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EPJ Web of Conferences

Effects of quantum interference in spectra of cascade spontaneous emission from multilevel systems

A.A. Makarov, Vladimir I. Yudson

Published Dec 13, 2016• 0 citations
Publisher

Abstract

A general expression for the spectrum of cascade spontaneous emission from an arbitrary multilevel system is presented. Effects of the quantum interference of photons emitted in different transitions are analyzed. These effects are especially essential when the transition frequencies are close. Several examples are considered: (i) Three-level system; (ii) Harmonic oscillator; (iii) System with equidistant levels and equal rates of the spontaneous decay for all the transitions; (iv) Dicke superradiance model.

DOI
10.1051/epjconf/201713202014

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A general expression for the spectrum of cascade spontaneous emission from an arbitrary multilevel system is presented. Effects of the quantum interference of photons emitted in different transitions are analyzed. These effects are especially essential when the transition frequencies are close. Several examples are considered: (i) Three-level system; (ii) Harmonic oscillator; (iii) System with equidistant levels and equal rates of the spontaneous decay for all the transitions; (iv) Dicke superradiance model.
The process of a cascade light emission by an excited multilevel quantum system has been described exactly. A multiphoton wave function of the system at an arbitrary time has been derived, which allows one to find any characteristic of the emitted field. Using this wave function, we have obtained a general expression for the cascade emission spectrum. This expression is of special interest when some transitions have close frequencies; this case has not been treated before. We present several examples of application of the obtained general expression.
For pt.I see ibid., vol.18, p.3811 (1985). This paper is the second of a theoretical study of subradiance, i.e. of the cooperative inhibition of spontaneous emission by a destructive interatomic interference, a phenomenon which has recently been observed. It is devoted to the particular case of atomic systems with degenerate transitions, i.e. with several transitions of the same frequency and the same polarisation. The interatomic interference which then occurs between the different transitions is responsible, when destructive, for a new sort of subradiance. The phenomenon is studied for a few typical level configurations, using both quantum mechanical and semiclassical models. The first example concerns a four-level configuration with two transitions of the same frequency and polarisation. The other examples concern three-level configurations with a degenerate transition; in the case of the 'degenerate' cascade, new superradiant beats and subradiance effects are predicted.
In this review the author discusses the major effects resulting from the modification of spontaneous emission by quantum interference. He begins in Section II by presenting elementary concepts and definitions of the first- and second-order correlation functions, which are frequently used in the analysis of the interference phenomena. Section III describes the master equation approach used for analyzing quantum interference effects in atomic and molecular systems. In Sections IV and V the author reviews the fundamental quentum interference effects in spontaneous emission and in coherently driven systems. He discusses different schemes for suppression of spontaneous emission and population trapping and gives an alternative explanation of these effects in the dressed-atom picture. Section VI deals with the problem of amplification on dark transitions, which are important for information processing without spontaneous emission. The effect of quantum interference on photon correlations is discussed in Section VII. Multilevel systems composed of two transitions with parallel dipole moments and methods for generating two transitions with nonorthogonal dipole moments are briefly discussed in Section VIII. The final section (Section IX) deals with the experimental demonstration of constructive and desctructive interference effects in a driven molecular system.
Atomic systems with three or more equidistant energy levels, in which a cascade process is possible, are considered. Hamiltonians obtained for such systems are analogous to Heisenberg Hamiltonians, but for systems with integral spins. For Dicke states in multilevel systems, quantum-mechanical mean values of the energy of a cooperative system are calculated taking into account weak interactions between atoms. The type of emission preceding superradiant avalanche emission of the system is analyzed. It can be expected that a coherent state may be formed, in which collective processes affect one another not only via population of the intermediate common layer, but also via phasing of pure quantum states. The single superfluorescence pulse that can be formed in this case is not a simple superposition of two or more pulses of sequential superradiant transitions in two-level systems.