It has been accepted that the polarization of the photon in vector beams is entangled with its momentum. Here a quantum description is advanced for the polarization that shows entanglement with the momentum. This is done by showing that the Jones vector at each value of the momentum plays the role of the polarization wavefunction in the sense that the Pauli matrices represent the Cartesian components of the polarization in the local reference system with respect to which the Jones vector is defined. The unit vector that the constraint of transversality condition requires to specify the local reference system turns out to be a gauge degree of freedom that determines the entanglement of the polarization with the momentum and has observable effects.
It has been accepted that the polarization of the photon in vector beams is entangled with its momentum. Here a quantum description is advanced for the polarization that shows entanglement with the momentum. This is done by showing that the Jones vector at each value of the momentum plays the role of the polarization wavefunction in the sense that the Pauli matrices represent the Cartesian components of the polarization in the local reference system with respect to which the Jones vector is defined. The unit vector that the constraint of transversality condition requires to specify the local reference system turns out to be a gauge degree of freedom that determines the entanglement of the polarization with the momentum and has observable effects.
In the paper a quantum description of an effective state of polarization for an electromagnetic field containing variously polarized photons is presented. The discussion of the problem includes the quantum character of a single photon, comparison with a classical field, matrix description of photon polarization and physical interpretation of the Pauli representation of a density operator that represents photons in a statistical ensemble. Full text: PDF References: R.J. Glauber, Quantum Theory of Optical Coherence (Wiley-VCH 2007). C.C. Gerry, P.L. Knight, Introductory Quantum Optics (Cambrige Univeristy Press 2005) R.J. Glauber, New Techn. Ideas Quant. Measur. Theory 480, 336 (1986). L. Michalik, J. Jasinski, P.L. Makowski, A.W. Domanski,"Problem of degree of polarization for photons", Proc. SPIE 7745, 77450K (2010). [CrossRef] T. Tudor, A. Gheondea, "Pauli algebraic forms of normal and nonnormal operators", Jour. Opt. Soc. Am. A 24, 204 (2007). [CrossRef]
Whether the total angular momentum of the photon can be separated into spin and orbital parts has been a long-standing problem due to the constraint of transversality condition on its vector wavefunction. A careful analysis shows that the situation arises from a misuse of the constraint in quantum mechanics. To use the constraint properly, we convert the vector representation into a two-component representation in which the wavefunction is not constrained by any conditions. Upon doing so, we not only separate the spin conceptually from the orbital angular momentum but also identify the Berry gauge in which the two-component wavefunction can be canonically quantized. A corollary is that only in one particular Berry gauge can a radiation field be canonically quantized in terms of the plane waves. The degree of freedom to fix the Berry gauge, which reflects a symmetry of the constraint, turns out to have observable quantum effects.
Photons may have homogeneous polarization and may carry quantized orbital angular momentum (OAM). Photon entanglement has been realized in various degrees of freedom such as polarization and OAM. Using a pair of orthogonally polarized states carrying opposite-handedness quantized OAMs could create "quantized" vector polarization states with space-variant polarization structures. It is thus possible to extend the polarization degree of freedom from two dimensional space to indefinite dimensional discrete Hilbert space. We present a class of vector-polarization entangled Bell states, which use the spatial modes of the vector fields with space-variant polarization structure. We propose a scheme of creating the vector-polarization entangled Bell states using a Sagnac interferometer. We also design an analyzer for identifying the vector-polarization entangled Bell states. Such a class of entanglement is important for quantum information science and technology, and fundamental issues of quantum theory, due to its advantage of the increase in information capacity.
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 the paper a quantum description of an effective state of polarization for an electromagnetic field containing variously polarized photons is presented. The discussion of the problem includes the quantum character of a single photon, comparison with a classical field, matrix description of photon polarization and physical interpretation of the representation of a density operator that represents photons in a statistical ensemble. Full text: PDF References: R.J. Glauber, Quantum Theory of Optical Coherence (Wiley-VCH 2007). C.C. Gerry, P.L. Knight, Introductory Quantum Optics (Cambrige Univeristy Press 2005) R.J. Glauber, New Techn. Ideas Quant. Measur. Theory 480, 336 (1986). L. Michalik, J. Jasinski, P.L. Makowski, A.W. Domanski,Problem of degree of polarization for photons, Proc. SPIE 7745, 77450K (2010). [CrossRef] T. Tudor, A. Gheondea, Pauli algebraic forms of normal and nonnormal operators, Jour. Opt. Soc. Am. A 24, 204 (2007). [CrossRef]
We report that the true intrinsic degree of freedom of the photon is neither the polarization nor the spin. It describes a local property in momentum space and is represented in the local representation by the Pauli matrices. This result is achieved by treating the transversality condition on the vector wavefunction as a nonholonomic quantum constraint. We find that the quantum constraint makes it possible to generalize the Stokes parameters to characterize the polarization of a general state. Unexpectedly, the generalized Stokes parameters are specified in a momentum-space local reference system that is fixed by another degree of freedom, called Stratton vector. Only constant Stokes parameters in one particular local reference system can convey the intrinsic degree of freedom of the photon. We show that the optical rotation is one of such processes that change the Stratton vector with the intrinsic quantum number remaining fixed. Changing the Stratton vector of the eigenstate of the helicity will give rise to a Berry's phase.