Excitation of electromagnetic waves in a waveguide with a medium, which is a two-level system, is considered. To describe the processes, both classical electrodynamics methods and quantum mechanics methods are used. The nature of the processes under study turns out to depend on the relationship between the Rabi frequency and the line width of the excited wave packet. It is shown that if the field energy density is high, then spatially inhomogeneous Rabi frequencies arise, which leads to oscillatory behavior of the wave field amplitudes. If the levels of the excited field are small, then the dynamics of the two-level quantum system becomes monotonic and the population inversion tends to zero.
Excitation of electromagnetic waves in a waveguide with a medium, which is a two-level system, is considered. To describe the processes, both classical electrodynamics methods and quantum mechanics methods are used. The nature of the processes under study turns out to depend on the relationship between the Rabi frequency and the line width of the excited wave packet. It is shown that if the field energy density is high, then spatially inhomogeneous Rabi frequencies arise, which leads to oscillatory behavior of the wave field amplitudes. If the levels of the excited field are small, then the dynamics of the two-level quantum system becomes monotonic and the population inversion tends to zero.
In the article, for limited system conditions that form the spatial structure of the field, the attenuation processes of wave packets of finite amplitude are considered. The line width of the wave field may be the result of the dissipative processes (in a quantum system it is inverse of the lifetime of energy levels) or the result of reactive processes (in classical waveguide systems this is the spectral width of the packet). In the case of filling the waveguide with an active two-level medium, a description is possible using a quasiclassical model of the interaction of the field and particles. In this case, the quantum-mechanical description of the medium is combined with the classical representation of the field. Here, the Rabi frequency plays an important role, which determines the probabilities of induced radiation or absorption of field quanta and the oscillatory change in population inversion (nutation). Depending on the relationship between the Rabi frequency and the line width of the wave packet, the process can change the nature of the field behavior. In strong fields or with a significant population inversion, the line width can be neglected, while the field energy density is quite high. In this case, one should expect noticeable nutations of population inversions with different frequencies corresponding to the local Rabi frequency in different regions of the waveguide, the interference of which will determine the oscillatory behavior of the wave field. At a low level of electric field intensity or a slight population inversion, the mode of changing the field amplitude becomes monotonic. Plasma field damping (Landau damping) is considered. The role of population inversion is assumed by a quantity proportional to the derivative with respect to velocity of the electron distribution function. If the spectral width of the packet is small, the process of wave attenuation acquires a characteristic oscillatory form due to the exchange of energy between the wave and the plasma electrons captured by its field. The attenuation of wide packets is almost monotonic with the formation of a characteristic “plateau” in the vicinity of the phase velocity of the wave on the electron velocity distribution function.
The work based on a semiclassical description, presents the results of studying the processes of absorption and radiation of a field in the form of a standing wave in a waveguide filled with a two-level active medium. Under conditions of spatial inhomogeneity of the field intensity, interference of quasi-periodic oscillations of population inversion occurs in different local regions of the waveguide. A quasiperiodic change in population inversion is determined by the Rabi frequency, which is known to be associated with the probability of induced radiation with a positive population inversion, or induced absorption with its negative value. Since the population inversion change is accompanied by absorption or emission of field quanta, this leads to the exchange of energy between the field and the active medium located in the waveguide. It is shown that the attenuation of a large-amplitude field to a waveguide filled with an unexcited active medium is nonlinear. In the developed mode, this process has the character of energy exchange between the field and the active medium. In this case, the wave attenuation is replaced by its growth, just as it happens in the well-known case of Landau kinetic damping. Competition of the processes of radiation and absorption leads to the fact that the nature of the oscillations (nutations) of the population inversion at different points of the waveguide space is different. The interference of nonsynchronous spatially localized oscillations of the population inversion in the volume of the waveguide leads to changes in the field amplitude. The paper also discusses the process of field excitation in a waveguide with a pre-inverted two-level active medium, taking into account external mechanisms for the absorption of wave energy. Consideration of these problems is important for understanding the processes of generation of induced radiation, which, as noted by C. Towns, is to a large extent coherent radiation.
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.
It is shown that the population Rabi oscillations in a lossless two-level atom, interacting with a monochromatic electromagnetic field, in general, are convergent in time. The well-known continuous oscillations take place because the restricted choosing of initial conditions, that is, when the atom is chosen on ground or excited level before the interaction, simultaneously having a definite value of momentum there. The convergence of Rabi oscillations in atomic wave-packet states is a direct consequence of the Doppler effect on optical transition rates (Rabi frequencies): it gradually leads to ``irregular'' chaotic-type distributions of momentum in ground and excited energy levels, smearing the amplitudes of Rabi oscillations. Conjointly with Rabi oscillations, the coherent accumulation of momentum on each internal energy level monotonically diminishes too.
Rabi oscillations of quantum population are known to occur in two-level systems driven by spectrally narrow laser fields. In this work we study Rabi oscillations induced by shaped broadband femtosecond laser pulses. Due to the broad spectral width of the driving field, the oscillations are initiated between a ground state and a coherent superposition of excited states, or a ``wave packet,'' rather than a single excited state. Our experiments reveal an intricate dependence of the wave-packet phase on the intensity of the laser field. We confirm numerically that the effect is associated with the strong-field nature of the interaction and provide a qualitative picture by invoking a simple theoretical model.
Using the intertwining relation we construct a pseudosuperpartner for a (non-Hermitian) Dirac-like Hamiltonian describing a two-level system interacting in the rotating wave approximation with the electric component of an electromagnetic field. The two pseudosuperpartners and pseudosupersymmetry generators close a quadratic pseudosuperalgebra. A class of time-dependent electric fields for which the equation of motion for a two-level system placed in this field can be solved exactly is obtained. A new interesting phenomenon is observed. There exists a time-dependent detuning of the field frequency from the resonance value such that the probability to populate the excited level ceases to oscillate and becomes a monotonically growing function of time tending to 3/4. It is shown that near this fixed excitation regime the probability exhibits two kinds of oscillations. The oscillations with small amplitude and frequency close to the Rabi frequency (fast oscillations) take place at the background of those with big amplitude and small frequency (slow oscillations). During the period of slow oscillations, the minimal value of the probability to populate the excited level may exceed 1/2, suggesting for an ensemble of such two-level atoms the possibility of acquiring an inverse population and exhibit lasing properties.