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AIP conference proceedings

Quantum correlations in directional emission

Qurrat-ul-Ain Gulfam, Z. Ficek

Published Jan 1, 2018• 3 citations
Publisher

Abstract

We examine angular distribution of the correlations of fluorescence photons emitted from a linear chain of coupled two-level atoms. Attention is focused on the simultaneous emission of correlated pairs of photons. It is found that the collective behaviour of the atoms can result in a strongly directional emission of correlated pairs of photons. The number of directions and the degree of the correlation between the photons depends strongly on whether the atoms in the chain are equally or unequally spaced. In the case of unequally spaced atoms anticorrelated pairs of photons are emitted into specific directions. For equally spaced atoms, the emitted pairs of photons are strongly correlated and highly focused into specific directions. Depending on the number of atoms, the strongly correlated pairs of photons can be emitted into well-defined single or two directions.

DOI
10.1063/1.5042370

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We examine angular distribution of the correlations of fluorescence photons emitted from a linear chain of coupled two-level atoms. Attention is focused on the simultaneous emission of correlated pairs of photons. It is found that the collective behaviour of the atoms can result in a strongly directional emission of correlated pairs of photons. The number of directions and the degree of the correlation between the photons depends strongly on whether the atoms in the chain are equally or unequally spaced. In the case of unequally spaced atoms anticorrelated pairs of photons are emitted into specific directions. For equally spaced atoms, the emitted pairs of photons are strongly correlated and highly focused into specific directions. Depending on the number of atoms, the strongly correlated pairs of photons can be emitted into well-defined single or two directions.
We examine angular distribution of the probability of correlated fluorescence photon emission from a linear chain of identical equidistant two-level atoms. We selectively excite one of the atoms by a resonant laser field. The atoms are coupled to each other via the dipole-dipole interaction and collective spontaneous emission. Our attention is focused on the simultaneous observation of correlated pairs of photons. It is found that the interference between the emitting atoms can result in a highly directional emission of photon pairs. These pairs of photons exhibit strong correlations and their emission is highly concentrated into specific directions. We demonstrate the crucial role of the selective coherent excitation in such a geometrical configuration. Shifting the driving field from an atom located at one end of the chain to the other causes the radiation pattern to flip to the opposite half of the detection plane. Furthermore, we find that atomic systems in which only an atom situated at a particular position within the linear chain is driven by a laser field can radiate correlated twin photons in directions along which the radiation of single photons is significantly reduced. Alternatively, superbunching in the emitted photon statistics preferentially occurs in directions of negligible or vanishing single-photon emission. The effect of superbunching strengthens as more emitters are added to the chain. Depending on the number of atoms and the position of the driven atom within the chain, the strongly correlated pairs of photons can be emitted into few well-defined directions.
The probability of correlated emission of fluorescent photons as a function of detection directions has been investigated. The model system comprises identical two-level atoms arranged in the form of a line. A weak laser field resonantly excites only one of the atoms in the line. Two interaction mechanisms, namely, the vacuum-induced dipole–dipole interaction and the collective spontaneous emission couple the system of atoms. The aim is to observe the emission of a set of photon twins synchronized in time. It is seen that strongly directional emission of pairs of photons can take place due to the interference between the emitters. These highly correlated pairs of photons can be observed in very precise geometric directions. The observation is made based on two different detection procedures. It is found that the superradiant photons always tend to be bunched along the same direction.
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 $\ensuremath{\lambda}∕2$.
Correlations between the emission of photons from an excited three-level atom with one transition more strongly driven than the other are studied. Antibunching, anticorrelation, and superbunching are exhibited in the four possible configurations: ``vee'' (V), ``lambda'' (\ensuremath{\Lambda}), and two cascades with the upper or lower transition strongly driven. We pay particular attention to the projection of the atom into particular states by the measurement of fluorescence, and its significance for detecting quantum jumps in the weak transition by observing the fluorescence from the strong transition. For incoherent excitation we find that cross antibunching (the anticorrelation between emissions of different types of photons) manifests itself as prolonged periods of darkness. For the V and the cascade configuration with a strongly driven lower transition, these periods herald the emission of a weak-transition photon; for the other cascade and the \ensuremath{\Lambda} configuration the periods are heralded by the emission of a weak-transition photon. For on-resonance coherent excitation, dark periods are extremely infrequent for the former two configurations, and are extremely long or infinite for the latter two.
Systems of atoms coupled to a single or a few waveguide modes provide a test-bed for physically and practically interesting interference effects. We consider the dynamics of a pair of atoms, approximated as two-level quantum emitters, coupled to a linear guided mode. In particular, we analyze the evolution of an initial state in which both atoms are excited, which is expected to decay into an asymptotic two-photon state. We investigate the lifetime of the initial configuration and the properties of the asymptotic photon correlations, and analyze the probability that the two photons are emitted in the same or in opposite directions. We find that the ratio RRR between parallel and antiparallel emission probabilities is maximal when the interatomic distance is an odd multiple of a quarter wavelength of the emitted light. In such a case, R=3R=3R=3 in the small-coupling regime.
We examine the correlation between photons in the resonance fluorescence of a bichromatically driven four-level atom. The four-level atom consists of two twofold degenerate states and, as a consequence, spontaneous emission events become sensitive to polarization. Depending on the interaction strength with the bichromatic field as well as its polarization direction, nonlinear two-photon emission takes place which, in turn, leads to extremely strong correlations between certain polarized photons. On the other hand, correlations between photons differently polarized from the distinctive ones are suppressed. Thus, the light source establishes a promising candidate for the generation of Bell-type correlated photon pairs. We explain the unusual large correlations with a nonlinear four-photon process which crucially depends on the strength of the driving as well as its polarization.