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Frontiers in Optics

Quantum Polarization Tomography of Bright Squeezed Light

C. R. Müller, B. Stoklasa, Christian Peuntinger, C. Gabriel, Jaroslav Řeháček, Z. Hradil, A. B. Klimov, Gerd Leuchs, Christoph Marquardt, Luis Lorenzo Sánchez-Soto

Published Jan 1, 2012• 1 citation
Publisher

Abstract

We reconstruct the polarization sector of a bright polarization squeezed beam starting from a complete set of Stokes measurements. We use both the inverse Radon transformation and a novel maximum likelihood algorithm. We find that the maximum likelihood reconstruction provides significantly higher statistical inversion stability, which allows us to get reconstructions of the same quality but from far smaller data sets.

DOI
10.1364/fio.2012.ftu3a.27

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Journal of Experimental and Theoretical Physics Letters•Dec 1, 2012•2 citations
We reconstruct the polarization sector of a bright polarization squeezed beam starting from a complete set of Stokes measurements. We use both the inverse Radon transformation and a novel maximum likelihood algorithm. We find that the maximum likelihood reconstruction provides significantly higher statistical inversion stability, which allows us to get reconstructions of the same quality but from far smaller data sets.
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 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, thus finding excellent agreement.
The polarization properties of macroscopic Bell states are characterized using three-dimensional quantum polarization tomography. This method utilizes three-dimensional (3D) inverse Radon transform to reconstruct the polarization quasiprobability distribution function of a state from the probability distributions measured for various Stokes observables. The reconstructed 3D distributions obtained for the macroscopic Bell states are compared with those obtained for a coherent state with the same mean photon number. The results demonstrate squeezing in one or more Stokes observables.
Quantum-state tomography is proposed as a means to achieve a complete measurement of the quantum polarization state of a light wave. A set of measurements using dual-polarization balanced homodyne detection is shown to be tomographi-cally complete with respect to the statistics of the SU(2) Stokes operators on the Poincaré sphere. Complete reconstruction of the polarization sector of the density matrix of a partially polarized optical field can be achieved while randomizing the overall phase of the dual-polarization local oscillator.
In this paper authors present a novel idea for reconstructing quantum states of polarized optical field expressed in the one-photon basis. The quantum state reconstruction is a measurement of a quasidistribution function P that allows to obtain a density operator for the analyzed state. The most commonly used approach for a quantum state reconstruction is based on the so called quantum tomography. The marginal probability distributions for the Wigner function are measured for different angles of projection and then they are put together into the two-dimensional distribution by the inverse Radon transformation. In our approach the analyzed field is combined with the reference field which is well defined, it can be for example a photon-beam containing linearly polarized photons only. The proposed thought experiment assumes that we measure the degree of linear polarization of this combined beam using a rotating polarizer. We obtain the searched distribution P by changing the parameters of the reference beam – its intensity and state of polarization. This series of measurements allows to build the system of equations The values of the function P at various points P(θ i, ϕ j) are the searched variables of this system. Accuracy of that solution depends on how many measurements are done.