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arXiv:quant-ph/0109100 · Journal of Modern Optics

Quantum interference in optical fields and atomic radiation

Z. Ficek, S. Swain

Published Jan 1, 2002• 88 citations
arXivHTMLPDF

Abstract

We discuss the connection between quantum interference effects in optical beams and radiation fields emitted from atomic systems. We illustrate this connection by a study of the first- and second-order correlation functions of optical fields and atomic dipole moments. We explore the role of correlations between the emitting systems and present examples of practical methods to implement two systems with non-orthogonal dipole moments. We also derive general conditions for quantum interference in a two-atom system and for a control of spontaneous emission. The relation between population trapping and dark states is also discussed. Moreover, we present quantum dressed-atom models of cancellation of spontaneous emission, amplification on dark transitions, fluorescence quenching and coherent population trapping.

DOI
10.1080/09500340110065781

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Journal of Modern Optics•Nov 30, 2007•5 citations
We discuss the connection between quantum interference effects in optical beams and radiation fields emitted from atomic systems. We illustrate this connection by a study of the first- and second-order correlation functions of optical fields and atomic dipole moments. We explore the role of correlations between the emitting systems and present examples of practical methods to implement two systems with non-orthogonal dipole moments. We also derive general conditions for quantum interference in a two-atom system and for a control of spontaneous emission. The relation between population trapping and dark states is also discussed. Moreover, we present quantum dressed-atom models of cancellation of spontaneous emission, amplification on dark transitions, fluorescence quenching and coherent population trapping.
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.
Quantum interference and coherence effects in the interaction of atoms with the quantized electromagnetic field are investigated theoretically. A general master equation for the description of atom-field interactions is introduced. The interplay of the concepts of complementarity and interference in the time-energy domain are studied on the basis of the fluorescence light emitted by a single laser-driven atom, where the coherence of spontaneous processes gives rise to quantum interference in the spectrum of resonance fluorescence. The vacuum-induced dipole-dipole interaction in pairs of multi-level atoms is analyzed. It is shown that the interaction between orthogonal transition dipole moments of different atoms does not only influence the system dynamics crucially, but implies that the few-level approximation in general cannot be applied to near-degenerate Zeeman sublevels of the atomic level scheme. Potential applications of dipole-dipole interacting multi-level atoms for the implementation of decoherence-free subspaces and the generation of entanglement between atomic states are examined. The generation of an entangled state of the radiation field with a macroscopic number of photons is discussed on the basis of a single-atom laser.
Quantum interference and coherence lead to many interesting phenomenon and applications in quantum optics. In this dissertation, we study the quantum coherent properties in the following systems and aspects. We first investigate the optical bistability in a combined cavity-cold atoms system. In such a system the atom-photon interaction provides an optical lattice to the atoms and affects the mechanical motion of the atoms while atoms induce a position dependent phase shift on the cavity field. This highly nonlinearity induces optical bistability of intra-cavity photon number with respect to the pumping light added along the cavity axis. We show that the presence of this bistability can be controlled by a second pumping field added perpendicular to the cavity axis. It is also found that the critical input intensity of switching from one branch of bistability to the other depends on the the way of the field being added. This behavior is similar to the anomalous switching of the dispersive optical bistability of atomic media in the cavity. We also study the effect of counter-rotating terms in the control of spontaneous emission. We make use of a unitary transformation method and investigate the effect of dynamic energy shifts on the spontaneous emission modification via quantum interference in a four-level atomic system. We show that the counter-rotating terms, which are normally neglected in the usual investigation of atomic systems, do produce a significant influence on the evolution of the atomic amplitudes and the emission spectrum. This effect of counter-rotating terms can be observed in the time scale of the decay rate even when the dipole moments of the two upper levels are orthogonal to each other. The effect of counter-rotating terms on the spontaneous emission in a 3-D anisotropic photonic crystal is also discussed. It is shown that the behavior of the emission is similar to the case making rotating wave approximation, i.e., the localized and propagating fields are also separated by two characteristic atomic transition frequencies. However, the two characteristic frequencies are shifted due to the full Lamb shift which is obtained with counter-rotating terms being included in the Hamiltonian. We also utilize the unitary transformation method to show how the Lamb shift in a multi-level atom can be controlled by a driving field. Finally, we propose a subwavelength atom localization scheme for an atom located in a standing-wave field. The strategy is based on the observation that the photon statistics of resonance fluorescence depends on the position-dependent Rabi frequency.
Second-order interference effects in the spontaneous emission by two identical two-level atoms, separated a distance apart and both initially excited, are considered. On the basis of the analysis in our previous paper published in 2004, within fourth-order perturbation, detailed analysis of the second-order quantum interference in the emitted field is made. The interference arises both from single-photon states and two-photon states owing to interferences between different decaying sequences. By detailed analysis we have found some cancellations between single-photon and two-photon interference terms, and an interpretation of this is given. The contributions from the single- and the two-photon states as well as the total interference are analysed numerically for various interatomic distances and times. The contribution from a two-photon state is mostly larger than that from a single-photon state except when the atomic electric dipole is large, in which case the two contributions can be comparable. It is shown that the emission patterns from the two interacting atoms provide more information on atom–atom correlations than the decay time evolution of the atomic states population does. The number of interference fringes and the distance between them depend on the interatomic distance in a similar fashion to Young's interference fringes.
The control of the optical properties of a medium by atomic coherence and quantum interference effects is an important area of research, not only for its fundamental aspects in the understanding of radiation and matter interaction, but also for its potential applications in the design of optical devices. Atomic coherence can emerge in a medium through the coupling of a strong coherent field to an atomic transition. This coupling affects the optical properties of the medium in a very interesting ways. For example, it may yield light amplification without population inversion. Also, it can modify the traditional dispersion of an optical medium in such a way that maximum variations of the refractive index occur around a spectral region of vanishing absorption. In the first part of this work we investigate some fundamental aspects of this coherent dynamics. We investigate how this non-inversion gain is affected by the presence of atomic motion. The coherent interaction between atom and radiation can lead to the interference between optical paths of decay. We report on an atomic setting where the interference structures depend upon the phase of the coherent field, an new effect which is absent in other resonance fluorescent phenomena. As a potential application, we investigate a novel approach for the modulation of optical signal. This approach consists of injecting atomic coherence in the medium in order to tailor its optical properties so it is a more suitable medium for modulation.