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Journal of Modern Optics

Interference effects in the spontaneous emission from two initially excited atoms

H. Zhao, Kikuo Ujihara

Published Feb 21, 2006• 2 citations
Publisher

Abstract

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.

DOI
10.1080/09500340500159732

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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.
Collective effects in the spontaneous emission pattern of two identical two-level atoms a fixed distance apart and sharing initially a single excitation are investigated. It is shown that the interference can take place even when it is known for certain which atom is excited initially. This interference is due solely to the atomic coherence established through multiple photon absorptions and reemissions and will disappear if it is ignored. The interference patterns with and without collective effects are compared for symmetric and antisymmetric initial states. The dark center from an antisymmetric state is shown both analytically and numerically.
Spontaneous emission in a planar microcavity by two identical and spatially separated two-level atoms, both of them initially excited, is considered under fourth-order perturbation approximation in atom-field coupling constants. A delay-differential equation with proper retardation times for the probability of both atoms in the upper state is derived and expressions for the emitted-light intensity and spectrum are given. It is numerically shown that, while two-atom cooperation is enhanced for small interatomic distances, the two-atom vacuum Rabi oscillation is somewhat suppressed compared to the single-atom oscillation level when the interatomic separation is close to the cavity transverse coherence length.
Sub- and superradiant dynamics of spontaneously decaying atoms are manifestations of collective many-body systems. We study the internal dynamics and the radiation properties of two atoms in free space. Interesting results are obtained when the atoms are separated by less than half a wavelength of the atomic transition, where the dipole-dipole interaction gives rise to new coherent effects, such as (a) coherence between two intermediate collective states, (b) oscillations in the two-photon correlation G(2){G}^{(2)}G(2), (c) emission of two photons by one atom, and (d) the loss of directional correlation. We compare the population dynamics during the two-photon emission process with the dynamics of single-photon emission in the cases of a $\ensuremath{\Lambda}$ and a V scheme. We compute the temporal correlation and angular correlation of two successively emitted photons using the G(2){G}^{(2)}G(2) for different values of atomic separation. We find antibunching when the atomic separation is a quarter wavelength $\ensuremath{\lambda}∕4$. Oscillations in the temporal correlation provide a useful feature for measuring subwavelength atomic separation. Strong directional correlation between two emitted photons is found for atomic separation larger than a wavelength. We also compare the directionality of a photon spontaneously emitted by the two atoms prepared in phased-symmetric and phased-antisymmetric entangled states ${\ensuremath{\mid}\ifmmode\pm\else\textpm\fi{}⟩}_{{\mathbf{k}}_{0}}={e}^{i{\mathbf{k}}_{0}∙{\mathbf{r}}_{1}}\ensuremath{\mid}{a}_{1},{b}_{2}⟩\ifmmode\pm\else\textpm\fi{}{e}^{i{\mathbf{k}}_{0}∙{\mathbf{r}}_{2}}\ensuremath{\mid}{b}_{1},{a}_{2}⟩$ by a laser pulse with wave vector k0{\mathbf{k}}_{0}k0​. Photon emission is directionally suppressed along k0{\mathbf{k}}_{0}k0​ for the phased-antisymmetric state. The directionality ceases for interatomic distances less than $\ensuremath{\lambda}∕2$.
We present an analysis of the spontaneous emission by two identical two-level atoms a distance R apart, both of which are initially in the upper state. This analysis applies for two interacting atoms emitting both in a free space and in a cavity structure. In this paper we use the Heisenberg picture. We work under the dipole approximation and the rotating-wave approximation. We assume that all the field modes are initially in the vacuum state and the two atoms A and B are in the upper state. We will concentrate on the motion of the product of the dipole operators of two atoms. Because we have two excitations at t=0, and because we work under rotating-wave approximation, we will always have two excitations, i.e., two excited atoms, or one excited atom plus one photon, or two unexcited atoms with two photons.
As a contribution to quantum optics in the vicinity of surfaces we study the single atom spontaneous emission in a linear chain of two-level atoms. The electromagnetic field is thereby treated with the help of integro-differential equations which take into account the interaction with the other atoms in the chain. The life time of the excited atom, the frequency shift of the atomic transition and the angular distribution of emitted photons are worked out. They depend on the position of the emitting atom. As compared with the single atom in free space, considerable modifications occur for atoms a few interatomic distances away from the ends of the chain.
We study the collective spontaneous emission of three identical two-level atoms initially prepared in the excited states by measuring Glauber's third-order photon correlation function. Assuming two atoms at subwavelength distance from each other such that they are subject to the dipole-dipole interaction while the third one is located several wavelengths away, we observe super- and subradiant decay alike, depending on the direction of observation. Unlike the case where no remote atom is introduced or no conditional measurements are performed, the spontaneous emission behavior of the conditioned three-atom system is strongly modified, i.e., differing from the single-atom and the canonical two-atom configuration. The conditional measurements associated with the three-photon correlation function in combination with the dipole-dipole interaction between the adjacent atoms lead to quantum interference among the different decay channels allowing one to engineer the spontaneous emission in space and time.