Radiative Properties Of An Accelerated Atom In Interaction With The Derivative Of A Scalar Field In Minkowski Space-time

Mechanisms such as vacuum fluctuations, radiation reaction, or a combina-tion of them have been put forward to explain why spontaneous emission occurs.The ambiguity in physical interpretation arises from different choices of orderingof commuting operators of atom and field in a Heisenberg picture approach to theproblem. Significant progress has been made by Dalibard, Dupont-Roc, CohenTannoudji that there exists a symmetric operator ordering that the distinct con-tributions of vacuum fluctuations and radiation reaction to the rate of change ofan atomic observable are separately Hermitian. if one demands such an ordering,each contribution can possess an independent physical meaning. Such a procedureis generalized to the case of a small system S interacting with a large reservoir R,which is known as the formalism of DDC, and allows the separation of the twotypes of physical processes, those where R fluctuates and polarizes S (effects ofreservior fluctuations), those where S polarizes R (effects of self reaction).JÇ–rgen Audretsch and Rainer MÇ–ller have considered an atom in interactionwith a massless scalar quantum field. They have discussed the structure of therate of variation of the atomic energy for an arbitrary stationary motion of theatom through the quantum vacuum. Their main intention is to identify and toanalyze quantitatively the distinct contributions of vacuum fluctuations and radi-ation reaction to the spontaneous excitation of a uniformly accelerated atom inits ground state. This gives an understanding of the role of the different physicalprocesses underlying the Unruh effect. The atom's evolution into equilibrium forspontaneous excitation and spontaneous emission are calculated. Shizhuan Lu and Hongwei Yu have studied a two-level atom in interactionwith a real massless scalar quantum field in a spacetime with a reflecting boundary.The presence of the boundary modifies the quantum fluctuations of the scalar field,which in turn modifies the radiative properties of atoms. They have calculatedthe rate of change of the mean atomic energy for both inertial motion and uniformacceleration. It is found that the modifications induced by the presence of aboundary make the spontaneous radiation rate of an excited inertial atom oscillatenear the boundary and this oscillatory behavior may offer a possible opportunityfor experimental tests for geometrical (boundary) effects in flat spacetime. Whilefor accelerated atoms, the transitions from ground states to excited states arefound to be possible even in a vacuum due to changes in the vacuum fluctuationsinduced by both the presence of the boundary and acceleration of atoms, and thiscan be regarded as an actual physical process underlying the Unruh effect.JÇ–rgen Audretsch and Rainer MÇ–ller have also considered the influence of ac-celeration on the radiative energy shifts of atoms in Minkowski space. They havestudied a two-level atom coupled to a scalar quantum field. Using a Heisenberg pic-ture approach, they are able to separate the contributions of vacuum fluctuationsand radiation reaction to Lamb shift of the two-level atom. The resulting energyshifts for the special case of a uniformly accelerated atom are then compared withthose of an atom at rest.In this dissertation, we study the spontaneous excitation of an acceleratedmultilevel atom in dipole coupling to the derivative of a massless quantum scalarfield and separately calculate the contributions of the vacuum fluctuations andradiation reaction to the rate of change of the mean atomic energy of the atom. Itis found that, in contrast to the case where a monopole like interaction betweenthe atom and the field is assumed, there appear extra corrections proportional to the acceleration squared, in addition to corrections which can be viewed as aresult of an ambient thermal bath at the Unruh temperature, as compared withthe inertial case, and the acceleration induced correction terms show anisotropywith the contribution from longitudinal polarization being four times that from thetransverse polarization for isotropically polarized accelerated atoms. Our resultssuggest that the effect of acceleration on the rate of change of the mean atomicenergy is dependent not only on the quantum field to which the atom is coupled,but also on the type of the interaction even if the same scalar quantum field isconsidered.The presence of boundaries modifies the modes of quantum fields, which mayin turn modifies the spontaneous excitation rate of accelerated atoms in interactionwith these fields. We study the effect of the presence of a reflecting boundary onthe spontaneous excitation of a uniformly accelerated polarized multilevel atominteracting with quantum scalar fields in a dipole-derivative coupling scheme. Weseparately calculate the contributions of modified vacuum fluctuations and theradiation reaction to the spontaneous excitation rate of the atom. Our results showthat the presence of the boundary modulates the excitation rate and makes it afunction of the atom's distance from the boundary. When the atom is placed closerand closer to the boundary, the influence of the boundary becomes more and moredrastic, with the contribution of the atom's polarization in the direction parallelto the boundary to the spontaneous excitation rate dramatically suppressed whilethat in the normal direction greatly enhanced.We study the energy level shifts of an accelerated multilevel atom in dipolecoupling to the derivative of a quantum massless scalar field and separately calcu-late the contributions of vacuum fluctuations and radiation reaction to the shifts.We find that, in contrast to the case of a monopole like interaction, both the vac- uum fluctuations and radiation reaction contributions are altered by acceleration,and they all contain non-thermal correction terms, our results suggest that the ef-fect of acceleration on the energy shifts is dependent on the type of the interactionbetween the atom and the quantum field.The paper is organized as follows. We present a review of the formalism ofDDC in Chapter 1, and that of the works by others using the formalism of DDCon the spontaneous excitation and energy shifts of a two-level atom coupled toa scalar field in Chapter 2. Chapters 3-5 describe our work: the applications ofthe DDC formalism to discuss the spontaneous excitation and energy shifts of amultilevel accelerated atom interacting with the derivative of a scalar field. InChapter 6 we give a brief summary of our work and an outlook for possible futureresearch.