<p><br></p><p dir="ltr">Achieving high optical resolution imaging is one of the most important goals in the history of optics. However, due to finite aperture sizes, a diffraction limit is imposed on optical imaging. Therefore, the Rayleigh limit, which describes the minimum separation at which two point sources are resolvable, has served as a critical limit in optical resolution. Many methods have been studied to break the limit and succeed in resolving nearby sources below the Rayleigh criterion but only beyond a certain distance. Furthermore, it has been demonstrated that quantum-inspired optics techniques maintain consistent variance in estimating the separation of point sources even at low separations, but only with prior information like a known number of sources and equal brightness. Therefore, achieving the ultimate optical resolution remains an open question. This thesis will conclusively address this challenge considering real-world scenarios, i.e., no prior information or controlled lab environment as well as low signal-to-noise ratio (SNR), turbulence, and other practical challenges.</p><p><br></p><p dir="ltr">In information theory, the estimation variance of a random parameter can be quantified using the inverse of Fisher information. By maximizing the Fisher information, one can minimize the variance in estimation. In my thesis, we have shown that the measurement can be accelerated without sacrificing optical resolution using the adaptive mode so that quantum Fisher information per detected photon is maximized. The notable attribute that sets it apart from other quantum-inspired methods is that it does not require any prior information, making it more feasible for practical application. We have further shown that the space domain awareness (SDA) challenge can be effectively handled with the aforementioned approach with a very limited photon budget and even in the presence of turbulence. Toward solving the challenges, we designed a photon statistics-based direct imaging method that can also serve as a baseline method for quantum optics. In my thesis, atmospheric turbulence is also deeply explored and the effect is mitigated using reinforcement learning.</p><p><br></p>

<p dir="ltr">Quantum networking holds tremendous promise in transforming computation and communication. While matter-based systems excel as memory nodes, photons are ideal for long-distance transmission. Hence, a hybrid network combining both becomes essential. Moreover, developing entangled photon pair sources is critical for quantum repeaters and network implementation. The realization of these capabilities on integrated photonic circuits is vital for miniaturization and scalability. In this dissertation, we focus on two key aspects: establishing efficient photon-to-memory interfaces and generating and manipulating entangled states within integrated platforms.</p><p dir="ltr">One research direction involves developing an efficient interface between photons and matter-based memory, requiring spectral and temporal mode matching. Spectral compression is inevitable to realize low-loss interconnection between intrinsically narrowband memories and broadband photons. We proposed a novel approach using electro-optic time-varying cavities for spectral compression. Currently, we are working toward realizing this approach on the thin film lithium niobate platform.</p><p dir="ltr">In the other research focus, we encode quantum information as a coherent superposition of multiple optical frequencies; this approach is favorable due to its simplicity in generating high-dimensional entanglement and compatibility with fiber transmission. We successfully generated and reconstructed the density matrix of biphoton frequency combs from integrated silicon nitride microrings, achieving an 8x8 two-qudit dimensionality, the highest to date for frequency-bin qudits. Moreover, we employ Vernier electro-optic phase modulation methods to perform time-resolved measurements of biphoton correlation functions. Currently, we are exploring bidirectional pumping of microrings to generate indistinguishable entangled pairs in both directions, aiming to demonstrate key networking operations such as entanglement swapping and GHZ state generation in the frequency domain. We are also pursuing bidirectional pumping in a Sagnac configuration to generate simultaneous entanglement in both polarization and frequency, with the goal of deployment in a wavelength-multiplexed</p><p dir="ltr">network.</p>

With the increase in speculation about the nature of our universe, there has been a growing need to find the truth about Dark Matter. Recent research shows that the Planck-Mass range could be a well-motivated space to probe for the detection of Dark Matter through gravitational coupling. This thesis dives into the possibility of doing the same in two parts. The first part lays out the analysis framework that would sense such an interaction, while the second part outlines a prototype experiment that when scaled up using quantum optomechanical sensors would serve as the skeleton to perform the analysis with.

<p>Dipole-dipole interactions are ubiquitous fundamental physical phenomena that govern physical effects such as Casimir Forces, van der Waals forces, collective Lamb shifts, cooperative decay, and resonance energy transfer. These interactions are associated with real and virtual photon exchange between the interacting emitters. Such interactions are crucial in realizing quantum memories, novel super-radiant light sources, and light-harvesting devices. Owing to this, the control and modification of dipole-dipole interactions have been a longstanding theme. The electromagnetic environment plays a crucial role in enhancing the range and strength of the interactions. This work focuses on modifying the nanophotonic environment near interacting emitters to enhance dipole-dipole interactions instead of spontaneous emission. To this end, we focus on engineering the nanophotonic environment to enhance the strength and range of dipole-dipole interactions between an ensemble of emitters. We explore ordered and disordered nanophotonic structures. We experimentally demonstrate long-range dipole-dipole interactions mediated by surface lattice resonances in a periodic plasmonic nanoparticle lattice. Further, the modified electromagnetic environment reduces the apparent dimensionality of the interacting system compared to non-resonant in-homogeneous and homogeneous environments. We also develop a spectral domain inverse design technique for the accelerated discovery of disordered metamaterials with unique spectral features. </p> <p>Further, we explore the novel regimes of light localization at near-zero-index in such disordered media. The disordered near-zero-index medium reveals enhanced localization and near-field chirality. This work paves the way to engineer the electromagnetic nanophotonic environment to realize enhanced long-range dipole-dipole interactions.</p>

<p dir="ltr">This thesis is about the exciting discovery of a new kind of single photon emitter that<br>is suspected to occur at the interface of silicon nitride SixNy and silicon dioxide SiO2 after<br>being rapidly annealed. Since SixNy is one of the most developed platforms for integrated<br>photonics the discovery of a native emitter in this platform opened up the possibility for<br>seamless integration of these single photon emitters with photonic circuitry for the first<br>time. This seamless integration was demonstrated as is shown in Chapter 3 by creating the<br>emitters and then patterning the SixNy layer into a waveguide. This work demonstrated for<br>the first time the coupling of such single photon emitters with on-chip integrated photonics.<br>However, the integration approach demonstrated was based on the stochastic integration of<br>emitters which limits the efficiency of the devices and the possible types of devices that can<br>be designed. This is why the next stage of research focused on the development of a site-<br>controlled process for creating these single photon emitters. Remarkably, it was found that<br>if the SixNy and SiO2 are nanostructured into nanopillars and then annealed then a single<br>photon emitter forms over 65% of the time within the nanopillar! Due to the lithography<br>defined nature of this process for creating the single photon emitters the first multi-mask<br>integration process was also developed and demonstrated. This fabrication process was used<br>to demonstrate the integration of several thousand single photon emitters with complex<br>integrated photonic structures such as topology optimized couplers. These developments<br>has generated a great deal of excitement due to the inherent scalability of the approach and<br>it’s obvious applications for the development of very large scale integrated (VLSI) on-chip<br>quantum photonic systems.</p>

<p><br></p><p dir="ltr">Over the past decade, optical frequency combs have spurred significant advancements in both classical ultrafast optics and quantum optics. My research contributes to these two fields, catering to applications in precision metrology and optical networking. In the domain of quantum optics, the study delves into biphoton frequency combs with time-energy entanglement, employing novel electro-optic modulation schemes to enhance sensitivity and enable precise measurements of temporal correlations. Additionally, Bell states, a crucial class of entangled quantum bases, are generated in the frequency domain, showcasing their utility in delay metrology and quantum cryptographic protocols. </p><p dir="ltr">In the realm of classical optical frequency combs, this work explores dynamic steering of pulsed optical beams, holding promise for applications in imaging and remote sensing. The concept of time-efficient dynamic beam steering using a spatial array of optical frequency combs is elucidated and experimentally demonstrated through the utilization of a high-resolution spectral disperser, specifically a virtually imaged phased array (VIPA). Furthermore, integrated photonic designs featuring wavelength-selective switches and spectral dispersers are proposed to enable a versatile on-chip implementation of the beam steering approach. In sum, this research leverages the capabilities of classical and quantum optical frequency combs, with implications for emerging applications such as distributed sensing, quantum networking, and light detection and ranging (LIDAR).</p>

<p dir="ltr">Quantum-enhanced approaches enable high-resolution imaging and sensing with signal-to-noise ratios beyond classical limits. However, operating in the quantum regime is highly susceptible to environmental influences and experimental conditions. Implementing these techniques necessitates highly controlled environments or intricate preparation methods, which can restrict their practical applications. This thesis explores the practical applications of quantum sensing, focusing on thermal sensing with bright quantum sources in biological and electronic contexts. Additionally, I discuss the development of a multimode source for quantum imaging applications and an on-chip atomic interface for scalable light-atom interactions. I built all the experimental setups from the beginning; a microscope setup for nanodiamond-based thermal sensing inside living cells, a four-wave mixing setup using a Rb cell for thermal imaging of microelectronics and multimode source, and a vacuum chamber for on-chip atomic interface.</p><p dir="ltr">Quantum sensing can be realized using atomic spins or optical photons possessing quantum information. Among these, color centers inside diamonds stand out as robust quantum spin defects (effective atomic spins), maintaining their quantum properties even in ambient conditions. In this thesis, I studied the role of an ensemble of color centers inside nanodiamonds as a probe of temperature in a living cell. Our approach involves incubating nanodiamonds in endothelial culture cells to achieve sub-kelvin sensitivity in temperature measurement. The results reveal a temperature error of 0.38 K and a sensitivity of 3.46 K/sqrt(Hz)<i> </i>after 83 seconds of measurement. Furthermore, I discuss the constraints of nanodiamond temperature sensing in living cells, propose strategies to surmount these limitations, and explore potential applications arising from such measurements.</p><p dir="ltr">Another ubiquitous quantum probe is light with quantum properties. Photons, the particles of light, can carry quantum correlations and have minimal interactions with each other and, to some extent, the environment. This capability theoretically allows for quantum-enhanced imaging or sensing of sample’s properties. In this thesis, I report on the demonstration of quantum-enhanced temperature sensing in microelectronics using bright quantum optical signals. I discuss the first demonstration of quantum thermal imaging used to identify hot spots and analyze heat transport in electronic systems.</p><p dir="ltr">To achieve this, we employed lock-in detection of thermoreflectivity, enabling us to measure temperature changes in a micro-wire induced by an electric current with an accuracy better than 0.04 degrees, averaged over 0.1 seconds. Our results demonstrate a nearly 50 % improvement in accuracy compared to using classical light at the same power, marking the first demonstration of below-shot-noise thermoreflectivity sensing. We applied this imaging technique to both aluminum and niobium-based circuits, achieving a thermal resolution of 42 mK during imaging. We scanned a 48 × 48 μm<i> </i>area with 3-4 dB squeezing compared to classical measurements. Based on these results, we infer possibility of generating a 256×256 pixel image with a temperature sensitivity of 42 mK within 10 minutes. This quantum thermoreflective imaging technique offers a more accurate method for detecting electronic hot spots and assessing heat distribution, and it may provide insights into the fundamental properties of electronic materials and superconductors.</p><p dir="ltr">In transitioning from single-mode to multimode quantum imaging, I conducted further research on techniques aimed at generating multimode quantum light. This involved an in-depth analysis of the correlation characteristics essential for utilizing quantum light sources in imaging applications. To achieve the desired multimode correlation regime, I developed a system centered on warm Rubidium vapor with nonlinear gain and feedback processes. The dynamics of optical nonlinearity in the presence of gain and feedback can lead to complexity, even chaos, in certain scenarios. Instabilities in temporal, spectral, spatial, or polarization aspects of optical fields may arise from chaotic responses within an optical <i>x</i>(2) or <i>x</i>(3) nonlinear medium positioned between two cavity mirrors or preceding a single feedback mirror. However, the complex mode dynamics, high-order correlations, and transitions to instability in such systems remain insufficiently understood.</p><p dir="ltr">In this study, we focused on a <i>x</i>(3) medium featuring an amplified four-wave mixing process, investigating noise and correlations among multiple optical modes. While individual modes displayed intensity fluctuations, we observed a reduction in relative intensity noise approaching the standard quantum limit, constrained by the camera speed. Remarkably, we recorded a relative noise reduction exceeding 20 dB and detected fourth-order intensity correlations among four spatial modes. Moreover, this process demonstrated the capability to generate over 100 distinct correlated quadruple modes.</p><p dir="ltr">In addition to conducting multimode analysis to develop a scalable imaging system, I have explored methodologies aimed at miniaturizing light-atom interactions on a chip for the scalable generation of quantum correlations. While warm atomic vapors have been utilized for generating or storing quantum correlations, they are plagued by challenges such as inhomogeneous broadening and low coherence time. Enhancing control over the velocity, location, and density of atomic gases could significantly improve light-atom interaction. Although laser cooling is a common technique for cooling and trapping atoms in a vacuum, its implementation in large-scale systems poses substantial challenges. As an alternative, I focused on developing an on-chip system integrated with atomic vapor controlled by surface acoustic waves (SAWs).</p><p dir="ltr">Surface acoustic waves are induced by an RF signal along the surface of a piezoelectric material and have already been proven to be effective for manipulating particles within microfluidic channels. Expanding upon this concept, I investigated the feasibility of employing a similar approach to manipulate atoms near the surface of a photonic circuit. The interaction between SAWs and warm atomic vapor is expected as a mechanism for controlling atomic gases in proximity to photonic chips for quantum applications. Through theoretical analysis spanning molecular dynamics and fluid dynamics regimes, I identified the experimental conditions necessary to observe acoustic wave behavior in atomic vapor. To validate this theory, I constructed an experiment comprising a vacuum chamber housing Rb atoms and a lithium niobate chip featuring interdigital transducers for launching SAWs. However, preliminary experimental results yielded no significant signals from SAW-atom interactions. Subsequent analysis revealed that observing such interactions requires sensitivity and signal-to-noise ratio (SNR) beyond the capabilities of the current setup. Multiple modifications, including increasing buffer gas pressure and mitigating RF cross-talk, are essential for conclusively observing and controlling these interactions.</p>