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IEEE Conference on Antenna Measurements & Applications

Quantum-Theoretic Numerical Study on Quantum Phase Sensing and Quantum Ghost Imaging Systems with NOON States

Dong-Yeop Na, Weng Cho Chew

Published Nov 15, 2021• 0 citations
Publisher

Abstract

We present a numerical study on the super-resolution of quantum phase sensing and ghost imaging systems operating with N00N states beyond the Rayleigh diffraction limit. Our computational simulations are based on canonical quantization via numerical mode-decomposition (CQ-NMD) [16], [17]. In the CQ-NMD process, electromagnetic fields in inhomogeneous dielectric media are canonically quantized based on macroscopic quantum electrodynamics, while eigenmodes are numerically found using computational electromagnetics methods; thus, this approach is suited for performing fully-quantum-theoretic numerical simulations on how arbitrary dielectric objects scatter entangled photon fields.

DOI
10.1109/cama49227.2021.9703461

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We present a numerical study on the super-resolution of quantum phase sensing and ghost imaging systems operating with N00N states beyond the Rayleigh diffraction limit. Our computational simulations are based on canonical quantization via numerical mode-decomposition (CQ-NMD) [16], [17]. In the CQ-NMD process, electromagnetic fields in inhomogeneous dielectric media are canonically quantized based on macroscopic quantum electrodynamics, while eigenmodes are numerically found using computational electromagnetics methods; thus, this approach is suited for performing fully-quantum-theoretic numerical simulations on how arbitrary dielectric objects scatter entangled photon fields.
We present a numerical study on the super-resolution of quantum phase sensing and ghost imaging systems operating with multimode N00N states beyond the Rayleigh diffraction limit. Our computational simulations are based on the canonical quantization via numerical mode-decomposition (CQ-NMD) [1,2], in which normal (eigen) modes of electromagnetic fields in inhomogeneous dielectric media are numerically found using computational electromagnetics methods. In the CQ-NMD framework and the Heisenberg picture, the expectation value of arbitrary observables with respect to initial quantum states of various non-classical lights can be evaluated with the use of Wick's theorem. The present numerical framework has a great potential to deal with scattering problems of entangled photons due to arbitrary dielectric objects.
We investigate quantum information preserving computational electromagnetics. To do so, we propose two different methods which are (1) numerical canonical quantization and (2) quantum finite-difference time-domain scheme. The proposed algorithms find numerical solutions of quantum Maxwell's equations involved in arbitrary inhomogeneous dielectric media based on the macroscopic theory on quantum electrodynamics; hence, they are useful to study the quantum nature of electromagnetic fields in arbitrary passive and lossless quantum optical instruments. We provide a numerical example associated with two photon interference occurring in a quantum beam splitter, which is the underlying principle of recent quantum technologies.
Quantum entanglement is a fascinating physical resource that is central to the field of quantum information processing with important applications in such areas as quantum computing, quantum communication, quantum metrology, and quantum imaging. \nIt describes the physical phenomenon in which the quantum state of a multipartite system cannot be written as consisting of constituents that are independent of each other. In this case, the state of the system is called an entangled state. In this \ndissertation, the entanglement of photons--the elementary excitations of the quantized electromagnetic field--is studied. A focus is made on a particular type of entangled states of light called the d-mode N-photon NOON state, which consists of N photons with the N photons as an ensemble appearing at d orthogonal modes simultaneously and are inseparable. \nIn quantum metrology, a field that investigates the ultimate precision of measurements of unknown physical parameters, the two-mode NOON state has been studied extensively with respect to its ability to achieve super-resolution and super-sensitivity in the estimation of a single parameter. A lot of theoretical research has been conducted on the generation of two-mode NOON states, and two-mode NOON states with up to 4 photons have been experimentally and efficiently produced. On the other hand, recently there has been increasing interest in the study of the simultaneous estimation of multiple parameters. Accordingly, the multi-mode NOON state has been attracting more and more attention in view of its potential for enhanced efficiency as compared to using multiple two-mode NOON states separately to estimate the parameters. Nevertheless, no known generation method of multi-mode NOON states with more than 2 photons or 2 modes exists so far. \nIn this dissertation, several scalable generation methods of multi-mode NOON states are proposed. These methods take advantage of multi-photon quantum interference and they can theoretically be applied to produce NOON states with an \narbitrary number of modes and an arbitrary number of photons. The intrinsic generation probability for each method is calculated, and the methods are compared in regards to their feasibility and efficiency. The advantages of using multi-mode NOON \nstates in quantum metrology are also analyzed and discussed in detail.
Quantum ghost imaging harnesses entangled photon pairs to form images using light that never directly interacts with the object. Conventional approaches rely on pixelated detectors or spatial masks, where the resolution is fundamentally limited by the pixel size and thus bounded by the Rayleigh criterion. In this work, we present a modal approach that replaces pixel-based detection with measurements in a basis of structured modes. By reconstructing images through tailored spatial modes, we decouple resolution from the physical limitations of detectors and instead tie it to the system’s optical precision and computational control. We demonstrate that even non-orthogonal modal sets can achieve high fidelity image reconstruction by exploiting modal sparsity, significantly reducing the number of required measurements. Using phase-only approximations of Hermite-Gaussian modes, we avoid the loss associated with complex amplitude modulation while retaining high reconstruction fidelity. The result is a high-resolution, high-efficiency quantum ghost imaging technique powered by structured light, opening new possibilities for photon-efficient imaging in low-light and quantum-limited regimes, such as biological microscopy and remote sensing.
We present a computational framework for canonical quantization in arbitrary inhomogeneous dielectric media by incorporating quantum electromagnetic effects into complex solutions of quantum Maxwell's equations. To do so, the proposed algorithm integrates and performs (1) numerical computation of normal modes and (2) evaluation of arbitrary products of ladder operators acting on multimode Fock states. The former is associated with Hermitian-Helmholtz linear systems using finite-element or finite-difference methods; consequently, the complete set of numerical normal modes diagonalizes the Hamiltonian operators up to floating-point precision. Its Hermiticity is retained, allowing its quantization. Then, we perform quantum numerical simulations of two-photon interference occurring in a 50:50 beam splitter to observe the Hong-Ou-Mandel effect. Our prototype model is useful for numerical analyses on various narrow-band quantum-optical multiphoton systems such as quantum metasurfaces, quantum-optical filters, and quantum electrodynamics in open optical cavities.
Quantum states of light, such as squeezed states or entangled states, can be used to make measurements (metrology), produce images, and sense objects with a precision that far exceeds what is possible classically, and also exceeds what was once thought to be possible quantum mechanically. The primary idea is to exploit quantum effects to beat the shot-noise limit in metrology and the Rayleigh diffraction limit in imaging and sensing. Quantum optical metrology has received a boost in recent years with an influx of ideas from the rapidly evolving field of optical quantum information processing. Both areas of research exploit the creation and manipulation of quantum-entangled states of light. We will review some of the recent theoretical and experimental advances in this exciting new field of quantum optical metrology, focusing on examples that exploit a particular two-mode entangled photon state – the High-N00N state.