With the advent of the information era, the ever-growing need for bandwidth and computing power is calling for the development of highly integrated and compact photonic circuits where controlling light at the nano-scale becomes the most critical aspect of information processing and transfer. However, the inherent cross-talk in densely packed waveguides is a major roadblock toward ultra-high density photonic integrated circuits. As a result, the diffraction limit is often considered as the lower bound for ultra-dense integrated photonics circuits. In recent years, analogies between light propagation in waveguides and atomic physics dynamics were explored leading to non-intuitive light propagation patterns in waveguides.

In this dissertation we discuss the application of the Adiabatic Elimination concept from atomic physics into integrated photonics. We experimentally demonstrate that this scheme allows the control via a dark mode of the coupling between two outer waveguides in a three-waveguide configuration. In particular, we show that at the nano-scale, where higher order couplings occur, a zero coupling between all the waveguides can be achieved, thus allowing perfect shielding in very dense waveguides configuration. We also show the applicability of the Adiabatic Elimination in larger arrays of waveguides.

We conclude by showing how dark mode interaction applied to a plasmonic system leads to a significant linewidth narrowing of the plasmonic resonance thus reducing the losses typically associated to these systems.

Metamaterials are artificial materials that consist of subwavelength unit cells (meta-atoms). They attain their electromagnetic properties from the unit cell response rather than the constituent materials, and can be designed to exhibit properties that are not readily found in natural materials. In the past decade, the study of metamaterials has opened up a route to many exciting applications, such as superresolution imaging and invisibility cloaks.

In recent years, metasurfaces, which can be considered as two-dimensional metamaterials, have attracted intensive research interests. Due to their reduced dimensionality, metasurfaces are much easier to fabricate and yet offer a higher degree of freedom in molding the flow of waves (optical, acoustic), compared to bulk metamaterials. Being optically thin, metasurface has reduced absorptive loss and thus offers higher efficiency. Metasurfaces utilize resonances to achieve abrupt phase shifts on subwavelength scale distances, in contrast to traditional optical devices that rely on propagation effect.

We are interested in investigating non-conventional interactions between light and meta-atoms. We show that by introducing novel types of light-matter interactions mediated by metamaterials, new degrees of freedoms can be elevated for precise controlling of light and matter at the nanoscale.

This dissertation consists of three independent studies: 1. We design a color sorting metasurface under the regime where neighboring meta-atoms are strongly coupled. The coupling enabled enhanced quality factor and reduced detrimental crosstalk, leading to a color sensor with a pixel size below the diffraction limit. 2. We study the interaction of metasurface with quantum light. By engineering the quantum vacuum by a phase gradient metasurface, we theoretically show that quantum interference and coherence and be induced in emitter transitions. 3. We investigate the magnetic interactions between light and meta-atoms that exhibit artificial optical magnetism, and perform the first demonstration that magnetic interactions can be applied to trap and manipulate nanoscopic particles.

Light-matter interactions critically exist in our life, ranging from photosynthesis to the optical high-speed Internet and datacenters. The quantum nature of light and its interactions with matter not only provide us the fundamental understanding of the subject but also enable the revolutionary fields of quantum information science and technologies. In this dissertation, I present our study of quantum light-matter interactions in emergent two-dimensional platforms such as van der Waals materials and nano-structured metasurface. The demonstrated novel physics and unprecedented control capability expand our knowledge on light-matter interactions and promise future applications in quantum communication and quantum computation.

The dissertation consists of three parts. The first part investigates quantum single-photon emission from color centers in van der Waals hexagonal boron nitride. We characterize those superb single-photon emitters and demonstrate the giant Stark effect of photon energy at room temperature. The surprisingly large 31 meV Stark shift is achieved by applying huge in-plane electric fields on scale of 0.1 V/nm. Moreover, we report, for the first time, the angle-resolved Stark effect in solid-state single-photon emitters by rotating the field direction. A permanent electric dipole is uncovered, which unveils that both inversion and three-fold rotation symmetries are broken at the color center. The remarkable giant Stark effect and the significant structural information of the color center pave a way towards the scalable solid-state quantum technologies at room temperature.

The second part focuses on nonlinear optics at excited states of exciton polaritons, the partial-light partial-matter quantum quasiparticles, in microcavity containing monolayer WS2. We directly probe the excited states of exciton polaritons by utilizing valley sensitive nonlinear selection rules. Specifically, we unravel the valley-dependent dark 2p excited states by resonant two-photon luminescence excitation spectroscopy. Moreover, we look into the dynamically unstable upper polariton band by the instantaneous second harmonic generation spectroscopy. Our study of the excited states of exciton polaritons in two dimensional materials clears the way for room-temperature valley polariton condensation and full control of these polaritons for quantum applications.

The third part is on steering quantum photon-photon interaction mediated by two-dimensional metasurface. We, for the first time, propose and experimentally demonstrate that the rotation of metasurface enables a new degree of freedom in optical quantum interference through its unique anisotropic phase responses. Specifically, we show that the output of two-photon interference can be dynamically tuned to be bunching state, split state, or their arbitrary intermediate state, by simply rotating the metasurface. Consequently, the effective photon-photon interaction at metasurface beam-splitter can be manipulated continuously from attractive to repulsive. Our metasurface opens a door for both fundamental quantum photon-photon interaction and the development of innovative quantum gates, algorithms and computing models.

The previous century was defined to a major extent by the digital revolution, which ushered in the information age. This rapid proliferation and improvement of electronic technology continues to have far-reaching effects on human existence. Similarly, advances in photonics have the potential to lead to technology that drastically changes our lives. So far, the vast potential of photonics, and especially nanophotonics, has not resulted in such sweeping societal change. While the laser, LED, and photovoltaic cell serve important, and increasing, functions, technological advances in photon control at the nanoscale are required for the full potential of photonics for computing, medicine, and energy to be realized. In this dissertation, we examine some methods and devices that can address these needs in photonics, particularly by exploiting the refractive index of materials, the phase of light, and the relation between the two.

The first chapter focuses on controlling the refractive index of silicon by inducing spatially varying porosity. This technique enables the fabrication of gradient index devices that can control light’s propagation through the device to a degree that is not possible with traditional optical elements. By using the transformation optics design technique, it is possible to design a device with complete control over the path of light in the device, limited only by the material properties available. Using photoelectrochemical etching, we demonstrate the ability to control the refractive index of light in a range from 1.2 to 2.1 in devices that can be as large as centimeters, a combination not possible with other methods. This method is used to fabricate gradient index waveguides and Min˜ano concentrators, ideal optical concentrators, which are of particular interest in photovoltaics.

The next two chapters focus on using nonlinearity to manipulate light. First, the thermo- optic effect is used to design a dynamically self-assembled band structure in a distributed Bragg reflector, which exhibits reconfigurability of its transmission and reflection properties as well as self-healing to mitigate the effects of defects in the device structure. Next, a metasurface, a subwavelength array of resonant antennas is used to generate third harmonic frequency light and directly impart phase delays to it to control its reflection and refraction. Generalized laws of reflection and refraction for nonlinear harmonic generation at an interface with phase discontinuities are developed and experimentally confirmed, and asymmetric transport, which is predicted by these laws, is demonstrated. Asymmetric transport is critical for the development of integrated photonics for computing applications.

In the final section, a technique for integrating quantum dots, nanoscale light sources, with other photonic components is demonstrated. The quantum dots are incorporated into electron beam resist materials in controlled concentrations and patterned with electron beam lithography, which can precisely control their location. Single quantum dots serve as non- classical emitters, capable of generating single photons necessary for quantum computing and many other emerging fields in quantum optics.

Since the discovery of graphene in 2004, there has been a tremendous effort in materials science, physics, and chemistry to isolate and research the properties of other two-dimensional compounds. From a historical view, these pursuits and interests in these materials may seem frivolous, as the entire field of nanomaterials has moved from zero-dimensional quantum dots, to one-dimensional carbon nanotubes, to present day two-dimensional materials. However, the uniform and large scale growth of these materials is definitely a factor which has contributed to this field's longevity in research and driven interest in future device integration. In addition, the dangling bond free surface and chemical stability has played an important role in the fabrication of such devices and observation of unique physical and chemical phenomena.

In particular, the lack of bonding in the out-of-plane direction means that these bulk crystals are only held together by van der Waals forces. Thus, the material's layer geometry has a significant effect on the van der Waals crystal's observable properties. We demonstrate how the layer stacking geometry can significantly alter the nonlinear optical properties of the crystal, as shown with second harmonic generation. Furthermore, these two-dimensional crystals allows for a unique opportunity to artificially create nanomaterials composed of distinct crystals, so-called van der Waals heterostructures. These heterostructures may be assembled using chemical means, or via manual transfer, both of which are extensively covered in this thesis. Chemically assembled heterostructures of single layer graphene and the transition metal dichalcogenide molybdenum disulfide form all-two-dimensional transistors, capable of demonstrating logic. Manually transferring exfoliated crystals can lead to both the demonstration of devices, as well as the observation of new physical phenomena, such as the Coulomb drag of transition metal dichalcogenides.

The electromagnetic force is one of the four basic interactions discovered in nature and it plays an essential role in determining the internal properties of most matter seen in daily life. In this dissertation, we present the endeavor on exploiting electromagnetic fields to actively control the dynamics of various nanoscopic matter, including atomic ion rings, monolayer semiconductors, and nanomechanical membranes. The achieved controls open up unique opportunities to study fundamental many-body quantum physics and to facilitate information and energy transfer processes at the nanoscale.

This dissertation consists of three sets of experiments. 1. We design and fabricate a surface-electrode Paul trap and confine up to fifteen 40Ca+ ions into a microscopic ring using radio-frequency electric fields. The achieved unprecedented circular symmetry enables the first observation of localization-delocalization transitions of ion rings at millikelvin temperatures. 2. We propose and demonstrate a scheme to couple electron valley degree-of-freedom with macroscopic mechanical motion using a magnetic field gradient perpendicular to suspended monolayer semiconducting transition metal dichalcogenides (for example MoS2). Direct transduction of valley excitation into mechanical states is realized for the first time. 3. We perform the first experiment to probe and manipulate the phonon energy transfer driven by quantum fluctuations of electromagnetic fields (the Casimir effect). With a delicate approach to place two nanomechanical membranes parallel and close to each other, we realize the first strong Casimir phonon coupling condition and thus observe the thermal energy exchange across vacuum between individual phonon modes.

The coupling of mechanical, electrical and optical properties of materials becomes more prominent when the dimensionality is reduced to two, such that the external manipulation from the higher dimension can directly apply to the interior, and the Coulomb interaction is greatly enhanced. Among the existing two-dimensional systems, the Group VIB transition metal dichalcogenides (TMDC) are semiconductors with direct band gap. They are potential solutions for field-effect transistors with 5 nanometer node and beyond, as well as broadband nano-optoelectronics. In addition, their broken inversion symmetry and spin-orbit coupling together give rise to a pair of nonequivalent valleys as energy-efficient information carriers.

This dissertation first presents the quasi-static measurement of piezoelectric effect, i.e. the generation of strain through electric field, in ultra-thin freestanding molybdenum disulfide (MoS₂) films by atomic force microscopy. Such van der Waals layered materials overcame the thermodynamic instability when the thickness of traditional bulk materials approaches single-molecular scale. The ambient piezoelectric coefficient of a single layer, e₁₁ = 2.9×10^-10 C/m, represented the intrinsic symmetry breaking and was free from substrate effects. The dependence of piezoelectric response on number of layers and angle of applied electric field agreed with the crystalline symmetry. In complimentary to the natural in-plane piezoelectricity, the single-layer TMDC was chemically engineered to possess out-of-plane piezoelectricity by selectively replacing the chalcogen atoms on one side. The measured piezoelectric coefficient of d₃₃ = 0.1 pm/V could be increased further by varying the substitute atoms. These discoveries are applicable to low-power logic switches for computing and electromechanical sensors at molecular level.

At higher frequency, the electromechanical coupling is replaced by phonon-photon interaction, such as Raman scattering and infrared absorption. We characterized the coupling between quasi-static strain and the optical phonon vibration as a result of mechanical nonlinearity in MoTe₂ by Raman spectroscopy. Small Grüneisen parameters of 0.45 and 0.25 were found for in-plane and out-of-plane optical phonon respectively under in-plane strain. More importantly, the hexagonal lattice enabled unique chiral phonons with intrinsic angular momentum and magnetic moment, that are capable of transporting electrons between valleys. We estimated the phonon energy from resonant Raman scattering, which came from both defect-activation and double-resonance process, and observed the phonon-assisted intervalence band

transition by transient infrared spectroscopy. Infrared spectrum showed distinctive steps from virtual electronic bands projected by the absorption and emission of the valley phonon, in accordance to our theoretical model. The investigation of the phononic chirality and angular momentum conservation by probing the circular polarization of the absorption is ongoing. The valley phonon has potential in information processing and ultrafast optoelectronic modulation.

Development of new instruments results in new discoveries and opens up new research directions. In particular novel imaging and optogenetics stimulation techniques merging classical photonics with other fields have a great potential to advance medicine, biology, physics, chemistry and engineering.

Here we present the development of two novel, plasmonic-aided imaging techniques (BOM and BEAST) and describe discovery of a new activity driven plastic alteration of dendritic excitability, which was enabled by utilizing a new dynamic light modulation scheme for neural activation.

The first technique, termed Brownian Emitter Adsorption Superresolution Technique (BEAST), is a novel single molecule super-resolution technique, which relies on stochastic adsorption of molecules to measure surface enhancement of an electromagnetic field. We used BEAST to map - for the first time - the electromagnetic field within single hotspots as small as 15nm on a metal surface with a resolution down to 1.2 nm. The hotspots are localized optical modes on the surface of noble metals exhibiting a giant enhancement effect and have attracted a broad interest, from understanding their mechanism to developing practical applications. However, characterizing these hotspots has been difficult, due to the limited resolution of current imaging techniques. BEAST improves the resolution significantly to single nanometer level, which allowed us to image the EM field inside single hotspots for the first time and discovered that the field distribution follows an exponential decay - strong experimental evidence for Anderson localization mechanism of the hotspots, which has been extensively debated over the last decades.

The second imaging technique described here - Brownian Optical Microscopy (BOM) - is the first technique to offer true three-dimensional imaging with nano-resolution. Scanning probe microscopy (SPM), which is commonly used to image 3D topology now, offers nanoscopic resolution but the use of the tip and slow scanning speed limits its throughput and makes it unable to image high aspect ratio or cavities. On the other hand optical tomography is able to image complex three-dimensional shapes but its resolution is limited to the micron range, while electron microscopy offers higher resolution but requires imaging in vacuum. BOM does not suffer from these limitations. It is an all-optical imaging technique, which relies on Brownian motion of gold nanoparticles to sample the shape of the object, akin to scanning the sample in parallel by millions of small, freely diffusing SPM tips. In BOM an object of an arbitrary shape is placed in a solution of randomly diffusing nanoparticles, which are illuminated with an evanescent field so that the scattering intensity of resonant NPs correlates with their vertical position. We demonstrate that BOM is capable of imaging complex shapes with 30nm resolution in all three dimensions, including overhang samples, which cannot be imaged with any other technique.

Finally we use optogenetics combined with dynamic light modulation to explore plasticity of dendritic excitability. It was long believed that that plasticity, which plays a crucial role in the formation of neural circuits, is based on alteration of synaptic weights. Recent studies indicate that modulations of dendritic excitability may contribute the other part of the engram and critically impact the emergence of complex network behavior. However, a fundamental question remains whether dendritic excitability is controlled by synaptic inputs or arises independently. We used a novel optical system, which offers high spatiotemporal control over neural stimulation to decouple synaptic and non-synaptic activity and observed plasticity of local dendritic excitability which is autonomous from synaptic plasticity and arises only as a result of local activity. This persistent change in dendritic excitability arises as a result of a back propagating action potential interacting with simultaneous dendritic depolarization and triggering MEK-regulated phosphorylation of Kv4.2 by CamKII. This major discovery of activity dependent dendritic plasticity sheds new light on the role of dendrites in plasticity and may profoundly impact our fundamental understanding of neural plasticity as well as a number of neurodegenerative diseases where Kv4.2 channel deregulation is thought to play a crucial role.

Acoustic metamaterials are artificial materials designed to realize unprecedented properties such as super-resolution imaging, asymmetric wave transport, cloaking, etc. The critical material parameters considered for the design of acoustic metamaterials are mass density and bulk modulus. Previous studies have demonstrated the existence of acoustic metamaterials with negative effective mass density and/or bulk modulus. In this thesis, the realization of acoustic metamaterials with extreme materials parameters including simultaneous zero effective mass density and infinite bulk modulus as well as complex-valued parameters is discussed. Metamaterials with simultaneous zero density and infinite bulk modulus exhibit zero refractive index properties called acoustic double zero index metamaterials in which the propagating sound wave has an infinite phase velocity. This infinite phase velocity results in an infinite wavelength, such that the propagating acoustic wave has a uniform phase inside the metamaterial, which can be used for the realization of acoustic wave tunneling and collimation. Our designed acoustic double zero index metamaterial is induced by a Dirac-like cone dispersion at the Brillouin zone center associated with triply degenerated monopolar and dipolar modes. The monopolar and dipolar modes induce an infinite bulk modulus and a zero mass density, respectively. Meanwhile, the simultaneous zero density and infinite bulk modulus induce a finite acoustic impedance, which can be designed to match with the background medium and enhance the transmission through the boundaries between the metamaterial and the surroundings.

On the other hand, metamaterials with complex-valued material parameters are related to the attenuation and amplification of acoustic waves. When the loss and gain inside the metamaterial are exactly balanced, the medium is parity-time (PT) symmetric so that the wave propagation is invariant under PT operator. Such PT symmetric systems contain two phases: "exact" and "broken" phases, with exceptional points where the system exhibits unidirectional transparency marking the transition between these two phases. Even though the real parts of the material parameters are usually non-dispersive, the imaginary parts can vary significantly with changing frequencies. In this case, the PT symmetric condition is satisfied only within a narrow frequency band, while the exceptional points can appear at different frequencies. This limitation challenges the observation of the exceptional points and the realization of unidirectional transparency. A systematic method to access these exceptional points can be achieved by tuning the spacing between the loss and gain materials, which modulates the multiple scattering inside the system to realize unidirectional transparency.

In most cases, acoustic metamaterials consists of deep subwavelength resonators operating around their resonance frequencies. When these resonators are arranged in a two-dimensional surface, they form a metasurface which modulates the phase of acoustic wave and reshape the propagating wavefront. This property can be used for the design of an ultrathin acoustic carpet cloak or diffuser, as shown by the metasurface formed by 3D printed Helmholtz resonators in this dissertation. In the case where the target object contains rapidly changing profiles, the cloaking effect of the designed carpet cloak is preserved. However, the design of acoustic diffuser with rapidly changing profiles requires resonators that can independently modulate the amplitude and phase of the reflected wave.

The control of the phase of acoustic waves enables the generation of vortex beams, which carry orbital angular momentum (OAM) of sound. A topological charge is defined to characterize the amount of OAM carried by the wave. Acoustic vortex beams with different topological charges are orthogonal to each other, which form independent channels to convey information when being multiplexed. Such OAM multiplexing technique increases the information capacity and spectral efficiency for acoustic communication, which holds the potential to increase the communication speed significantly. Besides OAM, acoustic spin defined as sound waves with rotating particle velocity field can be generated. Spin dependent propagation can be observed in a metamaterial waveguide formed by periodic grooves. When a probe meta-atom with acoustic dipole resonance is placed in wave with acoustic spin, a torque induced by spin matter interaction can be measured. The difference between the OAM and spin can be observed by the motion of probe particle. A probe particle moves along a circular trajectory centered at the field center when placed in wave with OAM, while rotates about its own axis when placed in wave with spin.

The interplay between charge, spin, and orbital degrees of freedom in many-electron solid systems results in a large variety of strongly correlated phenomena. Correlation of electrons lies in the heart of the strongly correlated physics, but also masks the essential physics leading to a certain observed phenomenon. The quest of a minimal model material and clean manipulation method is sometimes regarded as the key to solve problems in the field. Even though layered properties of certain strongly correlated materials have been known for decades, methods of preparation and manipulation of atomically thin materials have to wait until recent years. The last two decade have witnessed the booming of research in two-dimensional van der Waals materials and various methods have been developed for layered materials. The current development in this area allows the application of these methods into more complicated systems in order to search for the essential physics covered in the bulk compounds. In this dissertation, we explore the application of these techniques in the study of strongly correlated physics in $1T$-TaSe\textsubscript{2}, and Fe\textsubscript{3}GeTe\textsubscript{2}. The fabrication of high-quality samples enables the detection of intrinsic physics in these systems. Disentangling the in-plane and out-of-plane physics through mechanical exfoliation provides a minimal model of a bulk material and helps solve the mystery of metallic properties in bulk $1T$-TaSe\textsubscript{2}. The flexibility in the formation and tuning of various heterostructures provides not only interesting systems to study, but also useful tools to characterize and manipulate electronic states in layered strongly correlated systems. We use a novel Kondo heterostructure to probe monolayer magnetic properties in $1T$-TaSe\textsubscript{2}, which is challenging for bulk sensitive detection methods. On the other hand, due to their special layered structure, two-dimensional strongly-correlated systems may exhibit novel properties not present in the bulk, as in the case of Fe\textsubscript{3}GeTe\textsubscript{2} nanoflakes. We have discovered unusual magnetotransport properties in this system. Easy access of properties in two dimensional systems allows for a thorough diagnosis of this phenomenon. We hope to provide new perspectives from the study of constituents of complicated bulk materials.