Collective phenomena in strongly nonequilibrium systems interacting with electromagnetic field are considered. Such systems are described by complicated nonlinear differential or integro-differential equations. The aim of this review is to show that many nonlinear collective phenomena can be successfully treated by a recently developed method called the Scale Separation Approach whose name is due to the idea of separating different characteristic space-time scales existing in nonequilibrium statistical systems. This approach is rather general and can be applied to various nonequilibrium physical problems, several of which are discussed here. The problems considered not only serve as illustrations of the method but are quite important by themselves presenting interesting physical effects, such as Collective Liberation of Light, Turbulent Photon Filamentation, Superradiant Spin Relaxation, Negative Electric Current, and Magnetic Semiconfinement of Atoms.
Collective phenomena in strongly nonequilibrium systems interacting with electromagnetic field are considered. Such systems are described by complicated nonlinear differential or integro-differential equations. The aim of this review is to show that many nonlinear collective phenomena can be successfully treated by a recently developed method called the Scale Separation Approach whose name is due to the idea of separating different characteristic space-time scales existing in nonequilibrium statistical systems. This approach is rather general and can be applied to various nonequilibrium physical problems, several of which are discussed here. The problems considered not only serve as illustrations of the method but are quite important by themselves presenting interesting physical effects, such as Collective Liberation of Light, Turbulent Photon Filamentation, Superradiant Spin Relaxation, Negative Electric Current, and Magnetic Semiconfinement of Atoms.
The aim of this communication is to present in a concentrated form the main ideas of a method, developed by the author, for treating strongly nonequilibrium collective phenomena typical of the interaction of radiation with matter, as well as to give a survey of several applications of the method. The latter is called the Scale Separation Approach since its basic techniques rely on the possibility of separating different space-time scales in nonequilibrium statistical systems. This approach is rather general and can be applied to diverse physical problems, several of which are discussed here. These problems are: Superradiance of nuclear spins, filamentation in resonant media, semiconfinement of neutral atoms, negative electric current, and collective liberation of light.
Nonlinear systems are well known to exhibit many interesting and important phenomena that have profoundly changed our technological landscape over the last century. Recently our developments in quantum technologies has given us the ability to engineer systems through with no natural analog. We are now at the stage where we can explore nonlinear effect in quantum hybrid systems. In this presentation, we illustrate how these nonlinear effects allow the exploration of novel effects such as superradiance induced negative temperature relaxation.
In the previous chapter we studied the interaction between a single two-level atom and the electromagnetic field, both when the field is treated classically and when it is quantized. We encountered some interesting phenomena such as Rabi oscillations, the a.c. Stark effect, and photon antibunching, all of which have been observed. These phenomena are essentially single-atom effects, in the sense that either they require a single atom for the effect to be observed, as in the last case, or at least they do not require more than one, although a group of atoms may be used in practice. In this chapter we shall turn to a discussion of some effects that depend in an essential way on the presence of a group of atoms. In some cases we shall find that the group or collective behavior of the atomic system is relatively trivial, in the sense that we can account for the phenomenon by summing the contributions of the individual atoms to the total field, and treating each of them as if it acts almost independently of the others. This is the situation in free induction decay and in the photon echo . In other cases it is essential to include the effect of each atom on all the other atoms, because this modifies the behavior of each in a significant way. These phenomena, such as self-induced transparency and superradiance , are collective effects in a deeper sense. They are sometimes called cooperative effects .
When atoms are coupled to a common electromagnetic environment, the exchange of photons through dipole-dipole interactions leads to the emergence of cooperative effects. As a particular example, superradiance arises from spontaneous emission when this exchange leads to constructive interference of the emitted photons. Here, we introduce an integrated method for studying cooperative radiation in many-body systems. This method, which allows to study extended systems with arbitrarily large number of particles, can be formulated by an effective, nonlinear, two-atom master equation that describes the dynamics using a closed form which treats single- and many-body terms on an equal footing. We apply this method to a homogeneous gas of initially inverted two-level atoms, and demonstrate the appearance of both superradiance and subradiance, identifying a many-body coherence term as the source of these cooperative effects. We describe the many-body induced broadening -- which is analytically found to scale with the optical depth of the system -- and light shifts, and distinguish spontaneous effects from induced ones. In addition, we theoretically predict the time-dependence of subradiance, and the phase change of the radiated field during the cooperative decay.
The aim of this review is twofold. Firstly, a general approach is presented which can provide a unified description of the dynamics of radiating systems of different natures. Both atomic systems and spin assemblies can be treated within the same mathematical method, which is based on a pseudospin (or spin) representation of the evolution equations. The approach is applicable to all stages of radiation dynamics, including the most difficult initial quantum stage, where coherence is not yet developed. This makes it possible to study the process of coherent self-organization from the chaotic quantum stage. Secondly, the approach is illustrated by applying it to the description of several coherent phenomena. Different types of superradiance are characterized: pure superradiance, triggered superradiance, pulsing and punctuated superradiance. The theory of such interesting effects as triggering dipolar waves, turbulent photon filamentation, collective liberation of light, pseudospin atomic squeezing, and operator entanglement production is presented.
In recent years, the study of quantum electrodynamics (QED) in light-matter interactions has discovered various interesting phenomenons that orient many applications. However, due to the ambient entanglement among photons and atoms, few-particle dynamics remains challenging to analyze precisely and limits the progress in several fields. In few-particle systems, different number of atoms interacting with the light field generates drastically different results, even when there is only a single photon involved in the system. The interference between individual atom’s spontaneous emission wavefunctions can cooperatively alter the effective atom-light coupling strength. Depending on the spatial distance between individual of atoms and the involved cavities in the interaction progresses, the collective spontaneous emission rate can alter drastically from superradiance, where the emission rate is enhanced to a high value proportional to the atom number, to subradiance, where the excited atom ensemble stays in a dark state with the light trapped forever. Superradiance provides a promising mechanism to create an ultra-strong light-matter coupling environment, which is an important ingredient for the design of ultra-fast optical devices, frequency comb generation and quantum mirrors. The dark state of subradiance, on the other hand, is essential for the quantum memory implementation. Also, nontrivial phenomenons also occur when multiple photons interacting with a single atom simultaneously. When a finite number of photons incidents on an atom, their scattering through an atom is highly nonlinear, and one special eigenstate component of such nonlinear process, namely photonic bound states, exhibits many interesting properties in nonlinear quantum optical systems. The photons in such state are strongly bunched with each other, as if a virtual attractive force is in effect. Also, the frequency of photons are anti-correlated so that their total frequency remains a constant value, no matter how arbitrary the frequency of any individual is. Thesefeatures benefit certain nonlinear quantum processes for quantum computing and quantum imaging. Specially for two-photon excitation imaging, the same-parity two-level fluorophore molecules suffers from extremely low excitation efficiencies due to the far off-resonant intermediate states. However, by replacing the current commonly used ultrashort laser pulse illuminations with two photon bound state photon pairs, namely photonic dimers, the efficiency can be enhanced to orders of magnitude higher. Such exceptionally high excitation efficiency can potentially bring the current in vivo deep brain imaging depth from millimeter level to several centimeters. To obtain a stable source of such photonic dimers, it is found that a laser structure with gain medium of two-photon emission materials is capable of generating the coherent state of photonic dimer and can serve as a promising light source for nonlinear quantum optical devices.