Study On Quantum Properties Of Phase-sensitive And Two-beam Pumped Four-wave Mixing Processes

Quantum optics,as a discipline that studies the interaction between quantized op-tical fields and matter,can be divided into two categories of discrete variable and con-tinuous variable according to the dispersion and continuity of the eigenvalues of physical quantities of interest.In recent years,continuous-variable optical systems have attracted extensive attention because of their advantages in the deterministic preparation of optical quantum states.Among them,the four-wave mixing（FWM）process in⁸⁵Rb vapor cell,as a typical continuous-variable optical system,can generate strong third-order nonlin-ear effects without the use of an optical cavity.Moreover,its output optical fields have natural spatial multimode characteristics due to the lack of optical cavity.As a result,it has attracted strong research interest since its discovery.Generally,according to whether the intensities of the output optical fields in⁸⁵Rb vapor cell depend on the phases of the input optical fields,the FWM processes that occur within⁸⁵Rb vapor cell can be divided into two categories,namely phase-sensitive and phase-insensitive FWM processes.When the injected probe and conjugate fields are both vacuum fields or only one injected optical field is coherent field,the intensities of the output optical fields in⁸⁵Rb vapor cell are independent of the phases of the input optical fields,and the corresponding FWM process is commonly referred to as a phase-insensitive FWM process.When there is more than one coherent fields in the injected probe and conjugate fields,the intensities of the output optical fields in⁸⁵Rb vapor cell can vary with the phases of the input optical fields,and the corresponding FWM process is commonly referred to as the phase-sensitive FWM process.In addition,in order to prepare multiple quantum correlated beams,people fully utilize the multimode characteristics of the FWM process in⁸⁵Rb vapor cell,and innovatively design a two-beam pumped FWM process(i.e.,two strong pump beams are simultaneously injected into a⁸⁵Rb vapor cell and symmetrically cross at its center)in the foundation of the single-beam pumped FWM process(i.e.,only one strong pump beam is injected into a⁸⁵Rb vapor cell).This thesis focuses on the quantum properties of phase-sensitive and two-beam pumped FWM processes in the continuous-variable regime,and has completed the following four tasks:1.We give the general expressions of intensity-difference squeezing（IDS）generated from the phase-sensitive and phase-insensitive FWM processes in⁸⁵Rb vapor cell,which clearly shows the IDS transition between the ultra-low average input photon number regime and the ultra-high average input photon number regime.Moreover,we pay more attention to the IDSs produced by the phase-sensitive and phase-insensitive FWM pro-cesses in the ultra-low average input photon number regime and find that the IDSs of phase-sensitive and phase-insensitive FWM processes get enhanced with the increase of the intensity gain,the phase-sensitive FWM process acquires the optimal IDS when its phase is equal to zero,the IDSs of phase-sensitive and phase-insensitive FWM processes get enhanced with the decrease of the average input photon number,and the optimal IDS of phase-sensitive FWM process is better than the IDS of phase-insensitive FWM pro-cess with the same intensity gain.This theoretical work predicts the presence of strong quantum correlation in the ultra-low average input photon number regime for both phase-sensitive and phase-insensitive FWM processes,which may have potential applications for probing photon-sensitive biological samples.2.We theoretically study a scheme,which uses the phase-sensitive cascaded FWM（CFWM）process in⁸⁵Rb vapor cell to enhance the quadripartite quantum correlation generated by the corresponding phase-insensitive CFWM process with the same intensity gains.By calculating and comparing the IDS and intensity-sum squeezing（ISS）generated by the phase-sensitive CFWM process and the corresponding phase-insensitive CFWM process,we find that the IDS among the four beams generated from the phase-insensitive CFWM process can be greatly enhanced by introducing phase-sensitive CFWM process;the phase-sensitive CFWM process can produce ISS,which cannot be generated by the phase-insensitive CFWM process;when the intensity gains of the three FWM processes in the phase-sensitive CFWM process are equal,the value of maximum ISS is equal to that of maximum IDS.In addition,the effects of losses and phase fluctuations on the squeez-ing values of the phase-sensitive CFWM process and the corresponding phase-insensitive CFWM process are discussed through theoretically modeling.The results show that the quantum correlation enhancement of the phase-sensitive CFWM process compared with the corresponding phase-insensitive CFWM process holds also in presence of losses and phase fluctuations.These theoretical results pave the way for experimental imple-mentation and may find applications in quantum precision measurement and quantum communication.3.On the basis of the second work,the pairwise correlations in the quadripartite quantum correlation generated by the phase-sensitive CFWM process were theoretically studied.By respectively calculating the values of IDS of six pairs of beams in the quadri-partite quantum correlation generated by the phase-sensitive CFWM process,and com-paring them with that generated by the corresponding phase-insensitive CFWM process with the same intensity gains,we find that the introduction of phase-sensitive CFWM pro-cess can simultaneously convert a pair of quantum anti-correlated beams and two pairs of classical correlated beams generated by the corresponding phase-insensitive CFWM process into three pairs of quantum correlated beams,and can also cancel some of the intensity-difference noise in two pairs of quantum anti-correlated beams.These theoreti-cal results may find potential applications in classifying quantum states generated by the CFWM processes.4.We experimentally measure the quadrature squeezing in the quadripartite en-tanglement generated from the two-beam pumped CFWM process in⁸⁵Rb vapor cell.Firstly,we experimentally prepare the four-mode quantum state by using the two-beam pumped CFWM process in⁸⁵Rb vapor cell and establish four sets of balanced homodyne detectors.Then,by using the micro-control unit locking technology,we experimentally measure the normalized noise powers of all possible joint quadratures among the four out-put beams and the covariance matrix of the four output beams,so that we can analyze the quadrature squeezing and entanglement properties of the prepared four-mode quantum state.In the end,we experimentally measure the normalized noise powers of four kinds of joint quadratures between six pairs of beams and use the measured covariance matrix to verify the entanglement property of each pair of beams.The experimental results show that quadrature squeezing and entanglement only exist among four output beams,while each pair of beams is quadrature anti-squeezed and not entangled.Such quadripartite entangled state may find potential applications in constructing multi-user quantum secret sharing networks.