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Physical Review A

Spectrum of cascade spontaneous emission: General theory including systems with close transition frequencies

Alexander A. Makarov, Vladimir I. Yudson

Published May 7, 2014• 5 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.89.053806

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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.
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.
We describe the emission, detection and structure of multiphoton states of light. We include the effect of frequency filtering, which describes, at a fundamental level, physical detection of a quantum emitter. The case of the spontaneous emission of Fock states is treated fully and analytically. We stress this picture by contrasting it to the numerical simulation of two-photon bundles emitted from a two-level system in a cavity. We show that dynamical factors exist that allow for a more robust multiphoton emission than spontaneous emission. We also describe how this relates to thermal light.
The spontaneous emission of a set of NNN identical two-level atoms interacting with a quantized electromagnetic field is studied. The atoms are assumed to be close together compared to the mean wavelength of the emitted radiation, and their initial state is either a Dicke state or a superposition of the ground and excited state for each atom. Approximate expressions are obtained for transition probabilities, expectation values, and correlations as functions of time. The spontaneous emission for a very large separation of the atoms is also studied. In this case the directional properties of the emitted radiation, as well as the time within which the atoms decay to their ground state, depend on the position of each atom.
Expressions are derived for the intensity correlations or degrees of second-order coherence within and between two light beams of different frequency generated by cascade emission from a three-level atom. The atoms are assumed to be excited by two monochromatic coherent light beams in resonance with the upper and lower pairs of levels that constitute the triplet. The two emitted beams individually show photon antibunching and the correlation between the beams shows another complementary kind of non-classical effect. It is suggested that measurements on the system described here would provide more detailed information on quantum effects in cascade emission than previous observations with direct excitation to the uppermost atomic level by electron bombardment.
We present a theory of cascade emission from an array of NNN fixed, ``three-level'' atoms. The total angular momentum of the ground state of each atom is J=0J=0J=0, that of the intermediate state is J=1J=1J=1, and that of the upper state is J=0J=0J=0. The atoms are prepared in a spatially phased superposition of their ground and upper states, collectively sharing a single excitation. We calculate the time-integrated, joint probability distribution for radiation to be emitted in a given direction with a given polarization on each transition and use this joint probability distribution to calculate the time-integrated intensity emitted on each transition. The dipole-dipole interaction between the atoms is taken into account. Analytic expressions are obtained for two atoms and the calculation is then extended formally to an ensemble of NNN atoms at arbitrary positions. As expected, the radiation emitted on the upper transition is unpolarized and isotropic. However, somewhat surprisingly, we find that for excitation by counterpropagating fields and for nearly equal ground to intermediate and intermediate to upper level transition frequencies, the radiation on the lower transition is also isotropic and unpolarized, provided the atoms are prepared in a fully symmetric state. We also establish conditions for which there can be a phase-matched enhancement of the joint probability density for specific directions of emissions on the upper and lower transitions.