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Physical Review A

Submicron rectangular cylinders as atom guides

S. Al‐Awfi, M. Babiker

Published Dec 1, 1998• 16 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.58.4768

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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×\else\texttimes\fib.a\ifmmode\times\else\texttimes\fi{}b.a\ifmmode×\else\texttimes\fib. 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.
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)
The motion of atoms inside a long hollow cylindrical waveguide with a circular cross section is investigated. The guide is assumed to have subwavelength dimensions, in which case the spontaneous decay process is effected only by emission of a few possible cavity modes. The characteristics of the atomic motion in the guide are explored in the presence of an excited waveguide mode. We show that the atomic motion in this case is determined by an axial channelling force and a trapping dipole force, plus a quantized light torque associated with the orbital angular momentum property of excited waveguide modes of order l>0.\mathcal{l}>0.l>0. It is predicted that in addition to its axial motion, an atom subject to such a mode should be trapped radially in a vibrational state and should exhibit interesting rotational features due to the light torque, including a rotational frequency shift.
The time evolution of the radiation pressure forces due to the action of a laser light on two-level atom moving inside a long hollow cylinder with a rectangular cross-section of sub-wavelength dimensions a × b is presented.This evolution is considered when the frequency of the light is comparable to a dipole allowed transition frequency.In this limit, the decay emission Γ is possible only via a very small number of modes.From the solutions of the Bloch equations in the dynamic regime, we nd that the transient regime, applicable from the instant the laser is switched on.This is important for the gross motion, provided that the upper-state lifetime Γ -1 is relatively long while the steady-state regime, formally such that t Γ -1 , is appropriate for the evaluation of the forces and the dynamics for large Γ .Signicant variations of the characteristics of the system are emphasized.These features are illustrated using typical parameters for the case of Eu 3+ that has a particularly small Γ .
We calculate the atomic energy-level shift and the modified dipolar radiation rate inside a hollow dielectric cylinder and outside a solid cylinder using a quantum-mechanical linear-response formalism in the dipole approximation. We first derive the electromagnetic fields scattered by the cylindrical surface for an oscillating dipole inside and outside the cylinder. When an atom is located on the axis of the cylindrical hollow, we obtain analytic expressions of the atomic level shifts in two limiting cases: when bbb (radius of hollow) is very small, the level shift is proportional to ${b}^{\ensuremath{-}2}$ which is associated with the kinetic-energy change of the atomic electron, whereas when bbb is very large, the shift is proportional to ${b}^{\ensuremath{-}4}$ which is identified as the retarded (Casimir-Polder) interaction energy. Moreover, we calculate the atomic potentials as a function of the position of atoms in the hollow region, which is important for the atom-guiding experiment. We also calculate the decay rates and find enhanced rates inside and outside the cylinder. In particular, we compare the radiative properties of an atom inside the hollow cylinder with those between two plates, and those near a cylinder with near a single surface.
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.
The spontaneous decay rate of an excited atom placed near a dielectric cylinder is investigated. Special attention is paid to the case when the cylinder radius is small in comparison with radiation wavelength (nanofiber or photonic wire). In this case, the analytical expressions of the transition rates for different orientations of a dipole are derived. It is shown that the main contribution to decay rates is due to the quasistatic interaction of the atom dipole momentum with the nanofiber, and the contributions of guided modes are exponentially small. On the contrary, in the case when the radius of the fiber is only slightly less than the radiation wavelength, the influence of guided modes can be substantial. The results obtained are compared with the case of a dielectric nanospheroid and an ideally conducting wire.