Classical Polarization Optics Research Articles

Canonical forms of two-qubit states under local operations

Canonical forms of two-qubits under the action of stochastic local operations and classical communications (SLOCC) offer great insight for understanding non-locality and entanglement shared by them. They also enable geometric picture of two-qubit states within the Bloch ball. It has been shown (Verstraete et.al. {Phys. Rev. A, 64, 010101(R) (2001)) that an arbitrary two-qubit state gets transformed under SLOCC into one of the {\em two} different canonical forms. One of these happens to be the Bell diagonal form of two-qubit states and the other non-diagonal canonical form is obtained for a family of rank deficient two-qubit states. The method employed by Verstraete et.al. required highly non-trivial results on matrix decompositions in $n$ dimensional spaces with indefinite metric. Here we employ an entirely different approach -- inspired by the methods developed by Rao et. al., (J. Mod. Opt. 45, 955 (1998)) in classical polarization optics -- which leads naturally towards the identification of two inequivalent SLOCC invariant canonical forms for two-qubit states. In addition, our approach results in a simple geometric visualization of two-qubit states in terms of their SLOCC canonical forms.

Possibility of Classical Entanglement at LIGO

It is now established that entanglement in the sense of local non-factorizability of two or more degrees of freedom of a system occurs in classical polarization optics. We extend the idea to weak gravitational waves which are strikingly similar to optical waves. It is shown that a linearized classical gravity wave can in principle get entangled in the sense mentioned with the vibrational modes of an array of test masses in a plane perpendicular to its direction of propagation. A Bell-CHSH inequality based on the requirement of noncontextuality for classical realism is derived, and it is shown that the putative nonfactorizable state violates this inequality. The idea is therefore empirically falsifiable.

Single all-optical platform for measurement of twist and transverse stress using polarization modulation in distinct dual-mode fiber placed in a Sagnac loop.

We report here the experimental demonstration of measurement of both twist and transverse stress using polarization modulation in a single all-fiber circuit consisting of a single-mode fiber (SMF)/dual-mode fiber (DMF) in a Sagnac interferometer (SI) loop. The SMF-SI prototype setup is seen to be suitable for precise measurement of twist over a broad range of ±50° and transverse stress up to 5 N with a sensitivity as high as 2.85×10(6) pW/° and 2.08×10(7) pW/N, respectively. It is envisaged that nearly ideal operation for twist measurement can be achieved by appropriately selecting the operating domain (pretwisted Sagnac loop for practical realization of the device) and required magnitude of applied transverse stress (weight yielding maximum sensitivity). Unlike SMF-SI, a DMF assisted SI exhibits asymmetric transmittance yielding a peak shift (∼45°) in addition to falling/rising peak amplitude of effective power(∼20 μW). This key characteristic is further utilized for tunable measurement of torsion (unidirectional from -70° to 40°) while keeping the sensitivity fixed. This research problem is then analyzed on the avenue of theoretical consideration and using classical polarization optics; we have derived the Jones birefringence matrix that accurately describes the transmission behavior of the configured fiber circuit (SMF-SI and DMF-SI) for each of the three cases, namely, transverse stress, twist, and both twist and transverse stress. Series of experimental measurements for various conditions of induced birefringence (linear/circular) were performed at length, and the results were compared with those determined theoretically towards configuring a twist and stress measuring device. The study provides an understanding of the underlying physics of dual-mode interference in a Sagnac configuration experiencing linear and circular birefringence.

The Unfinished Search for Wave-Particle and Classical-Quantum Harmony

The main purpose of this paper is to review the progress that has taken place so far in the search for a single unifying principle that harmonizes (i) the wave and particle natures of matter and radiation, both at the quantum and the classical levels, on the one hand and (ii) the classical and quantum theories of matter and radiation on the other hand. The famous paradoxes of quantum theory, the mysterious nature of measurements in quantum theory and the principal no-go theorems for hidden variables are first briefly reviewed. The Koopman-von Neumann Hilbert space theory based on complex wave functions underlying particle trajectories in classical phase space, is an important step forward in that direction. It provides a clear and beautiful harmony of classical waves and particles. Sudarshan has given an alternative but equivalent formulation that shows that classical mechanics can be regarded as a quantum theory with essentially hidden non-commuting variables. An extension of KvNS theory to classical electrodynamics provides a sound Hilbert space foundation to it and satisfactorily accounts for entanglement and Bell-CHSH-like violations already observed in classical polarization optics. An important new insight that has been obtained through these developments is that entanglement and Bell-like inequality violations are neither unique signatures of quantumness nor of non-locality---they are rather signatures of non-separability. Finally, Sudarshan's proposed solution to the measurement problem using KvNS theory for the measuring apparatus is sketched to show to what extent wave and particles can be harmonized in quantum theory.

Entanglement in Classical Optics

The emerging field of entanglement or nonseparability in classical optics is reviewed, and its similarities with and differences from quantum entanglement clearly pointed out through a recapitulation of Hilbert spaces in general, the special restrictions on Hilbert spaces imposed in quantum mechanics and the role of Hilbert spaces in classical polarization optics. The production of Bell-like states in classical polarization optics is discussed, and new theorems are proved to discriminate between separable and nonseparable states in classical wave optics where no discreteness is involved. The influence of the Pancharatnam phase on a classical Bell-like state is deived. Finally, to what extent classical polarization optics can be used to simulate quantum information processing tasks is also discussed. This should be of great practical importance because coherence and entanglement are robust in classical optics but not in quantum systems.

Measures of quantum state purity and classical degree of polarization

There is a well-known mathematical similarity between two-dimensional classical polarization optics and two-level quantum systems, where the Poincare and Bloch spheres are identical mathematical structures. This analogy implies that the classical degree of polarization and quantum purity are in fact the same quantity. We make extensive use of this analogy to analyze various measures of polarization for higher dimensions proposed in the literature, in particular the $N = 3$ case, illustrating interesting relationships that emerge as well as the advantages of each measure. We also propose a different class of measures of entanglement based on the purity of subsystems.

Investigation on an Anomalous Behavior of the Polarimetric Measurements at JET

The far-infrared polarimeter at JET is affected by an anomaly that makes difficult the interpretation of both Faraday and Cotton-Mouton effect measurements. The anomaly is clearly displayed during calibration operations in the absence of plasma: As the polarization of the probing beam is rotated, the phase shift of the polarimetric signal with respect to the interferometric signal is not constant, as expected, and changes significantly. It affects all the polarimetric measurement channels and has so far been removed by an empirical preprocessing of the raw data. It can be ascribed to a nonideal behavior of some optical components. Looking for a possible explanation of the anomaly, in this paper, we analyze the optical setup of the JET polari-interferometer according to the laws of classical polarization optics. At first, the optical characteristics of the recombination plates are analyzed in detail. Although they produce ellipticity in the transmitted and reflected beams, the results show that the recombination plates should not be responsible of the anomaly of the polarimeter. Then, the dielectric waveguides used to transfer the recombined beams from the torus hall to the detectors are, for the first time, considered as a possible origin of the anomaly. The anomalous behavior is expected to be mainly originated by reflections on metal mirrors, which may produce rotations of the polarization of the beams. A calculation has been performed in order to analyze the effects of a rotation of the polarization of the recombined beam on the detector signals. As a result, a rotation of the polarization along the line could explain the anomaly. We also suggest some simple and feasible tests, which are useful to give an experimental support to this conclusion, and discuss possible modifications of the optical setup to remove or greatly reduce the anomaly in future measurements.

Polarization optics analogy of quantum wavefunctions in graphene

Detailed similarities between polarization states of light and ballistic charge carriers in graphene are derived. Based on these, the optical equivalent of quantum wavefunctions, Dirac equation, and the effect of an electrostatic potential are found, and the quantum analog of the refractive index of light and of the optical composition law of reflection coefficients are obtained. The differences between the behavior of quantum wavefunctions in graphene and electromagnetic fields, due to the chiral symmetry of ballistic charge carriers that cannot be mimicked in classical polarization optics, are also evidenced.

Birefringence matrix for a twisted single-mode fiber: Geometrical contribution

The elastic twisting of a fiber in the cold condition causes two effects: a geometrical rotation of the birefringence axes of the fiber with the twist rate and a torsional stress. In this work, considering only the geometrical contribution, we derive a matrix model based on classical polarization optics. The predictions of this model, useful for fibers with a low twist rate, are compared with experimental results.

Linear optics and quantum maps

We present a theoretical analysis of the connection between classical polarization optics and quantum mechanics of two-level systems. First, we review the matrix formalism of classical polarization optics from a quantum information perspective. In this manner the passage from the Stokes-Jones-Mueller description of classical optical processes to the representation of one- and two-qubit quantum operations, becomes straightforward. Second, as a practical application of our classical-\emph{vs}-quantum formalism, we show how two-qubit maximally entangled mixed states (MEMS), can be generated by using polarization and spatial modes of photons generated via spontaneous parametric down conversion.

Entangled mixed-state generation by twin-photon scattering

We report experimental results on mixed-state generation by multiple scattering of polarization-entangled photon pairs created from parametric down-conversion. By using a large variety of scattering optical systems we have experimentally obtained entangled mixed states that lie upon and below the Werner curve in the linear entropy-tangle plane. We have also introduced a simple phenomenological model built on the analogy between classical polarization optics and quantum maps. Theoretical predictions from such a model are in full agreement with our experimental findings.