Quantum Measurement Of Optical Transverse Small Displacements

Quantum optics is a subject developed from quantum mechanics. It majorly studies the quantum properties of light, i.e., treating light as a stream of photons rather than as electromagnetic waves. Since laser is invented in 1960, theories and experiment has been developed rapidly. In quantum optics, quantum noise is always an important object of study. According to Heisenberg uncertainty principle, the measurement fluctuation always exists for any measurement of a couple of conjugate quantities. Improving the precision of one quantity will decrease that of the other, which provides potential applications to quantum metrology and measurements beyond shot noise limit. Nowadays, quantum optics has applications in many science and technology areas such as quantum information transferring, quantum metrology, quantum imaging and interactions between light and atoms.The original quantum optics studies the photon distribution noise in the light propagation or in the time dimension. In 1999, Kolobov present the concept of spatial squeezing, expanding it to the noise of transvers position or angular direction of the light beam. Then the measurement techniques of beam’s transvers position or angular direction were developed rapidly. Since Treps et al. made a quantum laser pointer in 2003, Wagner et al. obtained spatial entanglement in 2008 and Taylor et al. applied spatial squeezing techniques into biological measurement beyond quantum noise limit in 2013.In this thesis, we studied about the relative theory and experiment on the small transvers displacement measurement of laser beam. The main contents are as follows:1. The spatially distribution properties of high-order Hermite-Gauss modes and its orthogonality and normalization are introduced based on which the properties and some applications of nonclassical optical field, especially spatially nonclassical field are briefly introduced.2. Some basic techniques in quantum optics experiment are introduced, including matching of Gaussian beams, factors influencing the detection efficiencies and solutions, analysis to experimental system’s stability and methods of improving it.3. The autolocking system of high-order Hermite-Gauss modes are devised in experiment, realizing autolocking for TEM00, TEM10 and TEM20 modes.4. Displacement measurement beyond quantum noise limit was implemented using spatial squeezing, increasing the precision of measurement.5. The scheme of small-displacement measurements based on high-order Hermite-Gauss modes is presented, proving that using high-order Hermite-Gauss modes can optimize the precision of small-displacement measurement; Possible detection setups to reach the quantum noise limit with high-order modes are analyzed; With TEM00 and TEM10 as the signal modes respectively, the displacement measurement are demonstrated, affirming the previous theory. The innovative wok during the doctoral period is in the following:1) Devised the autolocking system of high-order Hermite-Gauss modes; realized autolocking of TEM00, TEM10 and TEM20 modes.2) Experimentally obtained TEM10 mode amplitude squeezing; based on this, generating spatially squeezed light and demonstrated the displacement measurement beyond quantum noise limit.3) Theoretically presented the scheme of displacement measurement based on high-order Hermite-Gauss modes and proved that with higher-order modes can improve the measurement precision; experimentally demonstrated the displacement measurements with TEM00 and TEM10 modes, respectively, as the signal beams, affirming the previous theory.