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arXiv:1905.01112

Generalized Theoretical Approach for Analysing Optical Experiments

Arpita Maitra, Suvra Sekhar Das

Published May 3, 2019• 0 citations
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Abstract

A generalized approach towards modelling any optical experiment is presented. Beam splitter and phase retarders are described in terms of annihilation and creation operators. We notice that such description provides us a better way to analyze any optical experiment mathematically than Jones matrix algebra. We represent polarization of photon in Fock state basis. We consider recently demonstrated wave-particle superposition generation experiment (Nature Communication, 2017) and Passive BB84 with coherent light (Progress in Informatics, 2011) to test our methodology. We observe that our disciplined methodology can successfully describe the experiments with greater ease, hence offering a convenient tool for modelling any optical arrangement.

DOI
10.48550/arxiv.1905.01112

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A generalized approach towards modelling any optical experiment is presented. Beam splitter and phase retarders are described in terms of annihilation and creation operators. We notice that such description provides us a better way to analyze any optical experiment mathematically than Jones matrix algebra. We represent polarization of photon in Fock state basis. We consider recently demonstrated wave-particle superposition generation experiment (Nature Communication, 2017) and Passive BB84 with coherent light (Progress in Informatics, 2011) to test our methodology. We observe that our disciplined methodology can successfully describe the experiments with greater ease, hence offering a convenient tool for modelling any optical arrangement.
A quantum-mechanical description of the phase shifters, retarders, mirrors and beam splitters is given in the paper. The description is then applied on two types of states. On a coherent state, a classical-like state, and on a number state, hence the strict quantum state. The quantum description of a beam splitter can be found in the literature. However the description does not treat with the polarization concept. The paper is aimed to introduce quantum description of an arbitrary oriented retarder and give a description of a beam splitter which treats with the polarization.
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This study explores how optical beam splitters provide a conceptual and operational link between classical and quantum descriptions of light. In the classical picture, they are modeled through energy-conserving field amplitudes and a four-port scattering matrix, which successfully explain interference in systems such as Michelson and Mach–Zehnder interferometers. Moving to the quantum domain, the field amplitudes are replaced by bosonic creation and annihilation operators that obey the Weyl–Heisenberg algebra. Using the Glauber displacement operator, we define coherent states whose expectation values reproduce classical monochromatic fields while exhibiting Poissonian photon statistics. This unified approach shows that beam splitters diagnose the nature of incident light: coherent states yield classical interference, while indistinguishable single-photons reveal quantum signatures such as antibunching and Hong–Ou–Mandel interference. The analysis relies on operator formalism and correlation functions that capture both average-field behavior and nonclassical statistics. As beam-splitting technologies transition from bulk optics to integrated photonics and metasurfaces, this framework offers a consistent basis for modeling optical circuits across the classical-quantum divide. By highlighting the dual role of the beam splitter as a passive device and a quantum probe, we emphasize its importance for quantum optics, quantum information, and hybrid photonic platforms.
Quantum information science has traditionally relied on nonclassical resources, such as entangled photon pairs and squeezed states, to achieve measurement performance beyond classical limits. Here, we revisit the multi-pass photonic scheme reported in Nature 450, 393 (2007) to clarify the physical origin of the observed superresolution and the associated claim of supersensitivity. Using a rigorous Jones-matrix formalism, we show that the round-trip evolution of the HQMQ linear optics unit is equivalent to the product of two reflections in polarization space, resulting in an effective rotation operator. This equivalence reveals that the accumulated phase arises from coherent polarization-state rotation on the Poincare'e sphere. The resulting phase accumulation is interpreted geometrically as a progressive realignment of the polarization state during successive forward and backward propagations. To validate the theoretical model, a classical-wave implementation is experimentally conducted, analyzed, and compared with the corresponding Jones-matrix solution. Finally, the scaling behavior of the Fisher information is analyzed to examine the origin of the claimed supersensitivity. The results are further compared with a recently developed coherence de Broglie wavelength framework, which achieves identical superresolution through repeated coherent interactions in a cascaded interferometeric architecture.
The recent development of experimental techniques to implement the creation and the annihilation operators in the optical domain has found great interest for quantum information manipulation and processing. Quantum states of light obtained by the application of alternated sequences of the creation and annihilation operators a^†\hat{a}^\daggera^† and a^\hat{a}a^ to a thermal state of light depend on the order in which the two operations are performed. The non-commutativity of the bosonic operators, a^a^†≠a^†a^≠1\hat{a}\hat{a}^\dagger\ne \hat{a}^\dagger\hat{a}\ne 1a^a^†=a^†a^=1, has been experimentally verified in terms of density matrixes and Wigner functions, which are reconstructed by quantum homodyne tomography. Recently, a setup has been proposed to directly and completely prove the bosonic commutation relation where a single-photon interferometer is used to create coherent superpositions of two alternated sequences of operators, such as [a^a^†±a^†a^][\hat{a}\hat{a}^\dagger \pm \hat{a}^\dagger\hat{a}][a^a^†±a^†a^]. Some of the latest experimental results are discussed.