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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Squeezed states of light and photon-noise-free control of light wavefront

I. V. Sokolov

Published Dec 16, 1992• 1 citation
Publisher

Abstract

This paper provides a simple physical consideration of a new type of squeezed state of light: space-time squeezed state. As it was shown recently, spatial-multimode broadband squeezed light can generate (by homodyne detection) photon counting statistics that are regular not only in time, but also in the plane of observation. A possible advantage of application of space-time squeezed light in a number of areas of quantum optics (i.e., low-noise generation, detection of optical images, Fourier optics, and holography) is discussed from an elementary point of view.

DOI
10.1117/12.131815

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This paper provides a simple physical consideration of a new type of squeezed state of light: space-time squeezed state. As it was shown recently, spatial-multimode broadband squeezed light can generate (by homodyne detection) photon counting statistics that are regular not only in time, but also in the plane of observation. A possible advantage of application of space-time squeezed light in a number of areas of quantum optics (i.e., low-noise generation, detection of optical images, Fourier optics, and holography) is discussed from an elementary point of view.
Summary form only given.It has previously been shown that a traveling-wave optical parametric amplifier can generate multimode squeezed states of light. Homodyne detection of multimode squeezed light, under certain physical conditions, results in sub-Poissonian statistics of photons not only in time but also in the transverse plane of the light beam. Of particular relevance to applications is a situation when the cross section of the light beam contains several nonoverlapping areas with sub-Poissonian statistics of photons within each of them. Under photodetection of such a beam of light, several sub-shot-noise photocurrents can be produced according to the number of independent areas with sub-Poissonian statistics. This is in drastic contrast to the case of a single-mode sub-Poissonian light beam, where any attempt to collect light only from a part of the beam deteriorates the degree of shot-noise reduction. This property of multimode squeezed light opens a range of new interesting applications in optical imaging, optical parallel processing of information, parallel computing, and many other phenomena where it is desirable to have the regular statistics of photons across the transverse plane of the electromagnetic wave. We describe the application of multimode squeezed light in sub-shot-noise microscopy, noiseless amplifications of optical images, and optical imaging. We also consider the possibility of improving the resolution in optical imaging and microscopy beyond the Rayleigh limit via multimode squeezed light.
Recently a number of laboratories have demonstrated the generation of squeezed light, a new kind of light which in some of its aspects exhibits less quantum noise then coherent light. Here a description will be given of how such light is generated and detected. With the successful generation and detection of squeezed light by a number of laboratories1-5 a new degree of control over the quantum statistics of light has been achieved. Light can now be generated which, in some of its aspects, has less quantum noise than coherent light. Such light may find applications in optical communications and in sensitive and precision measurement. Here a description will be given of how squeezed light is generated and detected.6-8 The discussion will be restricted to what is called "quadrature squeezing". The electric field operator for a single mode of the electromagnetic field can be written in the form
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.
Summary form only given. To achieve super-resolution one must take into account a priori information about localization of the object. Such an a priori information exists in the case of an object of finite size. Its Fourier transform located in the focal plane of the lens is an entire analytic function, and analytic continuation of the object spectrum outside the spatial-frequency band allows for unlimited resolution. However such a super-resolution is extremely sensitive to the noise in the detected image. The ultimate limit of super-resolution is determined by the quantum fluctuations of light in the detection plane. We present the quantum theory of super-resolution for a one-dimensional coherent optical imaging scheme and discuss possibilities of improving the resolution limit by using multimode squeezed light. For quantum-mechanical description of this scheme we take into account the vacuum fluctuations of the electromagnetic field in the input plane outside the object. Interference of these vacuum fluctuations with the field amplitude of the object in the detection plane is the origin of the standard quantum limit or shot noise of photodetection in the image. To go beyond this limit we suggest to illuminate the object with multimode squeezed light having the spot size much larger than the object area. Then the vacuum fluctuations outside the object can be effectively suppressed resulting in sub-shot-noise detection of the image.