Abstract

The phenomenon of “dark resonances” is a well-known concept in quantum optics and laser spectroscopy. As a general rule, interactions involving in such a “dark state” lead to multiple quantum superposition states that interact coherently and are undesirable. In this paper, two types nonlinear interaction in an atomic cavity, namely the nested and cascaded interactions, are theoretically analyzed how the dark resonances form the dark state peak to modulate the vacuum Rabi splitting (VRS) and optical bistability (OB) behavior. In both the zero- and high order modes, there are four VRS peaks generated in the nested interaction and three in the cascade interaction. Dark resonance can modulate not only the peak number of VRS, but also the OB thresholds. It is found that dark state can determine the asymmetric OB distribution of nested type and symmetric OB distribution of cascade type. Besides that, the distinctive OB thresholds in two kinds of interaction also be studied. The observations not only conceptually extend the conventional “dark resonances” phenomenon, but also opens the door for a variety of new applications in tunable all-optical switch and quantum communication.

Highlights

  • The phenomenon of “dark resonances” is a well-known concept in quantum optics and laser spectroscopy

  • Because the dark state plays an important role in the modulation of vacuum Rabi splitting (VRS) and optical bistability (OB), our research model can be applied to many areas which dark state are limited, such as data s­ torage[25, 26], slow ­light[27], and quantum t­eleportation[28, 29]

  • This study developed the type of interaction between laser and atom in a ring resonator, named as nested interaction and cascaded interaction, and studies the influence of these two nonlinear processes on VRS and OB

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Summary

Basic theory

The tunable FWM signals under different dressed effects are carried out in a cavity-atom coupled system. In order to understand how nonlinear interaction regulates FWM signal, two kinds of interaction named as nested type and cascaded type are coupled with energy level transition tion |3 → |1. Additional coupling fields (E2 and E5) are injected into the nonlinear medium to couple with transition energy levels |1 → |2 and |5 → |2 , respectively. Following this process, the nested dressed FWM signal is produced and shows in the energy level diagram of Fig. 1b.

Modulation of the dressed VRS
OB behaviors under VRS
Ioc Ii
Conclusion
Author contributions
Additional information
Full Text
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