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So the collapse happens at a time on the order of II 9 [34, 178]. They occur because of the noise in the field, which leads to the finite variance of the photon

12It will become evident later that for this to be true. the cavity decay constant K. has to be at least much smaller than 9 / v'fi. where n is the average number of photons in the cavity mode.

liabilities are those that must be paid within one year. Long-term liabilities are debts your company will take more than one year to pay off. Examples of current liabilities include accounts payable to vendors and income, payroll, and sales taxes. Long-term liabilities include obligations such as a property mortgage, a long-term loan, or a major equipment lease. Liabilities can also include an obligation to provide goods or services. For example, receipt of payment in advance may give rise to a corresponding liability on the part of your company. Figure 4-5 shows the liability section of Larry s Landscaping s Balance Sheet.

1980 1985 1990 1995 2000

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number, causing the eventual dephasing of the various cosine terms in (6.92). This noise is of quantum origin here, but classical noise would be equally effective. Expression (6.95) is valid only for times much smaller than 10'1/ g. In fact, we notice by inspecting (6.93) that the destructive interference disappears when the oscillating complex exponential argument of the exponential function in (6.93) becomes unit again. So a revival of the oscillations should occur at (6.96) Although it is possible to recover the collapse of the oscillations in a calculation using a classical field with classical noise, the revival is a genuine quantum effect. Revivals can only take place because the field energy is discrete rather than continuous, so that the various cosine components of the oscillations can eventually come back in phase with each other. The recent observation of revivals [153, 517] provided more evidence of the quantum nature of the electromagnetic interaction. In this chapter we have applied QED to the problem of spontaneous emission by a single atom in the vacuum. We have seen that a cavity can make spontaneous emission become reversible, leading to Rabi oscillations. In 7 we study how QED can be modified to account for material media similar to the process in classical electrodynamics: through a dielectric permittivity.

RECOMMENDED READING For a discussion of atomic stability where coupling with the radiation field is neglected and only the Coulomb potential is considered, see [175, 177, 409. 575]. There are several approximations and assumptions in the Weisskopf-Wigner approach. For a detailed study of these and alternative improvements on the original Weisskopf- Wigner theory. see [7, 144, 360, 555]. For a discussion of renormalization in the context of atomic physics, I refer the reader to Weisskopf [630], Welton [632], Dalibard et al. [131], and Haroche [274]. For a thorough discussion of the two-level atom approximation, see Allen and Eberly [13].

Figure 4-5: The liabilities section of the Balance Sheet is divided into current and long-term liabilities to distinguish between obligations that must be met within one year of the reporting date and those that will be met in more than one year.

Cavity Quantum Electrodynamics: The Strange Theory of Light in a Box Sergio M. Dutra Copyright 2005 John Wiley & Sons, Inc.

gross domestic product (GDP), G-8 countries, 1981 2000.

... zu jener Zeit ... elektrische bezw. magnetische "Feldstiirken" und "Verschiebungen" wurden als gleich element are Grossen behandelt, der leere Raum als Spezialfall eines dielektrischen Korpers. Die Materie erschien als Thliger des Feldes, nicht der Raum .... Es war das grosse Verdienst von H. A. Lorentz, dass er hier in iiberzeugender Weise Wandel schur. 1m Prinzip gibt es nach ihm ein Feld nur im leeren Raume. Die atomistisch gedachte Materie ist einziger Sitz der elektrischen Ladungenj zwischen den materiellen Teilchen ist leerer Raum, der Sitz des elektromagnetischen Feldes ... Dielektrizitat, Leitungsfahigkeit, etc. sind ausschliesslich durch die Art der mechanischen Bindung der Teilchen bedingt, aus welchen die Korper bestehen. 1 -Albert Einstein [184]

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