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Photonics

Grating Lobes in Higher-Order Correlation Functions of Arrays of Quantum Emitters: Directional Photon Bunching Versus Correlated Directions

Iñigo Liberal, Íñigo Ederra, Richard W. Ziolkowski

Published Feb 12, 2019• 15 citations
Publisher

Abstract

Recent advances in nanofabrication and optical manipulation techniques are making it possible to build arrays of quantum emitters with accurate control over the locations of their individual elements. In analogy with classical antenna arrays, this poses new opportunities for tailoring quantum interference effects by designing the geometry of the array. Here, we investigate the N th -order directional correlation function of the photons emitted by an array of N initially-excited identical quantum emitters, addressing the impact of the appearance of grating lobes. Our analysis reveals that the absence of directivity in the first-order correlation function is contrasted by an enhanced directivity in the N th -order one. This suggests that the emitted light consists of a superposition of directionally entangled photon bunches. Moreover, the photon correlation landscape changes radically with the appearance of grating lobes. In fact, the photons no longer tend to be bunched along the same direction; rather, they are distributed in a set of correlated directions with equal probability. These results clarify basic aspects of light emission from ensembles of quantum emitters. Furthermore, they may find applications in the design of nonclassical light sources.

DOI
10.3390/photonics6010014

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Recent advances in nanofabrication and optical manipulation techniques are making it possible to build arrays of quantum emitters with accurate control over the locations of their individual elements. In analogy with classical antenna arrays, this poses new opportunities for tailoring quantum interference effects by designing the geometry of the array. Here, we investigate the N th -order directional correlation function of the photons emitted by an array of N initially-excited identical quantum emitters, addressing the impact of the appearance of grating lobes. Our analysis reveals that the absence of directivity in the first-order correlation function is contrasted by an enhanced directivity in the N th -order one. This suggests that the emitted light consists of a superposition of directionally entangled photon bunches. Moreover, the photon correlation landscape changes radically with the appearance of grating lobes. In fact, the photons no longer tend to be bunched along the same direction; rather, they are distributed in a set of correlated directions with equal probability. These results clarify basic aspects of light emission from ensembles of quantum emitters. Furthermore, they may find applications in the design of nonclassical light sources.
We investigate the role of quantum interference phenomena on the characteristics of the fields radiated by an array of quantum emitters. In analogy to, but distinct from, classical outcomes, we demonstrate that the array geometry empowers control over direction-dependent photon statistics of arbitrary order. Our formulation enables the recognition of configurations providing spatial correlations with no classical counterpart. For example, we identify a system in which the angular distribution of the average number of photons is independent of the number and position of the emitters, while its higher-order photon statistics exhibit a directional behavior. These results extend our understanding of the fields generated by ensembles of quantum emitters, with potential applications to nonclassical light sources.
Quantum antennas can shape the spatial entanglement of emitted photons originating from specific initial non-Dicke entangled states of antenna emitters. In contrast to a classical antenna, a quantum antenna might not be affecting the amplitudes and intensities distribution of the field, but only shaping the second and higher order correlations. The shape and directivity of the correlations can be optimized using quantum state inference techniques. The character of the correlations can also be controlled by changing both the geometry and the initial state of the antenna. Positive and negative correlated twin-photons, as well as multi-photons entangled states can be produced from the same antenna for different initial states of the emitters. Our approach to antenna design can find applications in imaging and high-precision sensing, as well as in the development of an emitter-field interface for quantum information processing.
Ensembles of atoms or other quantum emitters are envisioned to be an important component of quantum applications, ranging from quantum memories for light to photon-photon gates to metrology. It has historically been an outstanding challenge to exactly solve for the quantum dynamics of an optical field as it propagates through and interacts with an ensemble. The standard axiomatic approach is to use the one-dimensional Maxwell-Bloch equations, which assume that excited atoms emit independently into unwanted directions. This ignores the wave interference of the emitted light, which depends on correlations between the atoms. Here, we discuss an alternative theoretical approach, which accounts for interference and the precise atomic positions. In this formalism, an interacting quantum spin model describes the dynamics of the atomic internal degrees of freedom under multiple photon scattering, while the field properties can subsequently be re-constructed from the spin correlations. Using this model, we then show how interference can be exploited as an extremely powerful resource to suppress the unwanted emission of light and the subsequent loss of information into undesirable directions. The effects of interference are particularly prominent in ordered arrays of emitters. For example, it can be shown that an array acts as a perfectly lossless waveguide for light, in direct analogy to a conventional photonic crystal waveguide. By exploiting this concept, we derive a novel protocol for a quantum memory for light, whose error probability as a function of optical depth scales exponentially better than previously known bounds.
Superradiance has been an outstanding problem in quantum optics since Dicke introduced the concept of enhanced directional spontaneous emission by an ensemble of identical two-level atoms. The effect is based on the correlated collective Dicke states which turn out to be highly entangled. Here we show that enhanced directional emission of spontaneous radiation can be produced also with statistically independent incoherent sources, via the measurement of higher-order correlation functions of the emitted radiation. Our analysis is applicable to a wide variety of quantum emitters, like trapped atoms, ions, quantum dots, or nitrogen-vacancy centers, and is also valid for incoherent classical emitters. This is experimentally confirmed with up to eight statistically independent thermal light sources. The arrangement to measure the higher-order correlation functions corresponds to a generalized Hanbury Brown-Twiss setup, demonstrating that the two phenomena, superradiance and the Hanbury Brown-Twiss effect, stem from the same interference phenomenon.
A quantum antenna can shape spatial entanglement of emitted photons originating from entangled states of antennas emitters. In contrast to the classical antenna, the quantum antenna can shape the second and higher order correlations without affecting amplitudes of the field. The shape and directivity of the correlations can be optimized using techniques of quantum state inference. Positive and negative correlated twin-photon, and multi-photon entangled states can be produced from the same antenna for different initial states of emitters.
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.