JW4A.97.pdf CLEO Technical Digest © OSA 2012 Macroscopic Bell States and their Quantum Polarization Tomography Bhaskar Kanseri, Timur Iskhakov, Maria Chekhova and Gerd Leuchs Max-Planck Institute for the Science of Light, G.-Scharowsky Str. 1/Bau 24, 91058, Erlangen, Germany bhaskar.kanseri@mpl.mpg.de Abstract: Using three-dimensional quantum polarization tomography, the polarization properties of macroscopic Bell states are characterized. The reconstructed polarization quasi-probability distributions demonstrate squeezing in one or more Stokes parameters. © 2011 Optical Society of America OCIS codes: 260.5430, 270.6570. 1. Introduction Macroscopic Bell states manifest multi-photon entanglement in two polarization and two frequency (or angular) modes of radiation. These non-classical states of light are particularly useful owing to their stronger interaction with matter and with each other than their microscopic counterparts [1]. Various applications of macroscopic squeezed vacuum have been proposed, to name a few are macroscopic Bell tests, gravitational wave detection, quantum memory, optical metrology etc [1]. Non-classical states of light comprising polarization have been studied widely in the last couple of decades. Some of such states, called polarization squeezed states, are characterized by the reduction of noise in specific polarization observables [2]. The analysis of the fluctuations of the Stokes parameters makes it possible to more appropriately classify the polarization states of light beams. In this paper we aim to characterize macroscopic Bell states using a method known as quantum polarization tomography. This method involves direct experimental reconstruction of polarization quasi-probability distribution (QPD) functions from probability distributions obtained in simple polarization measurements [3]. As a result, this method turns out to be a very efficient tool to probe the polarization attributes of quantum states of light. 2. Macroscopic Bell States A strongly pumped four-mode optical parametric amplifier produces at its output the states,   Ψ ± mac  = e Γ  a † 1 b † 2 ±b † 1 a † 2 +H.c.) |vac〉 ,   Φ ± mac  = e Γ  a † 1 a † 2 ±b † 1 b † 2 +H.c.) |vac〉 ; (1) where a † 1 , b † 1 are photon creation operators in the horizontal and vertical polarization modes, respectively. Subscripts 1, 2 denote frequency or wavevector modes and Γ is the parametric gain coefficient. Owing to their close resemblance with two-photon Bell states, these states can be called macroscopic Bell states [1]. For these states, the mean values of the polarization Stokes observables vanish, showing their unpolarized nature in the first order in the intensity. For the triplet states |Ψ + mac 〉 , |Φ - mac 〉 and |Φ + mac 〉, fluctuations are suppressed for S 1 , S 2 and S 3 , respectively. At the same time, the singlet state |Ψ - mac 〉 has noise suppressed in all the Stokes parameters simultaneously. 3. Quantum Polarization Tomography Quantum polarization tomography is a method for the reproduction of polarization quasi-probability distribution (QPD) function, which characterizes the polarization properties of a quantum state from the simple polarization measurement results [3]. In quantum polarization tomography, the polarization QPD W (r , θ , φ ) (in spherical coor- dinates) is reconstructed by taking the second derivative of the probability distribution (shown as H ′′ s ) with respect to the Stokes observables (s) obtained for different directions (ϑ i , ϕ j ) on the Stokes space and then summing them up, W (r , θ , φ ) ∝ -Δϑ Δϕ N,M ∑ i, j=1 sin ϑ i H ′′ s (r , θ , φ , ϑ i , ϕ j ) , (2)