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.
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.
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.
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.
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.
In this thesis we discuss an extension of the historical Hanbury Brown and Twiss experiment and investigate spatial intensity correlations of higher-orders in the radiation field of statistically independent light sources. The light sources can be non-classical like single-photon emitters or classical, obeying thermal or coherent statistics. Although the light sources are assumed to emit the photons in an incoherent manner, we find spatial photon correlations in the far field which can be explained by the quantum mechanical concept of multi-photon interferences. We demonstrate that spatial correlation measurements between indistinguishable photons based on linear optical detection techniques can be used to overcome the resolution limit of classical optics (Abbe/Rayleigh limit) and also to manipulate the spatial radiation characteristic of the light sources. Both remarkable properties of higher-order intensity correlations have been experimentally verified using statistically independent pseudothermal light sources. Due to the fact that the reported correlation measurements require neither special quantum tailoring of light nor N-photon absorbing media, they are of particular interest for the field of quantum imaging and quantum information processing. The thesis is divided into three main parts: In the first part (Chapter 2 and 3) we introduce a quantum path formalism which allows to describe multi-photon interferences arising in both classical and nonclassical light fields. This quantum path approach explains the origin of the underlying interference mechanism of the higher-order spatial intensity correlation functions in a transparent and simple manner. Moreover, it enables us to compare the multi-photon interferences obtained by nonclassical single-photon emitters with those generated by classical light sources. In the course of this discussion it appears that Dirac's famous statement “Each photon interferes only with itself. Interference between two different photons never occurs.” should better read “A multi-photon state of independent photons only interferes with itself. Interference between different multi-photon states never occurs.” This general statement summarizes the physics behind all multi-photon interference phenomena investigated in this thesis. In the second part of the thesis (Chapter 4) we investigate particular multi-photon interference measurements of independent light sources in the context of quantum imaging. We demonstrate that the Nth-order spatial intensity correlation functions display at specific ‘magic’ detector positions the ability to filter sub-wavelength information out of the light fields arising from N incoherently radiating light sources. These multi-photon interference patterns achieve a higher resolution for N>2 than the classical Abbe/Rayleigh limit for imaging the light source. In case of N single-photon emitters we theoretically show that the super-resolving interference patterns obtained for the ‘magic’ detector positions are identical to the ones generated by NOON states with N-1 photons. Quite unexpected, the same is true for N thermal light sources, except for a reduced visibility. Experimental results with up to eight independent thermal light sources confirm this approach to improve the spatial resolution in imaging. In the last part of this thesis (Chapter 5) we finally demonstrate that multi-photon detections can lead to a strong angular focussing of incoherent photons emitted again by either uncorrelated single-photon sources or statistically independent classical light sources. For this effect the sources can be far away from each other and do not interact. The mth-order intensity correlation measurement causes source correlations which produce a heralded peaked emission pattern for the initially uncorrelated light sources. In particular, we show that if m-1 photons have been detected in a particular direction, the conditional probability to detect the mth photon in the same direction can be as high as 100 %. Owing to the great flexibility of detector positions for the correlation measurement, a wide variety of additional detection schemes exists which produces similar directional photon emission patterns. This theoretically predicted measurement-induced focussing was experimentally confirmed with up to eight pseudothermal light sources for three particular detection schemes.
By constructing a quantum filtering system to synthesize the spectral and spatial properties of stimulated radiation, the directionality of spectrally correlated nonclassical properties of resonance fluorescence from a three-body quantum antenna is investigated. The quantum antenna consists of three two-level quantum emitters, two of which are identical and strongly driven by an external laser field to radiate the collective resonance fluorescence with three distinct spectral components. The collective stimulated radiation is shaped by the remaining auxiliary emitter via its spontaneous emission, which is assumed to be resonant with the higher-frequency spectral component of the two identical emitters. Due to the presence of the auxiliary emitter, highly directional nonclassicality of the spectral correlations can be generated, which is the consequence of the internal interference of the source and the spatial interference of the radiation field. The electric dipole-dipole interaction between the undriven emitter and the dressed two-body radiating source plays a crucial role in breaking the rotational symmetry of nonclassical signals, which is embodied by various photon correlation functions with a frequency-resolved version for different spectral combinations. By correlating the two opposite sidebands, the frequency-resolved intensity-intensity correlation functions can signal highly directional nonclassicality, and the frequency-resolved two-mode entanglement along a specific emission direction can be tested by the frequency-resolved anomalous correlation function. While the directional nonclassical correlations between the central-frequency and the three-body collective higher-frequency components can be identified through the frequency-resolved intensity-field correlation function. These various frequency-resolved correlation functions characterize the spatial asymmetry of nonclassical properties of the collective stimulated radiation from different perspectives, including the particle properties and the quantum coherences of the filtered photons. When the three-body collective higher-frequency sidebands are correlated with the central band and the lower-frequency sideband, respectively, the schemes of using the auxiliary undriven emitter to generate optimal nonclassical correlations with well-defined directions are discussed analytically. In addition, the results obtained from the three-body quantum antenna and a dressed two-body quantum antenna are compared.
Photon statistics is a branch of physics that involves observing the behavior of single or a small number of photons and then aggregating the results through statistical averaging. This process is essential to obtain meaningful and reliable data, especially in quantum optics research. Photon statistics provides valuable information about correlations in the electromagnetic field and characteristics of the type of light being measured. For example, second-order correlation function obtained via Hanbury Brown and Twiss experiment is the fundamental way to differentiate between coherent, chaotic and quantum light. Moreover, extensive investigations into the quantum properties of light resulted in significant progress that allows for precise control of quantum optical systems and sets the stage for genuine quantum engineering. This progress extends to applications in confirming the generation of entangled photons and exploring their properties for various purposes. The non-classical correlation between the entangled photons has resulted in various quantum optical techniques that enable the practical implementation of conceptual experiments that probe the core principles of quantum theory. This enhanced control over quantum phenomena offers exciting opportunities to explore novel information-processing approaches, with the potential to revolutionize technologies rooted in quantum information science. Driven by the significance and pivotal role of photon statistics, our research pursuits were directed toward two specific domains: the characterization of nanolasers and the characterization of time-bin entangled photons. In the first segment, we delve into the realm of metallic coaxial nanolasers, renowned for their intriguing threshold-less lasing behavior. Through comprehensive photon statistics analysis, we seek to unravel the coherence properties inherent in these nanolasers. Our focus also lies on understanding the elusive threshold-less operation, which has remained a subject of debate and intrigue. To evaluate this unique lasing characteristic, we conduct rigorous second-order coherence measurements alongside time-resolved second-order correlation analyses. The second segment of this study ventures into the generation and characterization of high-dimensional time-bin entangled states, a critical resource for quantum technological applications. We simulate a synthetic photonic lattice by employing a coupled fiber-loop system to perform various quantum walk schemes to generate and process high-dimensional time-bin entangled states. Our investigation focuses on the quantum interference phenomena through detailed photon statistics analysis, with an emphasis on their applications across diverse quantum technologies. Through these two interconnected research endeavors, this thesis demonstrates the profound significance of photon statistics as a versatile tool, bridging classical and quantum realms, and paving the way for advancements in diverse applications, ranging from nanolasers to quantum technologies.