We show that a quantum-beat system with incoherent pump or coherent driving produces an entangled sub-shot-noise laser that operates well above threshold. The numerical results and physical analyses are presented using the combination modes of the lasing fields. The relative mode is decoupled from the active medium and thus remains in its vacuum state, while the sum mode operates well above threshold and has sub-shot-noise. The quantum beat and the sum mode intensity noise reduction combine to yield entanglement between two bright beams and sub-Poissonian photon statistics of the respective beams.
We study the dependence of absorption and dispersion spectra on amplitudes and phases of the driving fields in multiple electromagnetically induced transparency. For this purpose we consider trichromatic excitation in a three-level Λ atomic system, in which a trichromatic control laser and a monochromatic probe laser are applied to two different transitions, respectively. We numerically calculate the absorption and dispersion spectra. Two characteristic features are found. Firstly, the central transparency can be made to appear or to disappear by utilizing the amplitudes and phases of the driving components. Secondly, so long as we fix the sum of two relative phases of two sideband excitation components to the central component, the absorption and dispersion spectra keep their own lineshapes unchanged no matter how we vary the respective relative phases.
We study the absorption and dispersion in the near-degenerate closed three-level V system, in which a single coherent driving field is tuned resonant with the average frequency of two dipole-allowed transitions. Firstly, the switching from positive to negative dispersion can be achieved simply by increasing the driving field intensity. This is the same as in the driven Λ system. Secondly, the common feature originates from the fact that both V and Λ systems have the same transitions in terms of atomic dressed states under given conditions. These dressed transitions interfere destructively in the central spectrum while the sideband resonance transitions determine the possible appearance of two pairs of absorption doublet lines and two pairs of gain doublet lines in the sideband spectrum. Thirdly, there are two minor differences between these two systems. For large driving field intensity, a narrow steep structure is always present in the central negative dispersion spectrum in the V system but it disappears in the Λ system. The driving field intensity for the appearance of the outer sideband absorption or gain peaks is larger in the V system than in the Λ system.
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