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Acta Physica Polonica A

Transient Dynamics of Atoms Inside Submicron Rectangular Waveguides

S. Al‐Awfi

Published Apr 1, 2013• 1 citation
Publisher

Abstract

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 .

DOI
10.12693/aphyspola.123.631

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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 .
The time evolution of the radiation pressure forces due to the action of laser light on matter in the form of neutral molecules, atoms, and ions is considered when the frequency of the light is comparable to a dipole-allowed transition frequency. We find that the transient regime, applicable from the instant the laser is switched on, is important for the gross motion, provided that the upper-state lifetime ${\ensuremath{\Gamma}}^{\ensuremath{-}1}$ is relatively long, while the steady-state regime, formally such that $t⪢{\ensuremath{\Gamma}}^{\ensuremath{-}1}$, is appropriate for the evaluation of the forces and the dynamics for large $\ensuremath{\Gamma}$. With a focus on the orbital-angular-momentum-endowed laser light, the light-induced time-dependent forces and torques are determined and their full time dependence utilized to determine trajectories. Marked differences are found in both translational and rotational features in comparison with the results emerging when the steady-state forces are assumed from the outset. Intricate and detailed atom trajectories are plotted for Laguerre-Gaussian light at near resonance for a transition of Eu3+{\mathrm{Eu}}^{3+}Eu3+ that has a particularly small $\ensuremath{\Gamma}$. The implications of the results for trapping and manipulating atoms and ions using laser light are pointed out and discussed.
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.
We are concerned with an analytic separation approach of the optical Bloch equations in the case of the two-level atom interacting with a classical light. The conditions that permit a complete separation of these equations are extracted in a natural manner and the exact solutions are obtained. A theoretical comparison with Torrey method is given. In this context, we find that the transient regime, valid from the instant of the application of the laser on atom, is significant for the evolution of forces and the dynamics before the steady-state regime will be reached. The case of Eu3 + ion moving in plane-light wave and standing-wave is treated with some details. The implications of the results for operating atoms and ions using laser light are discussed.
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.
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)
A general, analytic theory is presented of the excitation of a two-level atom by a series of short optical laser pulses. The atom is assumed to be isolated (collisionless) with radiative decay from upper to lower state at rate γ. The laser pulses are assumed to have a duration tp such that γtp ≪ 1 (the transient regime), and the spacing between pulses tr is such that tr ≫ tp. In this regime the atomic density matrix is calculated as a function of time during each optical pulse. An analytic expression for the atomic state (Bloch vector) after n optical pulses is also derived. For large n the atomic state converges to a repeating (steady state) cycle of pump excitation followed by radiative decay. The excited-state population in the steady state can be large but only if the spacing between pulses tr is small so that γtr ≲ 0.5. These results indicate that lasers that produce trains of pulses, such as mode-locked conventional lasers and free-electron lasers, can be effective in optical pumping of atoms.