ABSTRACT We consider the radiation properties and processes of a gas with a population inversion using the formalism based on the Maxwell–Bloch equations. We focus on the maser action and Dicke’s superradiance to establish their relationship in the overall radiation process during the temporal evolution of the system as a function of position. We show that the maser action and superradiance are not competing phenomena but are rather complementary and define two distinct limits for the intensity of radiation. Masers characterize the quasi-steady state limit, when the population inversion density and the polarization amplitude vary on time-scales longer than those of non-coherent processes affecting their evolution (e.g. collisions), while superradiance defines the fast transient regime taking place when these conditions are reversed. We show how a transition from a maser regime to superradiance will take place whenever a critical threshold for the column density of the population inversion is reached, at which point a strong level of coherence is established in the system and a powerful burst of radiation can ensue during the transient regime. This critical level also determines the spatial region where a transition from the unsaturated to the saturated maser regimes will take place; superradiance can thus be seen as the intermediary between the two. We also quantify the gain in radiation intensity attained during the superradiance phase relative to the two maser regimes and show how the strong coherence level during superradiance is well suited to explain observations that reveal intense and fast radiation flares in maser-hosting regions.ABSTRACT We consider the radiation properties and processes of a gas with a population inversion using the formalism based on the Maxwell–Bloch equations. We focus on the maser action and Dicke’s superradiance to establish their relationship in the overall radiation process during the temporal evolution of the system as a function of position. We show that the maser action and superradiance are not competing phenomena but are rather complementary and define two distinct limits for the intensity of radiation. Masers characterize the quasi-steady state limit, when the population inversion density and the polarization amplitude vary on time-scales longer than those of non-coherent processes affecting their evolution (e.g. collisions), while superradiance defines the fast transient regime taking place when these conditions are reversed. We show how a transition from a maser regime to superradiance will take place whenever a critical threshold for the column density of the population inversion is reached, at which point a strong level of coherence is established in the system and a powerful burst of radiation can ensue during the transient regime. This critical level also determines the spatial region where a transition from the unsaturated to the saturated maser regimes will take place; superradiance can thus be seen as the intermediary between the two. We also quantify the gain in radiation intensity attained during the superradiance phase relative to the two maser regimes and show how the strong coherence level during superradiance is well suited to explain observations that reveal intense and fast radiation flares in maser-hosting regions.

arXiv:2004.07327Monthly Notices of the Royal Astronomical SocietyApr 23, 202010 citations

Quantum phase transition in the generalized single-mode superradiant model

G. Chen, Z.-D. Chen, Pei-cai Xuan

The European Physical Journal DMay 17, 20062 citations

Phase transition in a generalized Dicke model of superradiance

B. M. Pimentel, Abraham Hirsz Zimerman

Physics Letters AJun 1, 197513 citations

Equivalence of the Dicke Maser Model and the Ising Model at Equilibrium

R. W. Gibberd

The equilibrium properties of a system of N two-level atoms interacting with a quantized field, the so-called Dicke model of superradiance, are evaluated exactly by the 'thermodynamically equivalent Hamiltonian' method of Bogoliubov et at. (1957). The results are identical with those obtained by Hepp and Lieb (1973) and Wang and Hioe (1973). The thermodynamically equivalent Hamiltonian is shown to be equivalent to the mean field Hamiltonian of the Ising model, which indicates why the transition from the 'normal' to the 'superradiant' state of the Dicke model is similar to the transition from the disordered to the ordered state of the Ising model.The equilibrium properties of a system of N two-level atoms interacting with a quantized field, the so-called Dicke model of superradiance, are evaluated exactly by the 'thermodynamically equivalent Hamiltonian' method of Bogoliubov et at. (1957). The results are identical with those obtained by Hepp and Lieb (1973) and Wang and Hioe (1973). The thermodynamically equivalent Hamiltonian is shown to be equivalent to the mean field Hamiltonian of the Ising model, which indicates why the transition from the 'normal' to the 'superradiant' state of the Dicke model is similar to the transition from the disordered to the ordered state of the Ising model.

Australian Journal of PhysicsApr 1, 197417 citations

Recent theoretical advances on superradiant phase transitions

Alexandre Baksic, Pierre Nataf, Cristiano Ciuti

Bulletin of the American Physical SocietyMar 21, 20130 citations

Phase Transition in the Dicke Model of Superradiance

Y. K. Wang, F. T. Hioe

A system of $N$ two-level atoms interacting with a quantized field, the so-called Dicke model of superradiance, is studied. By making use of a set of Glauber's coherent states for the field, the free energy of the system is calculated exactly in the thermodynamic limit. The results agree precisely with those obtained by Hepp and Lieb, who studied the same model using a different method. The exhibition of a phase transition of the system is presented mathematically in an elementary manner in our approach. The generalization to the case of finitely many radiation modes is also presented.A system of $N$ two-level atoms interacting with a quantized field, the so-called Dicke model of superradiance, is studied. By making use of a set of Glauber's coherent states for the field, the free energy of the system is calculated exactly in the thermodynamic limit. The results agree precisely with those obtained by Hepp and Lieb, who studied the same model using a different method. The exhibition of a phase transition of the system is presented mathematically in an elementary manner in our approach. The generalization to the case of finitely many radiation modes is also presented.

Physical Review AMar 1, 1973745 citations

A system of

N

two-level atoms interacting with a quantized field, the so-called Dicke model of superradiance, is studied. By making use of a set of Glauber's coherent states for the field, the free energy of the system is calculated exactly in the thermodynamic limit. The results agree precisely with those obtained by Hepp and Lieb, who studied the same model using a different method. The exhibition of a phase transition of the system is presented mathematically in an elementary manner in our approach. The generalization to the case of finitely many radiation modes is also presented.