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arXiv:0812.4686

Spatial multimode entanglement within one laser beam

Jiří Janoušek, K. Wagner, J-F. Morizur, Nicolas Treps, Ping Koy Lam, C. C. Harb, Hans‐A. Bachor

Published Dec 26, 2008• 1 citation
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.0812.4686

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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.
The quantum nature of light imposes a limit to the detection of all properties of a laser beam. We show how we can reduce this limit for a measurement of the position of a light beam on a quadrant detector, simultaneously in two tranverse directions. This quantum laser pointer can measure the beam direction with greater precision than a usual laser. We achieve this by combining three beams, one intense coherent and two vacuum squeeezed beams, with minimum losses into one spatially multimode beam optimized for this application.
Quantum correlations, particularly squeezing and entanglement, are essential in quantum technologies such as metrology, computation, and simulation, as well as in foundational studies. In quantum optics, these phenomena are often intertwined: two squeezed beams can be transformed into entangled beams by mixing them at a beam splitter, and vice versa. However, it is less common to encounter states where two beams are simultaneously squeezed individually while retaining global entanglement. These hybrid states evidently present potential possibilities for applications. In this work, we propose a compact single-cavity source based on a nondegenerate optical parametric oscillator operated below threshold, capable of generating such light—signal and idler beams that are quadrature-squeezed individually while maintaining global entanglement. This behavior arises from an additional linear coupling between the signal and idler, resembling a beam-splitter interaction. We discuss two physical implementations of this system: one based on intra-cavity electro-optic modulators and the other on optomechanical interactions. This unique combination of local and non-local quantum correlations opens the door to novel quantum communication and metrology protocols.
A beam splitter is a basic linear optical element appearing in many optics experiments and is frequently used as a continuous-variable entangler transforming a pair of input modes from a separable Gaussian state into an entangled state. However, a beam splitter is a passive operation that can create entanglement from Gaussian states only under certain conditions. One such condition is that the input light is suitably squeezed. We demonstrate, experimentally, that a beam splitter can create entanglement even from modes which do not possess such a squeezing provided that they are correlated to, but not entangled with, a third mode. Specifically, we show that a beam splitter can create three-mode entanglement by acting on two modes of a three-mode fully separable Gaussian state without entangling the two modes themselves. This beam splitter property is a key mechanism behind the performance of the protocol for entanglement distribution by separable states. Moreover, the property also finds application in collaborative quantum dense coding in which decoding of transmitted information is assisted by interference with a mode of the collaborating party.
Entanglement between large numbers of quantum modes is the quintessential resource for future technologies such as the quantum internet. Conventionally, the generation of multimode entanglement in optics requires complex layouts of beamsplitters and phase shifters in order to transform the input modes into entangled modes. Here we report the highly versatile and efficient generation of various multimode entangled states with the ability to switch between different linear optics networks in real time. By defining our modes to be combinations of different spatial regions of one beam, we may use just one pair of multi-pixel detectors in order to measure multiple entangled modes. We programme virtual networks that are fully equivalent to the physical linear optics networks they are emulating. We present results for N=2 up to N=8 entangled modes here, including N=2, 3, 4 cluster states. Our approach introduces the highly sought after attributes of flexibility and scalability to multimode entanglement. Multi-partite entanglement is essential not only to understand large quantum ensembles but also to build useful quantum technologies. Armstronget al. demonstrate multimode entanglement of up to eight modes using programmable virtual networks based on linear optics that can be switched in real time.
The measurement sensitivity of the pointing direction of a laser beam is ultimately limited by the quantum nature of light. To reduce this limit, we have experimentally produced a quantum laser pointer, a beam of light whose direction is measured with a precision greater than that possible for a usual laser beam. The laser pointer is generated by combining three different beams in three orthogonal transverse modes, two of them in a squeezed-vacuum state and one in an intense coherent field. The result provides a demonstration of multichannel spatial squeezing, along with its application to the improvement of beam positioning sensitivity and, more generally, to imaging.
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.