Electromagnetic Field Induced Modification of Branching Ratios for Emission in Structured Vacuum

We report a fundamental effect of the electromagnetic field induced modification of the branching ratios for emission into several final states. The modifications are especially significant if the vacuum into which the atom is radiating has a finite spectral width comparable with the separation of the final states. This is easily realizable in cavity QED. Further our results are quite generic and are applicable to any system interacting with a structured reservoir. PACS numbers: 03.65.-w,42.50.Pq,42.50.Ct Electromagnetic Field Induced Modification of Branching Ratios for Emission in Structured Vacuum2 Mollow discovered in 1969 how the spectral characteristics of the radiation emitted by a system are modified quite significantly due to a coherent field driving the system [1]. Such spectral modifications have been the subject of extensive experimental and theoretical studies [2] and were explained neatly in terms of the dressed state picture [3]. The work of Mollow was extended to the case of emission in a cavity [4, 5]. It was further found specially in the context of multilevel systems that the driving fields can produce well defined interference minimum in the spectrum [6, 7, 8, 9]. Such minimum is usually interpreted in terms of the interferences produced by different dressed state emissions. Very often this interferences is also referred to as the quenching of spontaneous emission [10]. A related question is– what is the effect of driving fields on branching ratios in emission to multiple states. In a different class of experiments Suckewer and co-workers [11] found definite evidence of external field induced changes in branching ratios. Their experimental finding has been rather difficult to explain due to complicated nature of the laser plasma used in the experiment. It is therefore desirable to look for simpler systems where one can analyze how external fields could affect branching ratios. In this paper we analyze a cavity QED system to highlight the field induced modification of the branching ratios. In view of the enormous progress made in the context of cavity QED [12, 13, 14] such findings are within the reach of present experiments. Our analysis also suggests that change in the branching ratios are notable if one works in a regime where separation between the two final states is more than the width of the vacuum into which the system is radiating. Thus some of the dispersive effects are also important. These conditions are easy to satisfy in the context of cavity QED systems. Clearly if the spectral width of the vacuum is very large as in free space then one would not expect any significant change in branching ratios. Although the results that we present are specifically in the context of QED, they can be generally applicable to a much wider class of systems. For example we can consider the interaction of any system with a structured reservoir of finite width [15, 16, 17, 18]. Further the analysis would also be applicable to nano environments which lead to significant spectral modifications [19].