Exceptional points as lasing pre-thresholds in open-cavity lasers

Recently, the dynamics of non-Hermitian systems composed of subsystems has attracted much attention because they may have exceptional points (EPs). Until now, EPs have been connected with the transition from weak to strong coupling between the subsystems. We show that an ensemble of pumped atoms weakly coupled with a resonator has an EP at a certain pump rate. Moreover, even without a resonator, such a system may have an EP. At the EP pump rate, two eigenfrequencies coalesce, and a special mode arises. At the EP, the dynamics of the eigenfrequencies changes dramatically. Below the EP pump rate, all the eigenfrequencies of the system have negative imaginary parts, which absolute values decrease with an increase in the pump rate. Above the EP pump rate, the absolute value of the imaginary part of the eigenfrequency of the special mode continues decreasing, while the absolute values of the imaginary parts of all other eigenfrequencies increase. Consequently, most of the stimulated emission occurs into the special mode, leading to lasing when the pump rate reaches the laser threshold. We, therefore, refer to the pump rate corresponding to the EP as a lasing pre-threshold. We demonstrate that EPs and lasing pre-thresholds occur in systems with and without resonators.