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The propagation and scattering of electromagnetic waves in magnetized plasmas in a state where a global mode has been established or is in turbulence, are of theoretical and experimental interest in thermonuclear fusion research. Interpreting experimental results, as well as predicting plasma behavior requires the numerical solutions of the underlying physics, that is, the numerical solution of Maxwell equations under various initial conditions and, under the circumstances, complex boundary conditions. Casting, the underlying equations in a coordinate free form that exploits the symmetries and the conserved quantities in a form that can easily encompass a variety of initial and boundary conditions is of tantamount importance. Pursuing this task we utilize the advantages the Clifford Algebras can possibly provide. For simplicity we deal with a cold multi-species lossless magnetized plasma. The formulation renders a Dirac type evolution equation for am augmented state that consists of the electric and magnetic field bivectors as well as the polarizations and their associated currents for each species. This evolution equation can be dealt with a general spatial lattice disretization scheme. The evolution operator that dictates the temporal advancement of the state is Hermitian. This formulation is computationally simpler whatever the application could be. However, small wavelength capabilities (on the Debye length scale) for spatially large systems (magnetic confinement devices) is questionable even for conventional super-computers. However, the formulation provided in this work it is entirely suitable and it can be directly transferred in a quantum computer. It is shown that the simplified problem in the present work could be suitable for contemporary rudimentary quantum computers., Comment: 24 pages

Motivated by the contemporary advances in quantum implementation of non-unitary operations, we propose a new dilation method based on the biorthogonal representation of the non-unitary operator, mapping it to an isomorphic unitary matrix in the orthonormal computational basis. The proposed method excels in implementing non-unitary operators whose eigenvalues have absolute values exceeding one, when compared to other dilation and decomposition techniques. Unlike the Linear Combination of Unitaries (LCU) method, which becomes less efficient as the number of unitary summands grows, the proposed technique is optimal for small-dimensional non-unitary operators regardless of the number of unitary summands. Thus, it can complement the LCU method for implementing general non-unitary operators arising in positive only open quantum systems and pseudo-Hermitian systems., Comment: 8 Pages, 3 Figures

Compact photonic systems that offer high frequency stability and low noise are of increasing importance to applications in precision metrology, quantum computing, communication, and advanced sensing technologies. However, on-chip resonators comprised of dielectrics cannot match the frequency stability and noise characteristics of Fabry-Perot cavities, whose electromagnetic modes live almost entirely in vacuum. In this study, we present a novel strategy to interface micro-fabricated Fabry-Perot cavities with photonic integrated circuits to realize compact, high-performance integrated systems. Using this new integration approach, we demonstrate self-injection locking of an on-chip laser to a milimeter-scale vacuum-gap Fabry-Perot using a circuit interface that transforms the reflected cavity response to enable efficient feedback to the laser. This system achieves a phase noise of -97 dBc/Hz at 10 kHz offset frequency, a fractional frequency stability of 5*10-13 at 10 ms, a 150 Hz 1/pi integral linewidth, and a 35 mHz fundamental linewidth. We also present a complementary integration strategy that utilizes a vertical emission grating coupler and a back-reflection cancellation circuit to realize a fully co-integrated module that effectively redirects the reflected signals and isolates back-reflections with a 10 dB suppression ratio, readily adaptable for on-chip PDH locking. Together, these demonstrations significantly enhance the precision and functionality of RF photonic systems, paving the way for continued advancements in photonic applications.

Using the Madelung transformation on a generalized scalar Gross-Pitaevski equation, a nonlinear continuum fluid equations are derived for a classical fluid. A unitary quantum lattice algorithm is then determined as a second order discrete representation of this Gross-Pitaevski equation and the simulations are compared to those using classical fluid dynamic techniques., Comment: 4 pages, 1 figure

The remarkable frequency stability of resonant systems in the optical domain (optical cavities and atomic transitions) can be harnessed at frequency scales accessible by electronics using optical frequency division. This capability is revolutionizing technologies spanning time keeping to high-performance electrical signal sources. A version of the technique called 2-point optical frequency division (2P-OFD) is proving advantageous for application to high-performance signal sources. In 2P-OFD, an optical cavity anchors two spectral endpoints defined by lines of a frequency comb. The comb need not be self-referenced, which greatly simplifies the system architecture and reduces power requirements. Here, a 2P-OFD microwave signal source is demonstrated with record-low phase noise using a microcomb. Key to this advance is a spectral endpoint defined by a frequency agile single-mode dispersive wave that is emitted by the microcomb soliton. Moreover, the system frequency reference is a compact all-solid-state optical cavity with a record Q-factor. The results advance integrable microcomb-based signal sources into the performance realm of much larger microwave sources.

Optical frequency division based on bulk or fiber optics provides unprecedented spectral purity for microwave oscillators. To extend the applications of this approach, the big challenges are to develop miniaturized optical frequency division oscillators without trading off phase noise performance. In this paper, we report a chip-scale electro-optical frequency division microwave oscillator with ultra-low phase noise performance. Dual laser sources are co-self-injection-locked to a single silicon nitride spiral resonator to provide a record high-stability, fully on-chip optical reference. An integrated electro-optical frequency comb based on a novel thin-film lithium niobate phase modulator chip is incorporated for the first time to perform optical-to-microwave frequency division. The resulting chip-scale photonic microwave oscillator achieves a phase noise level of -129 dBc/Hz at 10 kHz offset for 37.7 GHz carrier. The results represent a major advance in high performance, integrated photonic microwave oscillators for applications including signal processing, radar, timing, and coherent communications.