We present a method to characterize the polarization state of a light field in the continuous-variable regime. Instead of using the abstract formalism of SU(2) quasidistributions, we model polarization in the classical spirit by superposing two harmonic oscillators of the same angular frequency along two orthogonal axes. By describing each oscillator by a $s$-parametrized quasidistribution, we derive in a consistent way the final function for the polarization. We compare with previous approaches and discuss how this formalism works in some relevant examples.
The properties of coherence and polarization of light has been the subject of intense investigations and form the basis of many technological applications. These concepts which historically have been treated independently can now be formulated under a single classical theory. Here, we derive a quantum counterpart for this theory, with basis on a density matrix formulation, which describes jointly the coherence and polarization properties of an ensemble of photons. The method is used to show how the degree of polarization of a specific class of mixed states changes on propagation in free space,…
We present a moment expansion method for the systematic characterization of the polarization properties of quantum states of light. Specifically, we link the method to the measurements of the Stokes operator in different directions on the Poincaré sphere, and provide a method of polarization tomography without resorting to full state tomography. We apply these ideas to the experimental first- and second-order polarization characterization of some two-photon quantum states. In addition, we show that there are classes of states whose polarization characteristics are dominated not by their first-…
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 r…
We study polarization squeezing of a light beam initially in the coherent state using the nonlinear interaction hamiltonian $ H=k\big(\hat a_{x}^{\dagger2}+{\hat a_{x}}^2\big)$. For the degree of polarization squeezing, we use a definition written in the final form by the authors and also used in earlier papers. We find that the polarization squeezing can be very high and the degree of polarization squeezing can be less than unity by a very small amount. We achieve the polarization squeezing even for very low beam intensity under some conditions involving phase angles in the polarization modes…
Driving on an analogy with the technique of composite pulses in quantum physics, we propose highly efficient broadband polarization converters composed of sequences of ordinary retarders rotated at specific angles with respect to their fast-polarization axes.
We recall the framework of a consistent quantum description of polarization of light. Accordingly, the degree of polarization of a two-mode state $\hat ρ$ of the quantum radiation field can be defined as a distance of a related state ${\hat ρ}_b$ to the convex set of all SU(2) invariant two-mode states. We explore a distance-type polarization measure in terms of the quantum Chernoff bound and derive its explicit expression. A comparison between the Chernoff and Bures degrees of polarization leads to interesting conclusions for some particular states chosen as illustrative examples.
Theoretical analysis is presented on quantum state evolution of polarization light waves at frequencies $ω_{o}$ and $ω_{e}$ in a periodically poled nonlinear crystal (PPNC). It is shown that the variances of all the four Stokes parameters can be squeezed.
A broadband technique for robust adiabatic rotation and conversion of light polarization is proposed. It uses the analogy between the equation describing the polarization state of light propagating through an optically anisotropic medium and the Schrodinger equation describing coherent laser excitation of a three-state atom. The proposed techniques is analogous to the stimulated Raman adiabatic passage (STIRAP) technique in quantum optics; it is applicable to a wide range of frequencies and it is robust to variations in the ropagation length.
The preparation of completely non-polarized light is seemingly easy: an everyday example is sunlight. The task is much more difficult if light has to be in a pure quantum state, as required by most quantum-technology applications. The pure quantum states of light obtained so far are either polarized or, in rare cases, manifest hidden polarization: even if their intensities are invariant to polarization transformations, higher-order moments are not. We experimentally demonstrate the preparation of the macroscopic singlet Bell state, which is pure, completely non-polarized, and has no polarizati…
Polarization of light is one of the fundamental concepts in optics. There are many ways to measure and characterise this feature of light but at the fundamental level it is quantum mechanics that imposes ultimate limits to such measurements. Here, I calculate the quantum limit to a precision of a polarization measurement of classical coherent light. This is a multiparameter estimation problem with a crucial feature of noncommuting optimal observables corresponding to each parameter which prohibits them to be measured at the same time. I explicitly minimize the quantum Holevo-Cramer-Rao bound w…
We experimentally demonstrate polarization entanglement for squeezed vacuum pulses containing more than 10^5 photons. We also study photon-number entanglement by calculating the Schmidt number and measuring its operational counterpart. Theoretically, our pulses are the more entangled the brighter they are. This promises important applications in quantum technologies, especially photonic quantum gates and quantum memories.
We describe a new method of coherent optical control of internal dynamics of atomic collisions by means of two correlated light beams having entangled polarizations. We show that if excitation of a colliding pair of atoms is by two photons having entangled polarizations, it is possible to redirect the output fragments of the collision into certain channels with a selected type of internal transition symmetry. The transition symmetry is defined in the body-fixed coordinate frame which has random and originally unknown orientation in space.
An experiment is proposed to show that after initial frequency and polarization selection, classical thermal light from two independent sources can be made path-polarization entangled. Such light will show new intensity-intensity correlations involving both path and polarization phases, formally similar to those for four-particle GHZ states. For fixed polarization phases, the correlations reduce to the Hanbury Brown-Twiss phase correlations. It is also shown that these classical correlations violate noncontextuality.
We report the experimental demonstration of polarization squeezed beam at 795 nm by combining a quadrature squeezed beam with a coherent beam. The quadrature squeezed beam is generated by a degenerate optical parametric amplifier based on a PPKTP crystal. Stokes parameter squeezing of -3.8 dB and anti squeezing of +5.0 dB is observed. This polarization squeezed beam resonant to rubidium D1 line has potential applications in quantum information networks and precise measurement beyond the shot noise limit.
The standard process for the production of strongly squeezed states of light is optical parametric amplification (OPA) below threshold in dielectric media such as LiNbO3 or periodically poled KTP. Here, we present a graphical description of squeezed light generation via OPA. It visualizes the interaction between the nonlinear dielectric polarization of the medium and the electromagnetic quantum field. We explicitly focus on the transfer from the field's ground state to a squeezed vacuum state and from a coherent state to a bright squeezed state by the medium's secondorder nonlinearity, respect…
According to quantum theory, two ensembles of quantum systems that are described by the same density operator are indistinguishable. For example, unpolarized light can be obtained either by an incoherent mixture of two orthogonal pure states or by tracing out a photon from a maximally polarization-entangled photon pair. In both cases, one is unable to guess with probability greater than 50% the outcome of any polarization measurement, but the reasons are conceptually different: whereas the first case is a matter of classical ignorance (the photons were prepared in a definite but unknown way), …
We propose a CNOT gate for quantum computation. The CNOT operation is based on existence of triactive molecules, which in one direction have dipole moment and cause rotation of the polarization plane of linearly polarized light and in perpendicular direction have a magnetic moment. The incoming linearly polarized laser beam is divided into two beams by beam splitter. In one beam a control state is prepared and the other beam is a target. The interaction of polarized states of both beams in a solution containing triactive molecules can be described as interaction of two qubits in CNOT.
We reconstruct the polarization sector of a bright polarization squeezed beam starting from a complete set of Stokes measurements. Given the symmetry that underlies the polarization structure of quantum fields, we use the unique SU(2) Wigner distribution to represent states. In the limit of localized and bright states, the Wigner function can be approximated by an inverse three-dimensional Radon transform. We compare this direct reconstruction with the results of a maximum likelihood estimation, finding an excellent agreement.
Polarization squeezing is shown to occur in non-degenerate parametric amplification of coherent light and the degree of squeezing at interaction time $T$ can be as large as $1-e^{-2T}$. This gives $86.4\%$ polarization squeezing for $T=1$ and $98.2\%$ for $T=2$. One simple case when this occurs is on taking initially plane polarized light having equal amplitudes in the two modes that finally has equal intensities of two circular polarizations. This suggest the experimental settings of parameters to achieve this extent of polarization squeezing in coherent light.
We observe the polarization squeezing in the mixture of a two mode squeezed vacuum and a simple coherent light through a linear polarization beam splitter. Squeezed vacuum not being squeezed in polarization, generates polarization squeezed light when superposed with coherent light. All the three Stokes parameters of the light produced on the output port of polarization beam splitter are found to be squeezed and squeezing factor also depends upon the parameters of coherent light.
We formulate the classical polarization theory for light by using entanglement analysis. We demonstrate a route to a systematic and consistent measure of ordinary light polarization that extends automatically to a new understanding of the degree of polarization at a point, when a distinct beam direction is absent. We have drawn on recent work [Qian and Eberly, arXiv 1009.5622] dealing with the conservation of quantum information.
When polarized light is absorbed by an atom, the excited atomic system carries information about the initial polarization of light. For the light that carries an orbital angular momentum, or the twisted light, the polarization states are described by eight independent parameters, as opposed to three Stokes parameters for plane waves. We use a parameterization of the spin-density matrix of the twisted light in terms of vector and tensor polarization, in analogy with massive spin-1 particles, and derive formulae that define atom's response to specific polarization components of the twisted light…
Polarization of light signifies transversal, anisotropic and asymmetrical statistical property of electromagnetic radiation about direction of propagation. Traditionally, optical-polarization is characterized by Stokes theory susceptible to be insufficient in assessing polarization structure of optical quantum fields and, also, does not decipher twin characteristic polarization parameters (ratio of real amplitudes and difference in phases). An alternative way, in spirit of classical description of optical-polarization, is introduced which can be generalized to deal higher-order polarization of…
We demonstrate on-demand control of localized surface plasmons in metamaterials by means of incident light polarization. An asymmetric mode, selectively excited by s-polarized light, interfere destructively with a bright element, thereby allowing the incident light to propagate at a fairly low loss, corresponding to electromagnetically induced transparency (EIT) in an atomic system. In contrast, a symmetric mode, excited by p-polarized light, directly couples with the incident light, which is analogous to the switch-off of EIT. The light polarization-dependent excitation of asymmetric and symm…
Polarization of light is harnessed in an abundance of classical and quantum applications. Characterizing polarization in a classical sense is done resoundingly successfully using the Stokes parameters, and numerous proposals offer new quantum counterparts of this characterization. The latter often rely on distance measures from completely polarized or unpolarized light. We here show that the accepted class of perfectly polarized quantum states of light is severely lacking in terms of both pure states and mixed states. By appealing to symmetry and geometry arguments we determine all of the stat…
Squeezed light, which is easily degraded by loss, could benefit from generation directly in optical fiber. Furthermore, highly nonlinear fiber could offer more efficient generation with lower pump power and shorter fiber lengths than standard single-mode fiber. We investigate non-polarization-maintaining highly nonlinear fiber (HNLF) for squeezed-light generation by characterizing possible sources of excess noise, including its zero-dispersion wavelength (ZDW) variation and polarization noise. We find significant ZDW variation and excess polarization noise. We believe the polarization noise is…
The comparison of the polarization and spin of light is presented in the paper. It is shown that it is more easier and clearer to use the polarization of the light to explain the effect of the interaction of light and atoms than that of spin of the light. The paper also gives rise to the question whether or not the concept of spin for photon have any essence for its existence.
We have studied relative-intensity fluctuations for a variable set of orthogonal elliptic polarization components of a linearly polarized laser beam traversing a resonant $^{87}$Rb vapor cell. Significant polarization squeezing at the threshold level (-3dB) required for the implementation of several continuous variables quantum protocols was observed. The extreme simplicity of the setup, based on standard polarization components, makes it particularly convenient for quantum information applications.
We report the experimental generation of a class of spin-orbit vector modes of light via an asymmetric Mach-Zehnder interferometer, obtained from an input beam prepared in a product state of its spin and orbital degrees of freedom. These modes contain a spatially varying polarization structure which may be controllably propagated about the beam axis by varying the retardance between the vertical and horizontal polarization components of the light. Additionally, their transverse spatial intensity distributions may be continuously manipulated by tuning the input polarization parameters. In the c…
Recently, it was shown that vector beams can be utilized for fast kinematic sensing via measurements of their global polarization state [Optica 2(10), 864 (2015)]. The method relies on correlations between the spatial and polarization degrees of freedom of the illuminating field which result from its nonseparable mode structure. Here, we extend the method to the nonparaxial regime. We study experimentally and theoretically the far-field polarization state generated by the scattering of a dielectric microsphere in a tightly focused vector beam as a function of the particle position. Using polar…
Liquid crystals allow for the real-time control of the polarization of light. We describe and provide some experimental examples of the types of general polarization transformations, including universal polarization transformations, that can be accomplished with liquid crystals in tandem with fixed waveplates. Implementing these transformations with an array of liquid crystals, e.g., a spatial light modulator, allows for the manipulation of the polarization across a beam's transverse plane. We outline applications of such general spatial polarization transformations in the generation of exotic…
The propagation of the arbitrarily polarized pulse of the weak probe field through the resonant medium of Lambda-type three-level atoms with degenerate levels adiabatically driven by the coherent coupling field is considered. It is shown that such pulse is decomposed in the medium into two orthogonally polarized dark-state polaritons propagating with different group velocities. The expressions for the polarizations and group velocities of these two polaritons are obtained. The dependence of these polarizations and group velocities on the values of the angular momenta of resonant levels, on the…
We derive the polarization tensor of graphene at nonzero temperature in (2+1)-dimensional space-time. The obtained tensor coincides with the previously known one at all Matsubara frequencies, but, in contrast to it, admits analytic continuation to the real frequency axis satisfying all physical requirements. Using the obtained representation for the polarization tensor, we develope quantum field theoretical description for the reflectivity of graphene. The analytic asymptotic expressions for the reflection coefficients and reflectivities at low and high frequencies are derived for both indepen…
When generalized from plane waves to general vector beams, the notion of polarization described by the Stokes parameters turns out to be defined in a momentum-associated system that is fixed by the so-called Stratton vector. As the true intrinsic degree of freedom in the language of quantum mechanics, the polarization of light beams in any fixed momentum-associated system is able to characterize their vectorial feature in the laboratory reference system. The Stratton vector is therefore the degree of freedom to distinguish the vectorial feature of light beams that have the same "polarization".…
Compton scattering of twisted photons is investigated within a non-relativistic framework using first-order perturbation theory. We formulate the problem in the density matrix theory, which enables one to gain new insights into scattering processes of twisted particles by exploiting the symmetries of the system. In particular, we analyze how the angular distribution and polarization of the scattered photons are affected by the parameters of the initial beam such as the opening angle and the projection of orbital angular momentum. We present analytical and numerical results for the angular dist…
Driving the analogy between the coherent excitation of a two-state quantum system and the torque equation of motion, we present exact analytic solutions to different models for manipulation of polarization in birefringent medium. These models include the one-dimensional model, the Landau-Zener model, and the Demkov-Kunike model. We also give an example for robust, broadband manipulation of polarization by suitably tailoring the birefringence vector.
