Abstract
In the present article, we investigate the behavior of a large collection of three-level atoms interacting with two quantized electromagnetic fields inside a second-order nonlinear quantum cavity. The nonlinearity of the cavity is supposed to be activated by the application of two classical pump fields. The total Hamiltonian of the combination, with due attention to the nonlinearity effects, is diagonalized. The corresponding ground-state energy then follows from minimizing the total Hamiltonian. The structure of the ground state indicates that four distinct optical phases can occur in such a system. These possible phases turn out to be trivial, dark, left-arm and right-arm superradiant ones. Conditions under which any of the four optical phases can actually occur are also analyzed and discussed. The analysis of the conditions, accompanied by several figures, then reveals that with a suitable choice of the pump field amplitudes and/or geometrical phases, one can intensify the two superradiant phases drastically. Moreover, we demonstrate that the dark optical phase cannot occur at all, while the trivial and superradiant ones can, in fact, coexist. Our calculations also show that transition from the trivial phase to left-arm (right-arm) superradiant one is continuous (discrete) and second (first) order in nature. Another important result of our investigation is that by adjusting the pump field strength, one can switch from the left-arm superradiant phase to the right-arm one and vice versa. This point, in turn, provides an alternative mechanism for the development of quantum optical switching devices.
- Received 12 October 2021
- Accepted 19 April 2022
DOI:https://doi.org/10.1103/PhysRevA.105.053702
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