Enhancing Interactions Among Dipole Excitations Using Surface Plasmon Polaritons: Quantum Entanglement and Classical Interactions - (:unkn) unknown (My University, 2024)
The interaction of light with matter at the nano-scale continues to be an important research area for the application of nano-optical devices in wide ranging areas such as biosensing, light harnessing, and optical communications, to name a few. An important aspect of this is the interaction among dipole excitations (which includes classical dipole emitters, and dipole approximations of atoms, molecules, and other quantum objects), mediated by the device medium where they are located. Since the dimensions of these devices, by design, are at the nano-scale, the size of the dipole-dipole interaction space is much less than the wavelength of light in vacuum. Therefore, we can't manipulate the optical fields using traditional optical manipulation techniques in order to focus and confine the propagating radiation among the dipoles due to the size of the dipole-dipole interaction space being much less than the diffraction limit, which is roughly half a wavelength. However, this can be accomplished by designing the medium as a plasmonic waveguide that supports surface plasmon polaritons (SPPs), which are subwavelength (the wavelength of the SPPs is less than the wavelength of light in vacuum) and confined to the interface surface. Thus, we can couple the light to the SPPs to confine it and manipulate it in a subwavelength space. This enhances the interaction among the dipole excitations by providing a way to guide energy among them through the environment (the medium) they are interacting with. This allows for more efficient coupling among the dipoles, and control of the dipole-dipole interaction and the path taken in the coupling medium, which in turn allows for sensing with higher sensitivity, optimal efficiency in light harnessing, and more precise control in optical communications among the dipoles. In the case of nonreciprocal systems (plasmonic waveguides supporting non-reciprocal SPPs) we can further enhance the interaction among the dipole excitations by utilizing unidirectional (one-way) beam-like wave propagation to further control and direct the energy among them, i.e., to efficiently transport photons from one dipole to another. This is also the case for systems where beam-like wave propagation occurs, albeit in a reciprocal way, where we still have directed energy; however, the energy is not unidirectional. Considering a quantum optical system, where the dipoles are treated as two-level atoms (quantum emitters) we can also utilize a plasmonic waveguide that supports SPPs to enhance the quantum entanglement between the emitters. As was the case for the enhancement of the classical interactions, here, the use of non-reciprocal SPPs is ideal for further enhancement, control, and preservation of quantum entanglement due to the potential for unidirectional beam-like wave propagation, i.e., efficiently transporting photons from one quantum emitter to another. In this work we focus on the investigation of nonreciprocal systems, and some reciprocal systems, where there is beam-like wave propagation that can be controlled, or, in general, systems where we can potentially manipulate and control the wave propagation and direction of energy. We consider the potential application of these systems to enhance the interactions among the dipole excitations, where we consider either enhancing classical interactions or quantum entanglement. For nonreciprocal systems, we focus on achieving nonreciprocity by an alternate means to the most traditional way, which is based on the magneto-optical effect, where plasma-like materials are biased with a static magnetic field. In other words, we focus on nonreciprocal systems were nonreciprocity can be achieved without an external magnet. We first consider long-lived phonon polaritons, namely hyperbolic phonon polaritons (HPPs), which are highly confined, sub-optical wavelength vibrations in the lattice of the material. These HPPs have lower loss than SPPs because they propagate in mediums with few free electrons, and the only loss mechanisms are phonon collisions. In hyperbolic materials, the permittivities along different principal axes have opposite signs, which allows for HPPs to propagate. In the near-infrared regime, natural materials such as α-phase molybdenum trioxide (α-MoO3), among others, support HPPs. We demonstrate that given the inherent beam-like wave propagation of the HPPs in the material this type of system can potentially be used for quantum entanglement control (controlling which two-level quantum emitters (qubits) are entangled by means of changing the excitation frequency), where, surprisingly, despite the occurrence of beam-like propagation, which focuses energy between the quantum emitters, the entanglement was not enhanced over that obtained from vacuum, at least for the particular operating frequency and material configuration that was investigated. We then investigate a system that consists of two two-level emitters dominantly interacting via electric direct current induced nonreciprocal plasmonic modes of a graphene waveguide. We determine that nonreciprocal graphene plasmon polaritons are a promising candidate to mediate entanglement, where it is shown that there is good enhancement and control of entanglement over vacuum. Time-varying media, which is a rich area of research in and of itself, may also allow for more freedom and practicality in manipulating the electromagnetic response of plasmonic waveguides in time, which in turn may enable more efficient and tunable interactions among dipole excitations. A time-varying media platform consists of a system where the material parameters of the media are changed in time, which results in unique electromagnetic phenomenon not seen in spatially-varying media, e.g., frequency shifting and splitting of the incident wave at the temporal boundary. The use of a time-varying media platform allows for the utilization of temporal modulation, which, when combined with plasmonic waveguides (reciprocal or nonreciprocal), may allow for modifying the resonance or direction of energy propagation in the system. In this dissertation we start down this path by establishing the framework for a time-varying media system that supports SPPs and analyze the interaction among dipole excitations. We reserve the goal of investigating the application to quantum entanglement enhancement, control, and preservation for future work. The overarching takeaway from the work in this dissertation is that we can continue to engineer the environment that classical systems and quantum emitters interact through, in a multitude of ways, that fundamentally alters the performance of classical and quantum devices. This enables efficient and tunable interactions among dipole excitations, which is a central goal in nano-optical devices and quantum technologies.
Keywords: Plasmonic Waveguides; Quantum Entanglement; Quantum Optics; Surface Plasmon Polaritons; Time-Varying Media