Entangling the Spatial Properties of Laser Beams

Image 1: Physicists Jiri Janousek, Hongxin Zou and Kate Wagner (left to right) control the entanglement experiment at the Australian National University.

The Quantum Imaging team (K. Wagner, J. Janousek, H. Zou, C. C. Harb, and H-A. Bachor) of the ARC Centre of Excellence for Quantum-Atom Optics (ACQAO) at the Australian National University has experimentally demonstrated entanglement of the spatial properties (position and momentum) of two laser beams. This research has been done in collaboration with the Laboratoire Kastler Brossel (J. F. Morizur, N. Treps) in France.

The scientists have achieved spatialy entangled beams by combining a TEM₀₀ reference beam with a squeezed TEM₁₀ beam, and then entangling this beam with another TEM₁₀ squeezed beam. For each entangled beam, a measurement can be made on the TEM₁₀ component in order to find the beam position (real part) or the transverse beam momentum (imaginary part).

A direct measurement of the correlations between the two beams allows a calculation of the degree of inseparability. The two beams are entangled if these correlations are stronger than can be attained by classical means. The EPR (Einstein, Podolsky and Rosen) entanglement is measured by making predictions on what will be measured on one beam, based on a measurement of the other beam, and this is quantified by the degree of EPR paradox. An inseparability measurement of 0.51 and a degree of EPR paradox of 0.62 have been achieved, showing a genuine proof of the entanglement of position and momentum of two laser beams.

Image 2: No laser beam can have a fixed position or momentum. Spatial entanglement manifests itself as a strong quantum correlation between the position and direction of two beams, A (blue) and B (red). On the left, this illustration shows the fluctuating directions θ_A and θ_B of two beams, which are correlated, and on the right, the positions X_A and X_B, which are anti-correlated. For perfectly entangled beams the differences (θ_A-θ_B) and (X_A+X_B) would both be zero. Real entangled beams have a small residual differential movement. The variances V(X_A+X_B) and V(θ_A-θ_B) are calibrated against their respective quantum noise limit (QNL), which corresponds to the differential movement of two laser beams with independent quantum noise. A good measure of entanglement is the Inseparability, which for a symmetric system is the product I = V(X_A+X_B) V(θ_A-θ_B). This is shown as the area of the filled rectangles in the centre of this figure. Each slice of the tower represents one measurement and the comparison of the area with the QNL (the green box) shows directly the degree of inseparability.

This is the first time optical multi-mode entanglement has been created, and this is a very clear demonstration of the original ideas of Einstein, Podolsky and Rosen, applied to the position and momentum of continuous laser beams. The technology developed by the Quantum Imaging team at ACQAO can be used to make high precision optical measurements, or as a resource for new quantum information applications, particularly those that require multi-mode entanglement.

Reference
[1] "Entangling the Spatial Properties of Laser Beams",
Katherine Wagner, Jiri Janousek, Vincent Delaubert, Hongxin Zou, Charles Harb, Nicolas Treps, Jean François Morizur, Ping Koy Lam, Hans A. Bachor,
Science, v.321. no. 5888, pp. 541 - 543 (2008). Abstract.
[2] Wikipedia page on EPR paradox.