. Our model is based on the optical confinement of a sodium atom between parallel plates with its dipole moment vector fixed in the axial direction of the cavity. The negative detuning situation and suitable parameters are taken in order to maintain a sufficiently deep central well of the optical dipole potential to allow many quasi harmonics trapped states of the atom.
We compute the energies of the interaction between two atoms placed in the middle of a perfectly reflecting planar cavity, in the weak-coupling nondegenerate regime. Both inhibition and enhancement of the interactions can be obtained by varying the size of the cavity. We derive exact expressions for the dyadic Green's function of the cavity field which mediates the interactions and apply time-dependent quantum perturbation theory in the adiabatic approximation. We provide explicit expressions for the van der Waals potentials of two polarizable atomic dipoles and the electrostatic potential of two induced dipoles. We compute the van der Waals potentials in three different scenarios: two atoms in their ground states, two atoms excited, and two dissimilar atoms with one of them excited. In addition, we calculate the phase-shift rate of the two-atom wave function in each case. The effect of the two-dimensional confinement of the electromagnetic field on the dipole-dipole interactions is analyzed. This effect depends on the atomic polarization. For dipole moments oriented parallel to the cavity plates, both the electrostatic and the van der Waals interactions are exponentially suppressed for values of the cavity width much less than the interatomic distance, whereas for values of the width close to the interatomic distance, the strength of both interactions is higher than their values in the absence of cavity. For dipole moments perpendicular to the plates, the strength of the van der Waals interaction decreases for values of the cavity width close to the interatomic distance, while it increases for values of the width much less than the interatomic distance with respect to its strength in the absence of cavity. We illustrate these effects by computing the dipole-dipole interactions between two alkali atoms in circular Rydberg states.
In the absence of external modes, cavity dimensions and dipole location are the main factors that increase, reduce and disallow dipole decay rate in the Cavity QED. The presence of external modes with short cavity length, high atom velocity and high intensity is con- sidered as a reasonable source of constrain to the dipole vector in a fixed direction. As a result, only two orthogonal directions can be as- sumed: π polarization and σ polarization. These directions can be used to illustrate the variations of Cavity QED effects with dipole adjust- ment. Thus the distribution of the dipole decay rate across the plates separation is independent of the excited cavity mode. In contrast, dur- ing the passage of a slow atom between the plates, the dipole can ad- just itself along a local electric field direction. In this work, it has been proven that the average dipole adjustment is determined at every point parallel to the direction of the electric mode vector of the excit- ed cavity mode. Also the subordination was shown to lead to observ- able changes in the dipole decay rate. The above cases have been explored for situations involving sodium atoms between conducting plates of the sub-wavelength range.