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arXiv:quant-ph/0701123 · Physical Review Letters

Quantum Reconstruction of an Intense Polarization Squeezed Optical State

Christoph Marquardt, J. Heersink, Ruifang Dong, Maria V. Chekhova, A. B. Klimov, Luis Lorenzo Sánchez-Soto, Ulrik L. Andersen, Gerd Leuchs

Published Nov 27, 2007• 43 citations
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Abstract

We perform a reconstruction of the polarization sector of the density matrix of an intense polarization squeezed beam starting from a complete set of Stokes measurements. By using an appropriate quasidistribution, we map this onto the Poincaré space, providing a full quantum mechanical characterization of the measured polarization state.

DOI
10.1103/physrevlett.99.220401

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Dec 18, 2012•1 citation
We perform a reconstruction of the polarization sector of the density matrix of an intense polarization squeezed beam starting from a complete set of Stokes measurements. By using an appropriate quasidistribution, we map this onto the Poincaré space, providing a full quantum mechanical characterization of the measured polarization state.
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.
We investigate polarization squeezing in squeezed coherent states with varying coherent amplitudes. In contrast to the traditional characterization based on the full Stokes parameters, we experimentally determine the Stokes vector of each excitation subspace separately. Only for states with a fixed photon number do the methods coincide; when the photon number is indefinite, we parse the state in Fock layers, finding that substantially higher squeezing can be observed in some of the single layers. By capitalizing on the properties of the Husimi QQQ function, we map this notion onto the Poincar\'e space, providing a full account of the measured squeezing.
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.