Spatial Higher-order Transverse Mode Squeezed State And Quantum Precision Measurement

Squeezed and entangled states are the core resources of quantum information,which have wide application in the field of quantum measurement,quantum communication and quantum computing.The spatial high-order transverse mode has a more complex directional distribution than the fundamental mode HG00 and has higher sensitivity to spatial information.Therefore,the non-classical spatial high order transverse mode light,such as the squeezed state of special spatial structures,the orbital angular momentum squeezed and entangled states,can achieve higher precision spatial measurements such as tilt,displacement,rotating-angle as well as laser interferometer gravitational-wave observatories.In addition,spatial higher-order transverse mode light further endows quantum states more room for manipulation,and it will increase further the dimensionality of the Hilbert space,greatly improving channel capacity;the spatial higher-order transverse mode will realize singular topological quantum states and provide new insight for further breaking the limits of optical coding,multiplexing,communication,and encryption.At present,the research based on non-classical spatial high order transverse mode light is mainly focused on discrete variable.However,the research on continuous variable（CV）spatial high-order transverse mode quantum state is relatively rare,and has not been explored in depth.Therefore,both the theoretical and experimental research of CV spatial high-order transverse mode quantum state have broad application in quantum information.This thesis focuses on the preparation,measurement,and application of spatial higherorder transverse mode squeezed and entangled states.（i.e.,higher-order Hermite-Gaussian and higher-order Laguerre-Gaussian light fields）.The main contents are as follows:1.We have achieved the preparation of high purity spatial high order transverse mode light.Based on theoretical analysis of a scheme for generating spatial higher-order transverse mode light using a mode conversion cavity and a spatial light modulator,we have experimentally prepared high-purity higher-order Hermite-Gaussian and Laguerre Gaussian lights.2.A higher order Hermite-Gaussian squeezed state is generated.First,we analyze the optimal pump mode corresponding to the higher order Hermite-Gaussian squeezed light,and design a high order mode optical parametric oscillator（OPO）with doubling resonant of the pump light and the seed light,which can not only enhance the optical power of pump light but also purify the pump mode,and experimentally achieve highquality generation and measurement of higher-order Hermite-Gaussian squeezed light.3.High order Laguerre Gaussian squeezed and entangled states is generated.Due to the astigmatism effect introduced by the propagation of higher-order Laguerre Gaussian modes in nonlinear crystals,we have designed an OPO with a folded angle to compensate for astigmatism,and experimentally achieved the generation and measurement of higher-order Laguerre Gaussian squeezed states.Meanwhile,we study a scheme to achieve manipulation of continuous variable orbital angular momentum squeezing and entanglement by pump shaping,and experimentally verify the scheme is feasible and effective.4.In the experiment,a beam of HGm+1,0 squeezed state and a beam of HGm-1,0 coherent state is coupled on the 99/1 beam splitter to generate a mth-order spatial squeezed light,used as probe beam to realize displacement and tilt measurement beyond the standard quantum limit.Compared with the traditional fundamental mode as probe light,the signal-to-noise ratio is increased by 8.6dB and 10 dB respectively.The creative works in the thesis are as follows:1.We designed a high-order mode OPO with pump and seed light doubling resonant,improving the pump power in the cavity and realizing the preparation of 4.3d B rectangular-shaped higher-order Hermite-Gaussian HG50 mode squeezed state for the first time.2.A ring OPO with folded angle was designed to achieve astigmatism compensation for Laguerre Gaussian modes in nonlinear crystals.we first produced OAM mode squeezed state of-5.4 d B and-5.3 d B for the 10LG+ mode and the 10LG-mode respectively in type I OPO below the threshold.In our setup,we generate continuous-wave squeezed states at a wavelength of 1080 nm in the higher-order Laguerre Gaussian modes up to a mode order of 6 using a type-I OPO.3.We first use the HG10（45°）mode and 01LG（l =0,p =1）mode as the pump mode and manipulate the single optical parametric oscillator to realize the mutual conversion of the continuous variable orbital angular momentum LG^±1₀ mode in squeezed state and entangled states.4.For the first time,we use higher-order spatial squeezed beam（fourth-order spatial squeezed beam）to realize displacement and tilt measurement beyond the standard quantum limit.Compared with the fundamental mode as the probe beam,the signal-tonoise ratio increases by 8.6d B and 10 d B,respectively.