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Europhysics Letters (EPL)

Virtual Field, Causal Photon Absorption and Photodetectors

Giuseppe Compagno, G. Massimo Palma, Roberto Passante, Franco Persico

Published Jun 1, 1989• 38 citations
Publisher

Abstract

The time-dependent electric-energy density surrounding a two-level atom fixed at r = 0 is studied, the atom being taken in its ground state at t = 0 and the field having initially only one photon in a delocalized mode. The atom-field coupling includes both rotating and counterrotating terms. The energy density in the rotating wave approximation is shown to behave noncausally, while in the presence of the complete coupling it is shown to be affected only within a sphere of radius r = ct centred on the atom. It is concluded that the counterrotating terms in the atom-field coupling are essential in order to ensure causality and cannot be neglected in any accurate treatment of photon absorption. Some consequences of this conclusion on the operation of photodetectors in one-photon absorption are discussed.

DOI
10.1209/0295-5075/9/3/005

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The time-dependent electric-energy density surrounding a two-level atom fixed at r = 0 is studied, the atom being taken in its ground state at t = 0 and the field having initially only one photon in a delocalized mode. The atom-field coupling includes both rotating and counterrotating terms. The energy density in the rotating wave approximation is shown to behave noncausally, while in the presence of the complete coupling it is shown to be affected only within a sphere of radius r = ct centred on the atom. It is concluded that the counterrotating terms in the atom-field coupling are essential in order to ensure causality and cannot be neglected in any accurate treatment of photon absorption. Some consequences of this conclusion on the operation of photodetectors in one-photon absorption are discussed.
The time-dependent electric energy density surrounding a two-level atom fixed at r = 0 is studied, the atom being taken in its excited state at t = 0 and the field being initially in the vacuum state. The atom-field coupling includes both rotating and counter-rotating terms. The energy density of the spontaneously emitted field in the rotating wave approximation is shown to behave non-causally, while in the presence of the complete coupling it is shown to vanish outside a sphere of radius r = ct centred on the atom. The deviations of atomic dynamics from the exponential Wigner-Weisskopf behaviour during spontaneous decay are shown to be deeply influenced by the counter-rotating terms. It is concluded that the virtual photons induced by the counter-rotating terms in the atom-field coupling are essential in order to ensure causality and cannot be neglected in any accurate treatment of spontaneous emission.
In this paper, we investigate the time evolution of the atomic operators of a two-level atom interacting with the field via a two-photon process within and without the rotating-wave approximation (RWA) by means of non-relativestic QED. We also verified that the virtual photon field is the cause for quantum chaos embodied by the periodic decay and revival effect of the atom using the numerical and analytic methods, and discussed the reason of neglecting the in-fluence of the virtual photon field on the revival time.
The problem of a single two level atom in its excited state, placed in a cavity in which no photons are present initially, and interacting with N modes of the electromagnetic field is solved exactly in the electric dipole, rotating wave approximation. Expressions for the energy eigenvalues and eigenvectors are derived, and an exact representation for the time dependent wavefunction of the system is given. These quantities are evaluated analytically for N=1,2 and 3, and the time dependent properties of the system for these values of N are investigated and discussed.
The dynamics of an initially bare pair of two-level atoms at distance R is investigated. The pair is coupled to the vacuum radiation field in the multipolar scheme and in the dipole approximation. The Heisenberg equations of motion for various atomic operators are obtained neglecting terms O(e3{\mathit{e}}^{3}e3) and for t smaller than the spontaneous relaxation time. A rigorous proof of causality in the atom-atom interaction is given. Interatomic correlations, however, are shown to develop for tR/c. This early development is shown to be compatible with the principle of relativistic causality, and to be related to the peculiar form of the vacuum zero-point fluctuations. The techniques adopted are applied to study dynamics and correlations of a superradiant state.
Atom-laser interaction is at the heart of the vibrant field of quantum optics. The dynamical properties of a moving atom submitted to a laser radiation are strongly \ninfluenced by the position- and time-dependence of the latter. The full physical state of the atom must include information about the centre-of-mass motion and the internal structure of the atom. It is challenging to obtain a complete description of the full state of the atom. However, there exists an alternative approach to the dynamics of an atom in the presence of a laser, which is based on the concept of matter-wave absorption. \n \nIn this thesis, we theoretically study the nonrelativistic one-dimensional motion of an electrically neutral quantum particle in the presence of a thin time-dependent absorber, representing the laser radiation. Our aim is to better understand the precise connection between time-dependent matter-wave absorption and the interaction between an atom and a localised time-dependent laser. \n \nOur analysis is based on two different approaches to the problem. The first one describes the moving atom by a two-level system, and represents the laser radiation \nby an off-diagonal δ-potential. The second model treats the atom as a structureless particle, and describes the laser by a time-dependent absorbing barrier. While the \nformer model can be derived from first principles, the treatment of the absorbing barrier in the latter model lacks a rigorous quantum mechanical justification. The \nmain outcome of our work is to provide a solid physical ground for the absorber model, by explicitly connecting it to the δ-potential model. We have thus extended \nthe range of theoretical tools useful for investigating the effects of time-dependent laser radiation on quantum matter.
The aim of this study is to investigate dynamical properties of a two-mode f-deformed cavity- field ‎coupled to an effective two-level atom with and without the rotating wave approximation. The first ‎section discusses the theoretical model of the interaction between a two-mode cavity-field and an ‎effective two-level atom within the framework of an f-DJCM without the rotating wave ‎approximation. After that, we obtain the reduced density matrix of the cavity-field with and without ‎the rotating-wave approximation. Then, we have investigated the effect of the counter-rotating ‎terms on temporal evolution of various non-classical properties of the cavity-field, i.e., photon-‎counting statistics, the cross correlation between the modes of the field, and the quantum ‎fluctuations of the quadrature components. Particularly, we compare the numerical result for three ‎different values of the deformation parameter q (q=1, q=1.1, q=0.9) with and without applying the rotating ‎wave approximation. By using of the numerical method, we concluded that even under the ‎condition in which the RWA is considered to be valid, there are the significant effects of virtual-‎photon field on the photon-counting statistics, the cross correlation between the modes of the ‎field, and the quantum fluctuations of the quadrature components‎.