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Nonlinear Optics

Quantum Theory of Electromagnetically Induced Transparency

Daniel F. Walls, Klaus M. Gheri

Published Jan 1, 1992• 0 citations
Publisher

Abstract

There have recently been several experiments which have observed electromagnetically induced transparency in atomic systems(1,2) This is based on the population trapping which may occur when two lower states are coupled to a common upper state by two laser fields. Due to destructive quantum mechanical interference this gives rise to a nonabsorbing resonance. Thus a strongly absorbing atomic transition may be rendered opaque.

DOI
10.1364/nlo.1992.tuc6

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There have recently been several experiments which have observed electromagnetically induced transparency in atomic systems(1,2) This is based on the population trapping which may occur when two lower states are coupled to a common upper state by two laser fields. Due to destructive quantum mechanical interference this gives rise to a nonabsorbing resonance. Thus a strongly absorbing atomic transition may be rendered opaque.
We report the first demonstration of a technique by which an optically thick medium may be rendered transparent. The transparency results from a destructive interference of two dressed states which are created by applying a temporally smooth coupling laser between a bound state of an atom and the upper state of the transition which is to be made transparent. The transmittance of an autoionizing (ultraviolet) transition in Sr is changed from exp(-20) without a coupling laser present to exp(-1) in the presence of a coupling laser.
When narrowband probe radiation traveling through a bulk material is tuned to a resonance transition from the ground state of the material, the radiation experiences strong attenuation and dispersion. Recent theoretical1 and experimental2,3 work has demonstrated that this attenuation can be almost completely eliminated by the addition of a strong coherent coupling radiation field coupling a third state to the upper state of the resonance transition. In effect, a destructive quantum interference blocks the excitation of the atom from its ground state and renders the atom transparent. We term this effect “electromagnetically induced transparency.”
Recently, there has been increasing interest on the idea of controlling optical responses using atomic-coherence or quantum-interferences. Typical example may be the concept of electomagnetically-induced transparency (EIT) [1]. The key idea of EIT is to apply a strong-coupling field between a metastable and upper states to dress them equivalently as two states decaying to a common level or continuum, and to induce the transparency at the split-center of Autler-Townes components. This idea of EIT may open new possibilities to various coherent processes, such as lasing without population inversion, enhanced refractive index without absorption], slow group velocity without absorption, enhanced nonlinearity without absorption, etc.
The phenomenon of electromagnetically induced transparency, which was discovered recently in atomic systems, is demonstrated for the first in a subband quantum well system. Applying strong coupling field (Rabi frequency is on the same order as the intersubband linewidth), which is two- photon-resonant with the 1 - 3 intersubband transition, produces dramatic change in the 1 - 2 intersubband absorption profile. This effect can be accounted for in terms of 1 - 2 and 2 - 3 dipoles being driven into coherence by a strong coupling field; it is not related to self- induced transparency or spectral hole-burning (the frequency of the coupling field is quite different from that of 1 - 2 resonance) and, similar to Fano-type interference, is a pure result of destructive interference of probability amplitudes.
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 energy lost by the radiation field through absorption is taken up by the atoms when they are excited from the lower to the upper state. As the radiation field intensity is progressively increased, a point is reached where the excitation absorption process begins to dominate the random decay processes that establish the status quo. There is an important conclusion that we can reach in this particular type of experiment. This is that a coherently trapped population is set up in the ground states so that no population transfer takes place to the excited state. The initial experiments were carried out in strontium vapour with pulsed lasers providing the radiation fields, and involved auto-ionising transitions in a lambda arrangement. The simple 3 state model, when solved numerically, provides considerable insight into the origins of electromagnetically induced transparency in both cascade, lambda and vee schemes.