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Quantum protocols with transverse spatial modes

Jean‐François Morizur

Published Jan 1, 2011• 1 citation
Publisher

Abstract

We present in this thesis a study of the spatial properties of light at the quantum level. More specifically, we focus on techniques to manipulate the quantum fluctuations of different degrees of freedom in a beam's transverse plane, and on the quantum protocols we can implement using these specific fluctuations. We begin by providing an experimental characterization of different methods to manipulate the quantum fluctuations of multiple transverse profiles, or modes, in one beam. While manipulating the quantum fluctuations of a mode, a process known as squeezing, for a single mode beam can be performed very efficiently using a conventional optical parametric oscillator, we present implementations of different, less conventional techniques able to generate a beam carrying multiple squeezed modes. Conventionally, the squeezed modes we can generate using these techniques are fixed by the optical design. We present a new optical system, called a Unitary Programmable Mode Converter (UPMC), able to reshape these modes at will. We show theoretically that such a UPMC can in principle perform any desired reshaping of the modes. We present the performances of an experimental implementation of the UPMC, both in a classical and quantum context. We find that the UPMC performs as predicted, and we present a method to optimize the UPMC settings taking into account experimental restrictions. The UPMC, combined with a technique to build a beam carrying multiple squeezed modes, allows us to generate a beam with squeezing in any desired set of spatial modes. In order to detect these fluctuations, we built a multipixel homodyne detection, a detection system able to record simultaneously the quantum fluctuations in all these modes. We provide in this thesis our solutions to overcome the electronic challenges associated with such a device, and present an experimental characterization of the performances of our multipixel homodyne detection. Finally, we combine these experimental characterizations to discuss how these techniques help us implement different quantum protocols involving multiple spatial modes, more specifically quantum enhanced detections and cluster states quantum computation.

DOI
10.25911/5d5e77938fdd5

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We present in this thesis a study of the spatial properties of light at the quantum level. More specifically, we focus on techniques to manipulate the quantum fluctuations of different degrees of freedom in a beam's transverse plane, and on the quantum protocols we can implement using these specific fluctuations. We begin by providing an experimental characterization of different methods to manipulate the quantum fluctuations of multiple transverse profiles, or modes, in one beam. While manipulating the quantum fluctuations of a mode, a process known as squeezing, for a single mode beam can be performed very efficiently using a conventional optical parametric oscillator, we present implementations of different, less conventional techniques able to generate a beam carrying multiple squeezed modes. Conventionally, the squeezed modes we can generate using these techniques are fixed by the optical design. We present a new optical system, called a Unitary Programmable Mode Converter (UPMC), able to reshape these modes at will. We show theoretically that such a UPMC can in principle perform any desired reshaping of the modes. We present the performances of an experimental implementation of the UPMC, both in a classical and quantum context. We find that the UPMC performs as predicted, and we present a method to optimize the UPMC settings taking into account experimental restrictions. The UPMC, combined with a technique to build a beam carrying multiple squeezed modes, allows us to generate a beam with squeezing in any desired set of spatial modes. In order to detect these fluctuations, we built a multipixel homodyne detection, a detection system able to record simultaneously the quantum fluctuations in all these modes. We provide in this thesis our solutions to overcome the electronic challenges associated with such a device, and present an experimental characterization of the performances of our multipixel homodyne detection. Finally, we combine these experimental characterizations to discuss how these techniques help us implement different quantum protocols involving multiple spatial modes, more specifically quantum enhanced detections and cluster states quantum computation.
As the generation of squeezed states of light has become a standard technique in laboratories, attention is increasingly directed towards adapting the optical parameters of squeezed beams to the specific requirements of individual applications. It is known that imaging, metrology, and quantum information may benefit from using squeezed light with a tailored transverse spatial mode. However, experiments have so far been limited to generating only a few squeezed spatial modes within a given setup. Here, we present the generation of single-mode squeezing in Laguerre-Gauss and Bessel-Gauss modes, as well as an arbitrary intensity pattern, all from a single setup using a spatial light modulator (SLM). The degree of squeezing obtained is limited mainly by the initial squeezing and diffractive losses introduced by the SLM, while no excess noise from the SLM is detectable at the measured sideband. The experiment illustrates the single-mode concept in quantum optics and demonstrates the viability of current SLMs as flexible tools for the spatial reshaping of squeezed light.
As the generation of squeezed states of light has become a standard technique in laboratories, attention is increasingly directed towards adapting the optical parameters of squeezed beams to the specific requirements of individual applications. It is known that imaging, metrology, and quantum information may benefit from using squeezed light with a tailored transverse spatial mode. However, experiments have so far been limited to generating only a few squeezed spatial modes within a given setup. Here, we present the generation of single-mode squeezing in Laguerre-Gauss and Bessel-Gauss modes, as well as an arbitrary intensity pattern, all from a single setup using a spatial light modulator (SLM). The degree of squeezing obtained is limited mainly by the initial squeezing and diffractive losses introduced by the SLM, while no excess noise from the SLM is detectable at the measured sideband. The experiment illustrates the single-mode concept in quantum optics and demonstrates the viability of current SLMs as flexible tools for the spatial reshaping of squeezed light. (C) 2016 Optical Society of America
We present the key elements required for continuous variable parallel quantum information protocols based on spatial multimode quantum correlations. We describe techniques for encoding, combining and detecting spatial quantum information with high efficiency in the individual transverse modes. Until now, the missing feature for the implementation of such protocols was the generation of squeezing in higher order transverse Hermite-Gauss modes. We experimentally demonstrate squeezing in selective modes by fine-tuning the phase matching condition of the nonlinear chi(2) material and the cavity resonance condition of an optical parametric amplifier. Combined, these results open the way to practical multimode optical quantum information systems.
Nonclassical effects such as squeezing, antibunching, and sub-Poissonian statistics of photons have been attracting attention in quantum optics over the last decade. Up to now most theoretical and experimental investigations have been carried out exclusively in the time domain while neglecting the spatial aspects by considering only one spatial mode of the electromagnetic field. In many situations such an approximation is well justified. There are, however, problems that do not allow in principle a single-mode consideration. This is the case when one wants to investigate the quantum fluctuations of light at different spatial points in the plane perpendicular to the direction of propagation of the light beam. Such an investigation requires a complete description of quantum fluctuations of light in both time and space and cannot be done within a single-mode theory. This space-time description brings about a natural generalization into the spatial domain of such notions as the standard quantum limit, squeezing, antibunching, etc. It predicts, for example, the possibility of generating a light beam with sub-Poissonian statistics of photons not only in time but also in the beam's transverse plane. Of particular relevance to the applications is a situation in which the cross section of the light beam contains several nonoverlapping areas with sub-Poissonian statistics of photons in each. Photodetection of such a beam produces several sub-shot-noise photocurrents depending on the number of independent areas with sub-Poissonian statistics. This is in marked contrast to the case of a single-mode sub-Poissonian light beam in which any attempt to collect light from only a part of the beam deteriorates the degree of shot-noise reduction. This property of multimode squeezed light opens a range of interesting new applications in optical imaging, optical parallel processing of information, parallel computing, and many other areas in which it is desirable to have a light beam with regular photon statistics across its transverse area. The aim of this review is to describe the recent development in this branch of quantum optics.
The spatial character of the noise on a light field affects its usefulness for imaging. Multi-spatial-mode (MSM) squeezed light has noise below the quantum noise limit in multiple spatial modes, and can be used for super resolution imaging. The generation of such light has long been an experimental goal within the field of quantum optics. \n \nThis work introduces the theory behind the generation of squeezed light, and its measurement using a homodyne detector. A four-wave mixing process in a rubidium 85 vapour is used to experimentally generate squeezed light. The properties of this squeezed light are investigated, through the use of homodyne detection with a bichromatic LO. \n \nThis thesis further investigates how the squeezed quadrature changes from amplitude to phase over a range of 40 MHz. The MSM nature of a squeezed light field is directly investigated. The field is shown to contain at least 75 squeezed spatial modes in the frequency domain, each squeezed at a level of up to -2.5 dB. This thesis develops techniques to measure the spatial character of noise on a light field in the time domain. These are promising techniques for the analysis of the MSM nature of a squeezed light in the time domain.
Multimode squeezed light is a key resource for high-dimensional quantum technologies, enhancing metrological sensitivity, boosting communication security, and enabling parallel processing in computation. Its practical potential, however, remains constrained by the inherent single-mode operation of homodyne detection, necessitating post-processing for multimode characterization. Here, we overcome this long-standing challenge by employing multimode optical parametric amplification, enabling loss-tolerant direct detection of squeezing in each mode, which in turn permits mode sorting after amplification. As a result, we demonstrate, for the first time to the best of our knowledge, the real-time monitoring of multimode squeezing. With a spatial light modulator sorting the modes, we simultaneously measure squeezing in nine spatial modes co-propagating within one beam. Although mode sorting and filtering reduce the detection efficiency to less than 0.3%, we observe high-purity squeezing of up to - 7.9 ± 0.6 dB - to the best of our knowledge, the highest squeezing recorded for pulsed light. Furthermore, we demonstrate real-time, loss-tolerant characterization of continuous-variable entanglement and extend it to the detection of cluster states. Similar methods can be applied in the frequency domain, facilitating a crucial capability for scalable quantum technologies.