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Journal of Modern Optics

Field-dipole orientation mechanism and higher order modes in atom guides

S. Al‐Awfi, M. Babiker

Published Apr 1, 2001• 6 citations
Publisher

Abstract

In cavity quantum electrodynamics (CQED), cavity size, dipole position and dipole orientation are the main factors controlling cavity effects, for example, suppression and enhancement of spontaneous emission. However, the dynamical effects of dipole orientation in CQED have, to date, remained largely unexplored, with most treatments simply concentrating on two (or three) orthogonal directions to illustrate the variations of CQED effects with dipole orientation. No mechanism which determines the evolution of the dipole orientation has been put forward to describe typical situations where atoms move in the field of an excited cavity mode. We emphasize here that in the presence of a cavity mode, the average dipole orientation is automatically determined at every point to be parallel to the direction of the electric field vector of the cavity mode. Besides giving rise to a single value for the spontaneous emission rate, this mechanism is shown to have important consequences for the dynamics of atoms in atom guides. In particular, it determines the average trapping potential distributions and the average radiation forces which guide the atoms along a cylindrical cavity. The effects of the field-dipole orientation mechanism are illustrated with reference to typical situations involving sodium atoms in sub-micron cylindrical guides. The role of a higher order cavity mode of the cylinder in the dynamics is highlighted in terms of its influence on the rotational and vibrational motions in such guides.

DOI
10.1080/09500340010011727

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In cavity quantum electrodynamics (CQED), cavity size, dipole position and dipole orientation are the main factors controlling cavity effects, for example, suppression and enhancement of spontaneous emission. However, the dynamical effects of dipole orientation in CQED have, to date, remained largely unexplored, with most treatments simply concentrating on two (or three) orthogonal directions to illustrate the variations of CQED effects with dipole orientation. No mechanism which determines the evolution of the dipole orientation has been put forward to describe typical situations where atoms move in the field of an excited cavity mode. We emphasize here that in the presence of a cavity mode, the average dipole orientation is automatically determined at every point to be parallel to the direction of the electric field vector of the cavity mode. Besides giving rise to a single value for the spontaneous emission rate, this mechanism is shown to have important consequences for the dynamics of atoms in atom guides. In particular, it determines the average trapping potential distributions and the average radiation forces which guide the atoms along a cylindrical cavity. The effects of the field-dipole orientation mechanism are illustrated with reference to typical situations involving sodium atoms in sub-micron cylindrical guides. The role of a higher order cavity mode of the cylinder in the dynamics is highlighted in terms of its influence on the rotational and vibrational motions in such guides.
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.
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)
Exploring the spontaneous emission control of an excited two-level atom interacting with the vacuum within a circular waveguide surrounded by a perfect electric conductor is the main objective of this work. This type of emission is dependent on the intrinsic properties of the emitter, such as the emitter’s transition frequency and dipole moment direction, as well as the surrounding electromagnetic environment. Due to being statistical in nature, the fields do not have a well-defined phase, and thus the emission is considered incoherent or in an uncontrollable direction. We propose an approach to direct the emission from an atom embedded in a circular waveguide . To achieve this, multimode waveguides should be excluded because the total emission is simply presented in three orthogonal directions. In contrast, with mono-mode waveguides, the single photon transports in a single-mode waveguide coupled to a cavity embedded with an atom. Thus, the electric dipole moment vector is forced to take the direction of the only mode in which it is allowed to propagate. Besides giving rise to a single value for the emission, this also provides a way to control direction. Such waveguides have already been produced by recent advances in microfabrication technology.
The guiding of atoms by laser light is investigated for atoms inside a long hollow cylinder with a rectangular cross section of subwavelength dimensions $a\ifmmode\times\else\texttimes\fi{}b.$ The cavity modes are quantized, allowing the position-dependent spontaneous emission rate to be evaluated for an electric dipole inside the cylinder. Useful limits of the spontaneous rate are derived. In particular, results appropriate for the parallel-plate case are recovered when side a of the rectangular cross section becomes large, while side b is kept fixed. In the limit of the small cross section, especially when both a and b are less than \ensuremath{\lambda} (the atom electric dipole transition wavelength), the spontaneous emission process is possible only via a few cavity modes. If a cavity mode is now excited with sufficient intensity, the atoms become subject to a transverse dipole potential and an axial dissipative force, both of which vary across the cylinder and are also functions of the atom axial velocity. The dipole potential is responsible for the transverse trapping (and hence the channeling) of atoms at specific regions of the cross section, while the dissipative force controls the axial motion of the channeled atoms. The conditions facilitating atom guiding are explored using typical parameters for sodium atoms in rectangular cylinders of subwavelength dimensions.
Rydberg atoms excited in microwave resonators are ideal systems to test quantum electrodynamics on an unusual scale.1 Owing to their very large electric dipole sizes, these atoms are indeed coupled so strongly to infrared and millimeter-wave radiation that the field of a few photons—ultimately the one of a single photon—stored in a cavity is large enough to induce important transition rates during the atomic time of flight across the cavity. As a result quantum radiative effects are observed in a range of frequencies where usual atomic systems behave as purely classical radiators. The enhancement of the spontaneous emission rate of a single atom prepared in a tuned cavity has already been observed.2 For a resonant cavity with very small losses, a point should be reached where the atom can no longer decay but instead reversibly oscillates between the two states involved in the transition resonant with the cavity mode. Experiments aimed at the observation of this new regime of quantum electrodynamics evolution are under way
The conditions for enhancement and inhibition of the spontaneous emission rate per second by an atom inside coaxial cavities are investigated in the electric-dipole approximation. A complete set of vector mode functions satisfying the boundary conditions is obtained utilizing field decomposition, which is needed to quantize the electromagnetic field. The behavior of the emission rate is generally quite complicated; there are sharp peaks at many resonance points, and the minimal values approach unity as the radius of the cavities increases. Emission is usually inhibited completely if the radius is very small. However, under certain conditions, one being a small radius, there is the possibility of very large emission due to the TEM mode.