The paper discusses three different modes of electromagnetic field generation by an ensemble of quantum emitters placed at the radiation wavelength in the one-dimensional case. The excitation of the resonator field is considered, which, as a rule, is determined by the geometry of the system, with and without taking into account the eigenfields of the emitters. The superradiance mode of the same ensemble of emitters is also analyzed. Since the main indicator of generation is the level of energy output from the system, the position of the maximum of this indicator determines the operating point of the device. Taking into account the intrinsic field of the emitters enhances the generation intensity and significantly changes the position of the operating point.
The paper discusses three different modes of electromagnetic field generation by an ensemble of oscillators placed at the radiation wavelength in the one-dimensional case. The excitation of the resonator field is considered, which, as a rule, is determined by the geometry of the system, with and without taking into account the eigenfields of the emitters. The superradiance regime of the same ensemble of oscillators is also analyzed. In fact, superradiance is formed due to the emitters' own fields even in the absence of a resonator. It is noted that the maximum achievable amplitudes of induced fields both in the superradiance regime and in the regime of excitation of the resonator field are comparable. This makes us think about the role of the self-fields of emitters in electronic devices. It is shown that in describing the resonator excitation mode, in addition to the resonator field, it is also necessary to take into account the sum of the natural fields of the emitters in the active zone. Synchronization of emitters leads not only to an increase in the resonator field, but also, as in the superradiance regime, it significantly increases the amplitude of the sum of the oscillator fields. It is shown that in the practically interesting case of open systems (dissipative generation modes), taking into account the eigenfields of the emitters significantly reduces the characteristic time for the development of the generation process and increases the maximum achievable oscillation amplitude. This account also changes the conditions for achieving the maximum energy flow from the system. This can change the operating point of the generation process, which is determined by the requirement for the maximum rate of energy output from the system.
The paper discusses the similarity between dissipative generation and superradiance regimes for systems of excited quantum emitters placed in an open cavity. In the case of the existence of a resonator field due to reflections from the ends of the system, a dissipative generation regime is usually realized. In this case, the decrement of oscillations in the waveguide in the absence of radiators turns out to be greater than the increment of the arising instability of the system of radiators placed in the resonator. When describing this mode, the influence of the emitters on each other and the sum of their own fields is neglected. The resonator field forces the oscillators to emit or absorb quanta synchronously with it, depending on the local value of the population inversion. Lasing takes on a weakly oscillatory character due to an asynchronous change in the population inversion of the system of emitting dipoles (nutations), which have a ground and excited energy levels. To describe the process, the equations of the semiclassical theory based on the use of the density matrix are quite sufficient. In the case when there is no resonator or waveguide field, taking into account the eigenfields of the oscillators becomes essential. To simulate the superradiance process, large emitting particles are used, to describe which one should use the equations for the density matrix. It is shown that the interaction of quantum emitters in this case is due to electromagnetic fields under conditions when the overlap of their wave functions is insignificant. Equations are obtained that allow considering the process of interaction of emitters. When the emitters interact, an integral field is formed in the resonator, an increase in the intensity of which leads to synchronization of the emitters. It is shown that the characteristic times of the development of the process, as well as the attainable amplitudes of the excited fields for dissipative regimes of generation and regimes of superradiance of emitters filling an open resonator, are comparable.
In order to study the cooperative emission of radiation from an extended system of
N two-level atoms, we use the master-equation approach within the Born and Markov approximations. All the properties of the emission of radiation can be deduced from the diagonalization of the coupling matrix $\ensuremath{\Gamma}$, where an element ${\ensuremath{\Gamma}}_{\mathrm{jk}}$ gives the coupling between the atoms labeled
j and
k via the electromagnetic field. We choose a pencil-shaped volume and study analytically the coupling matrix in the limit for small and large Fresnel numbers. For Fresnel numbers of order unity numerical methods are used. Thus we prove that, for the pencil-shaped geometry, any elaborated model must take into account the interaction of the atoms with the infinity of electromagnetic field modes lying inside two small solid angles about the axis of the largest linear dimension, which we label the
z axis. In other words, the intensity of radiation emitted by any atom of the system depends on its position with respect to the others and this "propagation effect" cannot be neglected when interpreting superradiance experiments. For small Fresnel numbers the
z dependence predominates, in the opposite case the (
x,y) dependence does, while for Fresnel numbers of order unity the dependence of all three components must be taken into account. Preliminary calculations are given for which only the
z dependence is considered; for Fresnel numbers of magnitude of order unity or smaller, the effect of propagation along the
z axis displays large delays for the appearance of superradiance with respect to the time at which the superradiant pulse is maximum when the "propagation effects" are neglected (one-mode model).
The problems of phase synchronization in an ensemble of oscillators or dipoles, and the mechanisms of coherent field generation in superradiance mode, are discussed. It is shown that an increase in the spread of the initial amplitudes of an ensemble of oscillators suppresses their phase synchronization and reduces the efficiency of field generation. The influence of noise is discussed; it is shown that, below the generation threshold, even an external initiating field cannot synchronize the phases of an ensemble of particles. When the generation threshold is exceeded, the initiating field may not be required. It is shown that the convergence of the oscillator phases with the field phases at the locations of moving oscillators is noticeable only near their exit from the system. At the same time, a complete coincidence of the phases of synchronized oscillators and the field phases in the region of their localization is not observed. Nevertheless, the intensity of the generation field in the superradiance mode significantly exceeds the spontaneous level, which allows us to speak about the signs of induced radiation. The features of the development of the quantum process of superradiance of an ensemble of dipoles are discussed, and a system of equations for its description is given. The features of the quantum analog of superradiance are qualitatively modeled, and the role of the Rabi frequency determining the dynamics of the population inversion is noted. The nutation of the population inversion in the region occupied by the field affect the field intensity not only in this local zone, but also in subsequent regions of the active zone. This explains the unusual nature of the generation development: the field growth in a certain region of the active zone first stabilizes and then decreases significantly. This decrease in intensity also occurs in the direction of radiation in the peripheral regions of the active zone, despite the large energy reserve in them in the form of unperturbed population inversion.
The interaction of light with nanoscale structures is at the core of nano-optics. As the structures become smaller and smaller the laws of quantum mechanics will become apparent. In this limit, the discrete nature of atomic states gives rise to resonant light-matter interactions. In atoms, molecules, and nanoparticles, such as semiconductor nanocrystals and other “quantum confined” systems, these resonances occur when the photon energy matches the energy difference of discrete internal (electronic) energy levels. Owing to the resonant character, light-matter interaction can often be approximated by treating these quantum emitters as effective two-level systems, i.e. by considering only those two (electronic) levels whose difference in energy is close to the interacting photon energy ħω 0 . In this chapter we discuss quantum emitters that are used in optical experiments. We will discuss their use as single-photon sources and analyze their photon statistics. While the radiative properties of quantum emitters have been discussed in Chapter 8, this chapter focuses on the properties of the quantum emitters themselves. We adopt a rather practical perspective since more detailed accounts can be found elsewhere (see e.g. [1–4]). Types of quantum emitters The possibility of detecting single quantum emitters optically relies mostly on the fact that redshifted emission can be very efficiently discriminated against excitation light [5, 6]. This opens the road for experiments in which the properties of these emitters are studied or in which they are used as discrete light sources.