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Quantum-Atom Optics Downunder (QAO)

Demonstrating spatial entanglement for the position and momentum of laser beams

C. C. Harb, K. Wagner, Hongxin Zou, Jiří Janoušek, V. Delaubert, Nicolas Treps, Ping Koy Lam, Hans‐A. Bachor

Published Jan 1, 2007• 0 citations
Publisher

Abstract

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.

DOI
10.1364/qao.2007.qmb4

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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.
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.
Biphoton systems exhibiting entanglement in position-momentum variables, known as spatial entanglement, are among the most intriguing and well-studied phenomena in quantum optics. A notable subset of these are phase entangled states, where entanglement manifests purely through correlations in the spatial phase of the wavefunction. While the generation of such states from biphotons via spontaneous parametric down-conversion has been explored, their physical implications and applications remain under-investigated. In this work, we theoretically and experimentally examine a unique form of phase entanglement known as `pure' phase entanglement. This state exhibits the unusual feature that the position of one photon is correlated with the momentum of the other. Unlike typical spatially entangled states, it shows no direct correlation in position or momentum between the two photons, underscoring that all correlations arise purely from the spatial phase of the wavefunction. We delve deeper into the theory of this state and experimentally construct it from known phase-entangled states. To certify its properties, we propose a setup that performs a "one-particle momentum measurement" and explore the various tunable parameters. We also highlight potential applications of this state in quantum optics and imaging experiments.
Abstract Spatial entanglement is at the heart of quantum enhanced imaging applications and high-dimensional quantum information protocols. In particular, for imaging and sensing applications, quantum states with a macroscopic number of photons are needed to provide a real advantage over the classical state-of-the-art. We demonstrate the Einstein–Podolsky–Rosen (EPR) paradox in its original position and momentum form with bright twin beams of light by showing the presence of EPR spatial (position–momentum) entanglement. An electron-multiplying charge-coupled-device camera is used to record images of the bright twin beams in the near and far field regimes to achieve an apparent violation of the uncertainty principle by more than an order of magnitude, which remains statistically significant even in the limit of a small number of images. We further show that the presence of quantum correlations in the spatial and temporal degrees of freedom leads to spatial squeezing of the bright twin beams in both the near and far fields. This provides another verification of the spatial entanglement and points to the presence of hyperentanglement in the bright twin beams.
Optical entanglement is a key requirement for many quantum communication protocols. Conventionally entanglement is formed between two distinct beams, with the quantum correlations being measured at separate locations. We show entanglement between the modes within one beam. Our technique is particularly elegant and a major advance towards practical systems with minimum complexity. We demonstrate three major experimental achievements: (i) only one source is required to produce squeezed light in two orthogonal spatial modes, (ii) the entanglement is formed through lenses and beam rotation, without the need of a beam splitter and (iii) the quantum correlations are measured directly and simultaneously using a multi pixel, quadrant detector.