Why a hole is like a beam splitter: A general diffraction theory for multimode quantum states of light

Abstract

Within the second-quantization framework, we develop a formalism for describing a spatially multimode optical field diffracted through a spatial mask and show that this process can be described as an effective interaction between various spatial modes. We demonstrate a method to calculate the quantum state in the diffracted optical field for any given quantum state in the incident field. Using numerical simulations, we also show that with single-mode squeezed-vacuum state input, the prediction of our theory is in qualitative agreement with our experimental data. We also give several additional examples of how the theory works, for various quantum input states, which may be easily tested in the lab; including two single-mode squeezed vacuums, single-and two-photon inputs, where we show the diffraction process produces two-mode squeezed vacuum, number-path entanglement and a Hong-Ou-Mandel-like effect-analogous to a beam splitter.

Angular-spectrum-based analysis on the self-healing effect of Laguerre-Gaussian beams after an obstacle

“…On the one hand, the rotational symmetry of the obstacle prevents the changes in azimuthal indexes and further enforces angular spectrum conservation. On the other hand, due to the limitation in the radial direction, different radial modes will interact and change [26]. Based on the above statement, the field amplitude after the obstacle can be described as a superposition of LG modes, all with the same azimuthal index but a range of radial indices [52,53].…”

“…Mathematically, the beams carrying OAM-Laguerre-Gaussian (LG) and Bessel-Gaussian (BG) beams-are characterized by a spiral phase term of the form exp (i θ), where and θ are azimuthal mode index and coordinate, respectively. Different azimuthal modes are orthogonal and thus form an infinite-dimensional Hilbert space [26,27], which provides a route to improve information capacity in a single photon.…”

Weak Thermal State Quadrature-Noise Shadow Imaging

“…x [19,20]. Defining N1,2 ( x) as the number operator for mode 1 or 2, correspondingly at the output ports, we can write moments of the photon-number difference op- erator N ( x) = N1 ( x) − N2 ( x) as:…”

Double-slit interferometry as a lossy beam splitter

“…Such a formalism provides an alternative to the implementation of higher-dimensional QIP using the orbital angular momentum (OAM) of light [7]. slit-diffraction based optical interferometers can be used to construct qudits encoded in spatial modes [12,13], with robustness, unlike in the case of OAM based qudits which have practical limitations in state-preparation and state-readability [7]. Another potential advantage of the multi-slit-diffraction-based interferometer is scalability of table-top experiments.…”