Frequency Conversion Of Orbital Angular Momentum Carrying Light And Applications In Quantum Information Processing

Human’s scientific cognition of light can be traced back to the era of Newton, people generally believe that light is particle like at that time, they use this property of light to explain some basic optical phenomenon such as reflection and refraction of light. Later on, Huygens developed wave optics to explain optical interference and diffraction which can not be explained with Newton optics. Until the beginning of twentieth century, the birth of quantum mechanics advances people’s conception on light to a new height, now they all believe that light is wave-particle like. Human’s cognition of light’s degree of freedoms also developed gradually for the wavelength and polarization degree of freedoms to orbital angular momentum (OAM) degree of freedoms. The polarization and wavelength degree of freedoms of light are widely used in many applications like high precision optical measurements, optical sensing and optical communications. Besides polarization and wavelength degree of freedoms of light, it also has OAM degree of freedoms. Because of special transverse spatial structure and unlimited dimensions in the Hilbert space for OAM carried light beams, they have many attractive applications include optical manipulation and trapping, optical tweezers, high capacity and security optical communications, high precision optical measurements and quantum information. Second harmonic generation (SHG), sum frequency generation (SFG) and difference frequency generation (DFG) in nonlinear crystals are effective ways to generate laser source at specific wavelengths. In the field of quantum optics, spontaneous parametric down conversion (SPDC) is widely used in generate many kinds of non-classical photon sources including entangled photon pairs and squeezing states. Furthermore, frequency up-conversion is an effective way for telecom band single photon up-conversion detection and building a quantum interface for telecom band wavelengths and quantum memories operation at visible wavelength band. This thesis is focus on the research of high efficiency frequency conversion of OAM-carrying beams in second order nonlinear processes. Frequency conversion of OAM-carrying photonic states is an effective way to building a wavelength interface for different quantum system operation at different wavelengths. This original study is of significant importance for building a high dimensional quantum network based on photon’s OAM degree of freedoms. The main content of this thesis includes:1. The frequency conversion of OAM-carrying light beams in SHG and SFG are studied based on periodically poled quasi-phase matching crystal. The conservation of OAM in second order nonlinear processes is verified, the possibility to convert OAM superposition states is also demonstrated. Systematic theoretical derivations of the interference and propagation behaviors of OAM beams in the conversion process are provided. In addition, we have studied the dependence of the SFG beam shape on the phase mismatching when pump with two Gaussian modes, we find that the SFG beam shapes change periodically with the change of phase mismatching.2. By putting the nonlinear crystal inside a confocal cavity and pumping the cavity using OAM carrying beam, after the cavity is locked to the cavity’s high order eigen mode the same as the pump mode, high efficiency second harmonic generation of OAM is demonstrated. When the cavity is locked to the pump mode, the circulation power is greatly enhanced, therefore the pump beam can be effectively converted.3. Heralded single photon OAM states at telecom band is up-converted with high efficiency based SFG in cavity. The non-classical properties of the single photon are preserved and the up-conversion OAM sates have non-classical spatial shapes. Furthermore by interference of two OAM states, the coherent property is verified in the conversion process, which shows the capability to convert OAM superposition states.4. Based on the cascade processes of SFG and SPDC, OAM information transfer between classical optical communication network and quantum network is realized. The classical telecom band OAM carrying beam is up-converted to classical visible OAM carrying beam using SFG, then the up-converted OAM beam is used to pump another nonlinear to generate non-degenerate two color OAM entangled photon pairs. The conservation of OAM in the whole transforming processes guarantees that the OAM information possesses by the classical beam is transferred to OAM entangled photon pairs.The innovations of this thesis are shown as following: 1. The frequency conversion of OAM carrying beams in second order nonlinear processes (SHG and SFG processes) are systematically studied based on quasi-phase matching nonlinear crystals. The OAM indexes of the frequency converted OAM beams are determined by using a special designed interferometer, the maximum OAM index obtained for the SHG UV beam is100. The possibility of conversion OAM superposition state is also demonstrated. The transforming and propagation behaviors of OAM beams in SHG and SFG processes are derived in detail, analytical expressions are obtained for the frequency converted beams. We also study the SFG process pumped with two Gaussian beam shapes. The SFG beam shapes change periodically with the change of phase mismatching, the dependence of the SFG beam shape with the crystal length and the pump beams’focus parameters are discussed in details.2. The coupling between OAM carrying beam and cavity’s high order eigen mode is realized for the first time, high efficiency SHG of beam carries OAM index of2is demonstrated. Long time stabilization is realized by using PDH cavity locking technique to lock the cavity to its high cavity mode, the maximum OAM-carrying SHG power is22.5mW with an efficiency of10.3%. The OAM index of the SHG beam determines using interference method is4, which implies that OAM is conservation in the cavity enhanced SHG process.3. High efficiency up-conversion of telecom band heralded single photon OAM states is studied for the first time, the non-classical properties of the single photon OAM states are preserved in the up-conversion process, up-converted photons have non-classical spatial shapes. We use Sagnac interferometer to generate OAM and polarization hyper superposition states and verify that OAM superposition states can be up-converted coherently. In the experiment, a single resonance bow-tie cavity for the pump beam is used to enhance the circulation power of the pump beam inside the cavity, therefore the conversion efficiency of OAM-carrying beam is enhanced, the quantum conversion efficecny for beam carries OAM index of1is0.083.4. For the first time, cascade processes of SFG and SPDC are used to realize OAM information transfer from classical network to quantum network. By cavity enhanced SFG, a1550nm OAM-carrying beam is up-conveted efficenctly to525.5nm OAM-carrying beam. The up-converted OAM-carrying beam is used to pump a SPDC crystal to generate795nm and1550nm nondegenerate photon pairs correlated in OAM degree of freedoms.The experiments demonstrated that via changing the OAM carries by the classical1550nm beam, the OAM correlation of the photon pairs are changed. We also caraterize the OAM entanglement quality of the photon pairs in2-dimensional OAM subspaces use different methods such as interference, CHSH inequality and quantum tomogapy.