Related papers: Basis-neutral Hilbert-space analyzers
The efficient creation and detection of spatial modes of light has become topical of late, driven by the need to increase photon-bit-rates in classical and quantum communications. Such mode creation/detection is traditionally achieved with…
Time delays between lensed multiple images have been known to provide an interesting probe of the Hubble constant, but such application is often limited by degeneracies with the shape of lens potentials. We propose a new statistical…
Many basis sets for electronic structure calculations evolve with varying external parameters, such as moving atoms in dynamic simulations, giving rise to extra derivative terms in the dynamical equations. Here we revisit these derivatives…
The classical Fourier analysis of a time signal, in the discrete sense, provides the frequency content of signal under the assumption of periodicity. Although the original signal can be exactly recovered using an inverse transform, the time…
Based on diffraction theory and the propagation of the light, Fourier optics is a powerful tool allowing the estimation of a visible-range imaging system to transfer the spatial frequency components of an object. The analyses of the imaging…
We analytically demonstrate the emergence of surface non-Hermitian boundary contributions that appear in an extended form of the quantum Ehrenfest theorem and are crucial (although so far overlooked) in the calculation of optical matrix…
The optical elements comprised of sub-diffractive light scatterers, or metasurfaces, hold a promise to reduce the footprint and unfold new functionalities of optical devices. A particular interest is focused on metasurfaces for manipulation…
Delay coordinates are a widely used technique to pass from observations of a dynamical system to a representation of the dynamical system as an embedding in Euclidean space. Current proofs show that delay coordinates of a given dynamical…
In this chapter, the Hilbert space framework in the mathematical theory of composite materials is introduced for studying the properties of effective operators. The goal is to introduce some of the key concepts and fundamental theorems in…
Let $A$ be a normal operator in a Hilbert space $\mathcal{H}$, and let $\mathcal{G} \subset \mathcal{H}$ be a countable set of vectors. We investigate the relations between $A$, $\mathcal{G}$ , and $L$ that makes the system of iterations…
We analyze the effects of aperture finiteness on interferograms recorded to unveil the modal content of optical beams in arbitrary basis using generalized interferometry. We develop a scheme for modal reconstruction from interferometric…
A fundamental limit to the sensitivity of optical interferometry is thermal noise that drives fluctuations in the positions of the surfaces of the interferometer's mirrors, and thereby in the phase of the intracavity field. Schemes for…
Atom interferometry is a natural laboratory for precision tests of general relativity, but there is no simple relationship between atom interferometer phase and geometric properties of spacetime. Here we show that a different atom…
A class of pseudo-hermitian quantum system with an explicit form of the positive-definite metric in the Hilbert space is presented. The general method involves a realization of the basic canonical commutation relations defining the quantum…
The Hermite-Gaussian (HG) modes make up a complete and orthonormal basis, which have been extensively used to describe optical fields. Here, we demonstrate, for the first time to our knowledge, deep learning-based modal decomposition (MD)…
Cancellation of laser frequency noise in interferometers is crucial for attaining the requisite sensitivity of the triangular 3-spacecraft LISA configuration. Raw laser noise is several orders of magnitude above the other noises and thus it…
Non-linear Fourier analysis on compact groups is used to construct an orthonormal basis of the physical (gauge invariant) Hilbert space of Hamiltonian lattice gauge theories. In particular, the matrix elements of the Hamiltonian operator…
It is shown that an aberrated wavefront incident upon a Fabry-Perot optical cavity excites higher order spatial modes in the cavity, and that the spectral width and distribution of these modes is indicative of the type and magnitude of the…
Recently, many evidences demonstrate that partial Differential Phase Shift Keying (i.e., when the delay inside the Delay Interferometer is shorter than the symbol period) can partially compensate the signal deformation caused by spectrally…
Hong-Ou-Mandel interference, the fact that identical photons that arrive simultaneously on different input ports of a beam splitter bunch into a common output port, can be used to measure optical delays between different paths. It is…