A diagrammatic representation of the steady-state solution for the density matrix of a multilevel atom under the action of coherent classical fields is presented. It provides an intuitive interpretation of the terms corresponding to quantum interference and dynamical Stark splitting in the equations describing the effects of atomic coherence, such as lasing without inversion, electromagnetically induced transparency and ultra-large index of refraction.
A diagrammatic representation of the steady-state solution for the density matrix of a multilevel atom under the action of coherent classical fields is presented. It provides an intuitive interpretation of the terms corresponding to quantum interference and dynamical Stark splitting in the equations describing the effects of atomic coherence, such as lasing without inversion, electromagnetically induced transparency and ultra-large index of refraction.
Quantum coherence and correlations in atomic and radiation physics have led to many interesting and unexpected consequences. For example, an atomic ensemble prepared in a coherent superposition of states yields the Hanle effect, quantum beats, photon echo, self-induced transparency, and coherent Raman beats. In fact, in Section 1.4, we saw that the quantum beat effect provides one of the most compelling reasons for quantizing the radiation field. A further interesting consequence of preparing an atomic system in a coherent superposition of states is that, under certain conditions, it is possible for atomic coherence to cancel absorption. Such atomic states are called trapping states †. The observation of nonabsorbing resonances via atomic coherence and interference impacts on the concepts of lasing without inversion (LWI),‡ enhancement of the index of refraction accompanied by vanishing absorption, and electromagnetically induced transparency. In lasing without inversion, the essential idea is the absorption cancellation by atomic coherence and interference. This phenomenon is also the essence of electromagnetically induced transparency. Usually this is accomplished in three-level atomic systems in which there are two coherent routes for absorption that can destructively interfere, thus leading to the cancellation of absorption. A small population in the excited state can thus lead to net gain. A related phenomenon is that of resonantly enhanced refractive index without absorption in an ensemble of phase-coherent atoms ( phaseonium ). In a phaseonium gas with no population in the excited level, the absorption cancellation always coincides with vanishing refractivity.
The study of an ensemble of phase–coherent atoms has recently lead to interesting theoretical innovations and experimental demonstrations of counter–intuitive effects such as electromagnetically induced transparency (EIT), lasing without inversion (LWI), enhancement of index of refraction and ultra–large nonlinear susceptibility. In the present notes, we report a couple of new effects along these lines. In fact, it would be fair to call them surprises even in the repertoire of ‘counter–intuitive effects’, i.e. ‘counter–counter–intuitive effects’. Specifically, we will show that the LWI concept, which is based on quantum coherence, has a surprising counterpart in the classical physics of free electron laser operation. In other current work, we find that it is possible to ‘lock’ atoms in an excited state via atomic coherence. It is, by now, not surprising that such a phase–coherent ensemble can show holes or dark lines in the emission spectrum. It is surprising that we can lock atoms in an excited (normally decaying) state via atomic coherence and interference. Such a phase–coherent collection of atoms, i.e. ‘phaseonium’, is indeed a novel new state of matter.
The appearance of quantum interference in the microscopic world is one of the deepest mysteries at the very root of quantum mechanics. When light interacts with atoms, it can induce transitions by way of distinct but indistinguishable pathways and yield unexpected and often counter-intuitive results. Electromagnetically Induced Transparency (EIT), Coherent Population Trapping (CPT), and Lasing Without Inversion (LWI) are modern examples of phenomena where the traditional rules that govern absorption and dispersion undergo major revisions. Spectacular consequences of this new state of affairs include the ability of a light beam to propagate through a normally absorbing medium with little or no absorption, or to undergo amplification even if the active medium is not prepared in a state of population inversion. Light signals have been shown to travel with strongly subluminal group velocities of only a handful of meters per second and, even, to propagate at speed greater than the ordinary speed of light, but without violation of causality or of the established rules that control the transfer of optical information through space. Three-level atoms can interact with two coherent electromagnetic fields according to three different systems, known as Cascade, Lambda and Vee systems. The propagation of a weak probe field can be deeply affected by the presence of a second stronger beam, the so-called coupling field. Transparency windows, splitting of emission and absorption lines and enormously enhanced dispersion have been documented in numerous experiments. In this thesis we explore the physical origin of the transparency induced in these systems by the simultaneous interplay of the coupling and probe fields. We focus our attention on the Cascade system and study its two configurations, Cascade-EIT and Cascade-AT. We develop a variety of complementary approaches for the description of these two configurations, some semiclassical and others fully quantum mechanical. We prove the existence of quantum interference in Electromagnetically Induced Transparency and also the surprising absence of interference in a closely related phenomenon, known as the Autler-Townes effect. Finally we complement the traditional machinery of theoretical quantum optics with techniques borrowed from quantum scattering theory, and offer what we believe is the most convincing physical evidence for the appearance, or for the absence, of quantum interference effects.
The model of an open four-level atomic system is presented on the basis of the closed four-level atomic system. In the rotating wave, slowly varying envelope and mean field approximations, the density-matrix motion equations of the system are solved, and the linear analytical solution in the steady state is obtained. The numerical calculation from the steady-state solution of the open system is presented. It is shown that a change from LWI to lasing with inversion action can occur due to the Rabi frequency of the driving field increasing; another change from lasing with inversion to LWI action can also occur as the exit rate or ratio of injection rates increases; high refractive index without absorption can be obtained; the curve of ρ33-ρ11(vs Δ2) presents the shape of the rectangle wave.
The LWI operation condition for an open Λ-type three level atomic system is obtained by solving the steady-state density-matrix equation with the system being driven by a strong coherent field while the inherent pumping rate and decay rate being arbitrary.It is shown that the inversions of inherent pumping rate and spontaneous decay rate replace the inversion of population,and together help to realize lasing without population inversion.Furthermore,the LWI can be realized if just either one of the two inversions is fulfilled.A schrodinger equation of three-level atomic system with appropriate conditions is analytically solved to explain the quantum interference process that leads to LWI.
A full quantum treatment is given of suppression of absorption and lasing without inversion in a ∧-type three-level atom induced by a strong driving field resonant with the two lower levels. The nature of the quantum interference leading to the suppression of absorption and lasing without inversion and its relation to the initial state preparation are studied. Particular attention is given to the effects that arise specifically from the quantum nature of the driving field. It is shown that, because of the distinguishability of the states of the driving field that have different photon numbers, destructive interference is confined to occur within a finite region of the photon number space. A complete cancellation of absorption predicted in the semiclassical theory should thus be regarded as resulting from an ideal behavior achieved only in the classical limit when the driving field is given as a strong coherent field.