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arXiv:quant-ph/0501144 · Physical Review A

Continuous-variable spatial entanglement for bright optical beams

Magnus T. L. Hsu, Warwick P. Bowen, Nicolas Treps, Ping Koy Lam

Published Jul 5, 2005• 26 citations
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Abstract

A light beam is said to be position squeezed if its position can be determined to an accuracy beyond the standard quantum limit. We identify the position and momentum observables for bright optical beams and show that position and momentum entanglement can be generated by interfering two position, or momentum, squeezed beams on a beam splitter. The position and momentum measurements of these beams can be performed using a homodyne detector with local oscillator of an appropriate transverse beam profile. We compare this form of spatial entanglement with split detection-based spatial entanglement.

DOI
10.1103/physreva.72.013802

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A light beam is said to be position squeezed if its position can be determined to an accuracy beyond the standard quantum limit. We identify the position and momentum observables for bright optical beams and show that position and momentum entanglement can be generated by interfering two position, or momentum, squeezed beams on a beam splitter. The position and momentum measurements of these beams can be performed using a homodyne detector with local oscillator of an appropriate transverse beam profile. We compare this form of spatial entanglement with split detection-based spatial entanglement.
We present the latest results on the experimental generation of the position and momentum (x-p) entanglement for bright optical beams [1]. Spatial entanglement of light is a direct demonstration of entanglement of the momentum and position of laser beam as envisioned in the original publication by Einstein, Podolsky and Rosen [2]. Spatial entanglement has potential applications in quantum imaging systems and for quantum communication protocols. The position-momentum entanglement was observed in the form of the degree of inseparability, which was measured to be no larger than 0.76.
Position and momentum were the first pair of conjugate observables explicitly used to illustrate the intricacy of quantum mechanics. We have extended position and momentum entanglement to bright optical beams. Applications in optical metrology and interferometry require the continuous measurement of laser beams, with the accuracy fundamentally limited by the uncertainty principle. Techniques based on spatial entanglement of the beams could overcome this limit, and high-quality entanglement is required. We report a value of 0.51 for inseparability and 0.62 for the Einstein-Podolsky-Rosen criterion, both normalized to a classical limit of 1. These results are a conclusive optical demonstration of macroscopic position and momentum quantum entanglement and also confirm that the resources for spatial multimode protocols are available.
The transverse spatial attributes of an optical beam can be decomposed into the position, momentum, and orbital angular momentum observables. The position and momentum of a beam are directly related to the quadrature amplitudes, while the orbital angular momentum is related to the polarization (spin) variables. In this paper, we study the quantum properties of these spatial variables, using a representation in the Stokes-operator basis. We propose a spatial detection scheme to measure all three spatial variables and, consequently, propose a scheme for the generation of spatial Stokes-operator squeezing and entanglement.
Three different methods have been discussed to verify continuous variable entanglement of intense light beams. We demonstrate all three methods using the same setup to facilitate the comparison. The nonlinearity used to generate entanglement is the Kerr effect in optical fibers. Due to the brightness of the entangled pulses, standard homodyne detection is not an appropriate tool for the verification. However, we show that by using large asymmetric interferometers on each beam individually, two noncommuting variables can be accessed and the presence of entanglement verified via joint measurements on the two beams. Alternatively, we witness entanglement by combining the two beams on a beam splitter that yields certain linear combinations of quadrature amplitudes which suffice to prove the presence of entanglement.