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Spontaneous emission and atom dynamics in planar and cylindrical structures

S. Al‐Awfi

Published Jan 1, 2000• 0 citations
OpenAlex

Abstract

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)

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Submicron rectangular cylinders as atom guides

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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 $a\ifmmode\times\else\texttimes\fi{}b.$ 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.

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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.

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Over the past ten years, our group has investigated the effects of confinement on atoms inside metallic micron–sized cavities in order to elucidate some basic phenomena in the field of cavity quantum electrodynamics (QED). The first of these was the inhibition of spontaneous emission from an atom inside a cavity. This was followed by a laser spectroscopic measurement of the van der Waals interaction between a single Rydberg atom and a gold cavity, which showed that a simple electrostatic model of the atom–cavity interaction is correct when the cavity is small enough. More recently, the retarded Casimir–Polder force was measured between a ground state sodium atom and a large cavity, demonstrating that the van der Waals potential fails at long enough range and that the vacuum fluctuations of the field then have an important role in the interaction of the atom with the cavity. Our group is now pushing forward these investigations to study cavities whose walls have losses and dispersion, where the theory of cavity QED is significantly more complicated. With real surfaces, we have to deal with the complex dielectric response ε(ω) of the material, which exhibits frequency–dependent absorption and dispersion. One particularly interesting case is when a downward transition in the atom is resonant with an excitation of the cavity walls. This opens a new branch for the atomic decay: as an alternative to creating a photon within the space surrounded by the cavity walls the atomic decay can now create an electromagnetic excitation of the walls themselves. Another novel feature of our experiments is that the Bohr frequencies of the atom are close to the kT/h, where T is room temperature. We therefore expect to be able to measure effects associated with QED at finite temperature; in other words, to study how the blackbody radiation affects our experiments. By conducting experiments with real surfaces, we hope to elucidate and perhaps simplify the theoretical models used to describe these systems.

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Spontaneous Emission in a Cylindrical Waveguide

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In this work we study the spontaneous emission of a two-level atom placed inside a hollow cylindrical waveguide of infinite length and with perfectly electric conducting walls. The atom, whose electric dipole moment is assumed to be oriented along the symmetry axis of the waveguide, couples to a photonic band structure with a non-linear dispersion relation. We address two different regimes of coupling between the atom and the photonic band structure. In particular, we refer to the regime where the internal frequency of the a.tom is close to a band edge as the strong coupling regime and to the regime where the internal frequency is far from a band edge as the weak coupling regime. In the weak coupling regime, we find that the a.tom decays exponentially with a modified decayed rate due to the presence of the waveguide, and that the line-shape of the emitted photons within every band takes the form of a Lorentzian. In the strong coupling regime, we find a non-exponential decay of the atom, which is due to non-Markovian dynamics of the system. Moreover, the population of the atom presents oscillations in time and it converges to a non-zero positive value, indicating that the a.tom never fully decays. In this regime the spectrum of the emitted photons becomes more involved.

•Jan 1, 2018•0 citations
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 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.
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 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.
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.
Over the past ten years, our group has investigated the effects of confinement on atoms inside metallic micron–sized cavities in order to elucidate some basic phenomena in the field of cavity quantum electrodynamics (QED). The first of these was the inhibition of spontaneous emission from an atom inside a cavity. This was followed by a laser spectroscopic measurement of the van der Waals interaction between a single Rydberg atom and a gold cavity, which showed that a simple electrostatic model of the atom–cavity interaction is correct when the cavity is small enough. More recently, the retarded Casimir–Polder force was measured between a ground state sodium atom and a large cavity, demonstrating that the van der Waals potential fails at long enough range and that the vacuum fluctuations of the field then have an important role in the interaction of the atom with the cavity. Our group is now pushing forward these investigations to study cavities whose walls have losses and dispersion, where the theory of cavity QED is significantly more complicated. With real surfaces, we have to deal with the complex dielectric response ε(ω) of the material, which exhibits frequency–dependent absorption and dispersion. One particularly interesting case is when a downward transition in the atom is resonant with an excitation of the cavity walls. This opens a new branch for the atomic decay: as an alternative to creating a photon within the space surrounded by the cavity walls the atomic decay can now create an electromagnetic excitation of the walls themselves. Another novel feature of our experiments is that the Bohr frequencies of the atom are close to the kT/h, where T is room temperature. We therefore expect to be able to measure effects associated with QED at finite temperature; in other words, to study how the blackbody radiation affects our experiments. By conducting experiments with real surfaces, we hope to elucidate and perhaps simplify the theoretical models used to describe these systems.
In this work we study the spontaneous emission of a two-level atom placed inside a hollow cylindrical waveguide of infinite length and with perfectly electric conducting walls. The atom, whose electric dipole moment is assumed to be oriented along the symmetry axis of the waveguide, couples to a photonic band structure with a non-linear dispersion relation. We address two different regimes of coupling between the atom and the photonic band structure. In particular, we refer to the regime where the internal frequency of the a.tom is close to a band edge as the strong coupling regime and to the regime where the internal frequency is far from a band edge as the weak coupling regime. In the weak coupling regime, we find that the a.tom decays exponentially with a modified decayed rate due to the presence of the waveguide, and that the line-shape of the emitted photons within every band takes the form of a Lorentzian. In the strong coupling regime, we find a non-exponential decay of the atom, which is due to non-Markovian dynamics of the system. Moreover, the population of the atom presents oscillations in time and it converges to a non-zero positive value, indicating that the a.tom never fully decays. In this regime the spectrum of the emitted photons becomes more involved.