Any polarization state of light occupies intrinsic quantum uncertainties due to the noncommutative behavior of the Stokes operators, which are manifested as unavoidable quantum fluctuations in the corresponding classical Stokes parameters.In this thesis, we explore such quantum polarization uncertainties exhibited by vectorial light fields in Young's seminal double-slit interference experiment.As a main result, by adopting a proper Stokes operator representation of double-slit interference, we establish general quantum polarization uncertainty relations for the Stokes parameters in the observation plane.The relations show how the lower bounds of the polarization uncertainties are periodically varying across the observation screen and how they are affected by the polarization and coherence properties of the light at the two slits.We also present various noncommutative, interlinked connections between coherence and polarization in the slit plane which have not been considered earlier in the literature.Our work sets the fundamental precision limits imposed by quantum physics for characterizing any polarization state in double-slit interference, which could find use in photonic applications exploiting polarimetric and interferometric techniques for high-resolution quantum-enhanced sensing.
Any polarization state of light occupies intrinsic quantum uncertainties due to the noncommutative behavior of the Stokes operators, which are manifested as unavoidable quantum fluctuations in the corresponding classical Stokes parameters.In this thesis, we explore such quantum polarization uncertainties exhibited by vectorial light fields in Young's seminal double-slit interference experiment.As a main result, by adopting a proper Stokes operator representation of double-slit interference, we establish general quantum polarization uncertainty relations for the Stokes parameters in the observation plane.The relations show how the lower bounds of the polarization uncertainties are periodically varying across the observation screen and how they are affected by the polarization and coherence properties of the light at the two slits.We also present various noncommutative, interlinked connections between coherence and polarization in the slit plane which have not been considered earlier in the literature.Our work sets the fundamental precision limits imposed by quantum physics for characterizing any polarization state in double-slit interference, which could find use in photonic applications exploiting polarimetric and interferometric techniques for high-resolution quantum-enhanced sensing.
Light is known to exhibit quantum uncertainty in terms of its amplitude, phase, and polarization. However, quantum uncertainty related to coherence, which is also a fundamental physical property of light, remains to be considered. Here, we formulate and explore the concept of quantum optical coherence uncertainty. We focus on the first-order coherence of the simplest possible light field, a purely monochromatic plane wave, which is classically completely stable. Starting from a scalar treatment, we show that the field displays zero coherence uncertainty only for a number state. We then proceed to the vectorial regime and establish that any state leads to coherence fluctuations, governed by a set of uncertainty relations depending on the polarization state and space-time points. Our work thus provides fundamental insights into the quantum character of optical coherence, with potential benefits in applications using highly sensitive interferometric and polarimetric techniques.
The principle of complementarity relationship introduced by Niels Bohr in 1927 states that particle and wave behavior are two mutually exclusive properties for a quantum system.This relationship has taken the attention of researchers for decades due to its conceptual importance.This thesis contains a theoretical research work conducted on quantum complementarity of vectorial light fields and in the doublepinhole interference.Here we have adopted the classical Stokes parameters within a quantum framework and calculated the Stokes parameters in the observation plane in double-pinhole interference.Based on these calculations, we further evaluated visibility and distinguishability parameters for an arbitrary pure single-photon state and for a specific single-photon pure state, where the photon is x polarized at the first pinhole and y polarized at the second pinhole.We have then examined and interpreted the wave-particle duality for the mentioned two states.Finally, we performed mixed state calculation where fully unpolarized photon is incident on the two pinholes, but with the photon at one pinhole rotated by an angle of π/2.From the obtained results we concluded that a priori which path information (WPI) regarding the complementarity relations for the single photon pure vectorial quantum state couples not to the intensity visibility but to the total visibility.We further found that the vectorial quantum state gives rise to polarization modulation.From the results obtained for the mixed state calculations, we discovered that the last Stokes parameter has a non-zero value and it contributes to the polarization modulation.Thereby we further recommended to repeat the calculation for different mixed states other than what we have considered here to extend the exploration about the nature of polarization modulation.
We introduce the concept of optical coherence squeezing in double-slit interference. We construct Hermitian operators that characterize the coherence at the slits, leading to coherence uncertainty relations and a corresponding squeezing condition. We also analyze states exhibiting such squeezing and show its manifestations in the uncertainty of the magnitudes and positions of the intensity fringes. Our work identifies coherence as a fundamental degree of freedom for squeezing, complementing phase, amplitude, and polarization, which could benefit quantum-enhanced interferometry.
The dual wave–particle nature of light and the degree of polarization are fundamental concepts in quantum physics and optical science, but their exact relation has not been explored within a full vector-light quantum framework that accounts for interferometric polarization modulation. Here, we consider vector-light quantum complementarity in double-pinhole photon interference and derive a general link between the degree of polarization and wave–particle duality of light. The relation leads to an interpretation for the degree of polarization as a measure describing the complementarity strength between photon path predictability and so-called Stokes visibility, the latter taking into account both intensity and polarization variations in the observation plane. It also unifies results advanced in classical studies by showing that the degree of polarization can be viewed as the ability of a light beam to exhibit intensity and polarization-state fringes. The framework we establish thus provides novel aspects and deeper insights into the role of the degree of polarization in quantum-light complementarity and photon interference.
In this work, we formulate a quantum-mechanical description of interference of electromagnetic fields in Young's interference experiment, thereby taking into account the polarization properties of the field and describing them in terms of quantum analogs of classical Stokes parameters.Commencing with the classical theory of interference of scalar fields, we proceed to a relatively advanced approach to electromagnetic interference, bringing into the equation cross-spectral density tensor, polarization matrix and Stokes parameters to analyze the polarization properties.Subsequently, the same phenomenon is analyzed in the domain of quantum optics, thereby expressing the fields as operators and observables as the expectation values.Firstly, an outline of the scalar approach of the operators in the interference experiment is presented to establish the foundation to base the electromagnetic approach on, followed by a full description of quantum analog of electromagnetic interference in Young's experiment.In particular, Stokes parameters are adopted to calculate the polarization effects in quantum theory. PrefaceThis report attempts to condense and present the theories related to the interference in the canonical Young's double pinhole experiment, prior to heading to investigate the phenomenon with the quantum analysis of electromagnetic fields.My interest in the realm of quantum mechanics has encouraged me to work on this thesis, wherefrom I have learnt a lot during these times.I am really grateful to my supervisors, Prof. Ari T. Friberg and Prof. Jani Tervo for guiding me and believing in me.I will always be indebted for their constant support and confidence on me.I would also like to offer my special thanks to the Faculty of Forestry and Sciences for providing the financial
This thesis concerns the role of polarization, coherence, and geometric phase in both quantum and classical light interference.In the quantum domain, the thesis analyzes vector-light interference in a doubleslit geometry for single-photon and multiphoton states.Using a coherence Stokes formalism, a unified description of polarization modulation, geometric phase, and wave-particle duality is established.Single-photon interference is shown to exhibit a fundamental complementarity relation that directly links the geometric phase at the observation screen to which-path information at the slits.This framework is further extended to higher-order interference of multimode N00N states, where Nth-order polarization modulation and geometric-phase accumulation scale linearly with photon number and lead to new higher-order vector-light complementarity relations.In the classical domain, the thesis explores beam and pulse shaping enabled by polarization gratings.Spatial polarization gratings are shown to provide control over the profiles, coherence, diffraction orders, and polarization of partially coherent and partially polarized pulsed beams.The analysis is further extended to ultrafast pulse shaping, where spectral polarization gratings generate multiple temporally shifted pulses with distinct polarization states.Furthermore, a novel Poincaré pulse in the spatiospectral domain is presented.