The classical theory of polarisation coherence is briefly summarised and then extended. The extension is motivated by the recognition that the traditional theory of two-point coherence provides only what we identify as ‘diagonal’ correlation functions and their associated two-point coherence matrices. It is pointed out that a wider focus is possible when taking account of the three-sector vector space underlying all two-point coherences in classical optics. This reveals the possibility of observing a new type of ‘off-diagonal’ correlations that arise when the correlation functions under investigation are associated with points in two distinct vector spaces, pairs of points that are not analogous to the pairs of space points or time points that underlie traditional measures of spatial and temporal coherence. Quantum theory has experience with correlations engaging such ‘cross-sector’ coherences, for example in tests of Bell inequalities, and the quantum formulations are shown to be easily adopted by classical theory without incorporating quantum features in the optical signals. The familiar theory of classical coherence that is associated with the pioneering work of Emil Wolf is extended in conformance with three criteria advanced by Abner Shimony to obtain formulas for correlation functions and for the Bell measure S of coherence. Values of S greater than the standard upper limit S=2 are predicted for certain classical Shimony–Wolf fields, indicating strong cross-sector coherence, but only when standard measures of coherence such as degree of polarisation P are minimised. Experimental results confirming the predictions for cross-sector coherence are exhibited.
The classical theory of polarisation coherence is briefly summarised and then extended. The extension is motivated by the recognition that the traditional theory of two-point coherence provides only what we identify as ‘diagonal’ correlation functions and their associated two-point coherence matrices. It is pointed out that a wider focus is possible when taking account of the three-sector vector space underlying all two-point coherences in classical optics. This reveals the possibility of observing a new type of ‘off-diagonal’ correlations that arise when the correlation functions under investigation are associated with points in two distinct vector spaces, pairs of points that are not analogous to the pairs of space points or time points that underlie traditional measures of spatial and temporal coherence. Quantum theory has experience with correlations engaging such ‘cross-sector’ coherences, for example in tests of Bell inequalities, and the quantum formulations are shown to be easily adopted by classical theory without incorporating quantum features in the optical signals. The familiar theory of classical coherence that is associated with the pioneering work of Emil Wolf is extended in conformance with three criteria advanced by Abner Shimony to obtain formulas for correlation functions and for the Bell measure S of coherence. Values of S greater than the standard upper limit S=2 are predicted for certain classical Shimony–Wolf fields, indicating strong cross-sector coherence, but only when standard measures of coherence such as degree of polarisation P are minimised. Experimental results confirming the predictions for cross-sector coherence are exhibited.
For many decades the word "entanglement" has been firmly attached to the world of quantum mechanics, as is the phrase "Bell violation". Here we introduce Shimony-Wolf fields, entirely classical non-deterministic states, as a basis for entanglement and Bell analyses. Such fields are well known in coherence optics and are open to test. We present experimental results showing that Shimony-Wolf states exhibit strong classical Bell violation, in effect opening a way of examining a new sector of the boundary between quantum and classical physics.
The growing recognition that entanglement is not exclusively a quantum property, and does not even originate with Schrödinger's famous remark about it [Proc. Camb. Phil. Soc. 31, 555 (1935)], prompts examination of its role in marking the quantum-classical boundary. We have done this by subjecting correlations of classical optical fields to new Bell-analysis experiments, and report here values of the Bell parameter greater than B=2.54. This is many standard deviations outside the limit B=2 established by the Clauser-Horne-Shimony-Holt (CHSH) Bell inequality [Phys. Rev. Lett. 23, 880 (1969)], in agreement with our theoretical classical prediction, and not far from the Tsirelson limit B=2.828.... These results cast a new light on the standard quantum-classical boundary description, and suggest a reinterpretation of it.
We explore the concepts of coherence and entanglement as they apply to both the classical and quantum natures of light. In the classical domain, we take inspiration from the tools and concepts developed in foundational quantum mechanics and quantum information science to gain a better understanding of classical coherence theory of light with multiple degrees of freedom (DoFs). First, we use polarization and spatial parity DoFs to demonstrate the notion of classical entanglement, and show that Bell's measure can serve as a useful tool in distinguishing between classical optical coherence theory. Second, we establish a methodical yet versatile approach called 'optical coherency matrix tomography' for reconstructing the coherency matrix of an electromagnetic beam with multiple DoFs. This technique exploits the analogy between this problem in classical optics and that of tomographically reconstructing the density matrix associated with multipartite quantum states in quantum information science. Third, we report the first experimental measurements of the 4 x 4 coherency matrix associated with an electromagnetic beam in which polarization and a spatial DoF are relevant, ranging from the traditional two-point Young's double slit to spatial parity and orbital angular momentum modes. In the quantum domain, we use the modal structure of classical fields to develop qubits and structure Hilbert spaces for use in quantum information processing. Advancing to three-qubit logic gates is an important step towards the success of optical schemes for quantum computing. We experimentally implement a variety of two- and three- qubit, linear and deterministic, single-photon, controlled, quantum logic gates using polarization and spatial parity qubits. Lastly, we demonstrate the implementation of two-qubit single-photon logic using polarization and orbital angular momentum qubits.
Abstract The modern theory of coherence is based on correlation functions. A generic example could be written 〈 V ∗ ( t 1 ) V ( t 2 ) 〉 , denoting an average of products of the values of a signal V ( t ) at two specified times. Here we infer that t is a degree of freedom that the signal depends on. Typically, physical variables depend on more than one degree of freedom, and recognition of this has prompted attention to some interesting questions for the correlation functions and the several coherences that can be attributed to the same optical field. We examine some of the questions arising from the standpoint of experimental contexts. Degree of polarizability and degree of entanglement (classical non-separability) can serve as starting points for quantitative assignments.
This thesis contains research related to random light fields.In particular, novel constructions of electromagnetic coherence in beam fields are introduced, and certain fundamental notions concerning the spectrum of light are assessed in the context of nonstationary fields.The singular-value decomposition (SVD) of the cross-spectral density matrix (CSDM) is analysed and interpreted for electromagnetic beams.In addition, the Gram matrix of the CSDM is invoked and combined with the SVD formalism.The Gram matrix shares the essential properties of the polarization matrix, thus appearing as a particularly potential descriptor of electromagnetic coherence.The SVD and the Gram matrix yield results analogous to those traditionally met in polarization theory of beam fields, but in the context of two-point spatial coherence analysis.In particular, two-point analogies of the usual decompositions of the polarization matrix are introduced by applying the SVD.In addition, the Poincaré sphere representation of electromagnetic coherence is established, which is analogous to the traditional Poincaré sphere in polarization optics.Cross-spectral purity and spectral invariance of light are two fundamental concepts concerning stationary random light fields, which were recently generalized to nonstationary fields.In this thesis, a reduction formula for time-integrated coherence functions of cross-spectrally pure nonstationary scalar fields is established.This reduction formula is an equivalent condition for the physical definition of crossspectral purity in nonstationary fields, similarly to the reducibility met in the case of cross-spectrally pure stationary light.In addition, optical systems consisting of hybrid refractive-diffractive lens designs which transform partially coherent isodiffracting pulsed beams into cross-spectrally pure or spectrally invariant nonstationary fields are developed.Furthermore, polarimetric measurement of temporal coherence in electromagnetic beam fields is performed.It is shown that the electromagnetic temporal degree of coherence can be deduced from these measurements, thus without the need for visibility detection or optical elements in the arms of the device, in contrast to earlier studies.
Quantum optics and classical optics are linked in ways that are becoming apparent as a result of numerous recent detailed examinations of the relationships that elementary notions of optics have with each other. These elementary notions include interference, polarization, coherence, complementarity and entanglement. All of them are present in both quantum and classical optics. They have historic origins, and at least partly for this reason not all of them have quantitative definitions that are universally accepted. This makes further investigation into their engagement in optics very desirable. We pay particular attention to effects that arise from the mere co-existence of separately identifiable and readily available vector spaces. Exploitation of these vector-space relationships are shown to have unfamiliar theoretical implications and new options for observation. It is our goal to bring emerging quantum–classical links into wider view and to indicate directions in which forthcoming and future work will promote discussion and lead to unified understanding.