Guide of this thesis

Here, we provide the guide of this thesis, for a part of readers who just want to find some information but do not want to read the whole thesis.

In Chapter2, we discuss the theoretical background of cavity-enhanced SPDC photon source. Some important properties of cavity-SPDC are presented in this Chapter. That includes the first-order correlation function of cavity-SPDC source and further show the cluster effect in the non-degeneracy photon source. After that, the second-order corre-lation function is introduced which can be used to illustrate the bandwidth of the photon source. At the end of this Chapter, we discuss the quantum benchmark for photon sources, such as the auto-correlation function and the Cauchy–Schwarz inequality.

Chapter3start to introduce the experimental system of the photon source. First, we present the detail of the design for the photon source. Afterward, we verify the charac-terization of optical parametric oscillators. By using a high pump power to generate the OPO fields, we can directly observe the cavity modes and frequency of generated fields.

doi:10.6342/NTU201901825 On the other hand, the strong OPO fields also allow us to use for locking the cavity and

stabilize the frequency of generated fields. After the verification for the OPO fields, we then show the observation of SPDC photon-pairs. The two-photon correlation function is presented. Furthermore, we verify the violation of Cauchy–Schwarz inequality of our source. In the end, by sending the photons to the cesium cell, we also demonstrate the photon-atom interaction and further show the frequency of generated photons are locked at the atomic transition.

Chapter4turn the attention to the theoretical background of EIT-based quantum mem-ories. We detail to describe the theory of three-level atomic system and calculate the im-portant properties in EIT system, including the slow light, the principle of light-storage by EIT, and the quantum fidelity of single photon in EIT. On the other hand, we con-sider the manipulation process in order to control the retrieval light and further improve the quantum fidelity. Final, we introduce the connection between the EIT-QMs and the photon source. By measuring the two-photon correlation function after interacting with EIT-QMs, we can further estimate the quantum fidelity of single photons.

Chapter5 integrate our system of the photon-pair source(Chapter 2 and 3) with the atomic quantum memories. In this chapter, we first introduce the experimental setups and the characterizations of the photon source and quantum memories. In order to connect two different systems(solid-state photon-source and atomic QMs), we then present the scheme for connecting. After that, several verifications for atom-photon interaction are shown, such as the OPO slow light, single-photon slow light, and the EIT- spectrum by photon source. Further, by the protocol of storage and manipulation processes in quan-tum memories, we achieve the storage and manipulation for the heralded single photons.

We systematically analyze the nonclassical correlations after storage and manipulation and further verify the process is to maintain the quantum nature of light. On the other hand, we also compare the agreement between the theory provided by Chapter4with the experimental results.

Chapter6conclude the theory, the experimental results and further gives suggestions for improving the photon source and quantum storage system.

Chapter 2

Theoretical background of doubly

resonant cavity-enhanced spontaneous parametric down-conversion

In this chapter, we detailed discusses the theoretical basis of cavity-enhanced spontaneous parametric down-conversion(SPDC) under doubly resonance conditions. Firstly, in Sec-tion.2.1, we introduce the setup of cavity-enhanced SPDC photon-pair source. In order to picture the behavior of generated fields, we further write down the field operators both inside and outside the cavity. By using the field operators, the interaction Hamiltonian of SPDC is characterized more clearly and further shows the cavity effect for the gener-ated fields. Thanks for the perturbation theory, we then evaluate the biphoton state by the interaction Hamiltonian. The biphoton state gives an outset let us consider deeper behav-ior of generated photon pairs, such as the first-order correlation function and two-photon correlation function. In the in Section.2.2, we demonstrate the first-order correlation that clearly shows the cluster effect which is an important effect for avoiding the multi-mode operation of the photon source. Furthermore, the two-photon correlation function pro-vides a way to estimate the bandwidth of photon pairs. After that, in Section.2.3, we start to consider the quantum properties of the generated quantum state. By introducing the auto-correlation function and Cauchy–Schwarz inequality, we then evaluate the quantum benchmark for the cavity-SPDC source. Final, we give the summary for this Chapter in Section.2.4. The discussion given in this Chapter provides useful tools for estimating the properties of the photon source in the real experiment.

doi:10.6342/NTU201901825

Pump, 𝑘𝑝 Signal, 𝑘𝑠

Idler, 𝑘𝑖

𝜒⁽²⁾

SPCM1

SPCM₂ SPDC cavity

Figure 2.1: Cavity-enhanced SPDC photon pair source. The pump beam injects into the optical cavity to generate the signal and idler fields. In our case, the cavity is a resonator for both the field of signal and idler. The output fields are detected by two single-photon counting modules(SPCM) in order to analyze the time-correlation between signal and idler.

2.1 Cavity-enhanced spontaneous parametric down-conversion

Now we start to introduce the system of the photon-pair source based on cavity-enhanced SPDC. The scheme is done by placing the nonlinear medium into the optical cavity, then let cavity modes to repress the bandwidth of generated photon-pairs, further to obtain the narrow-band photon pairs. Therefore, the cavity must be designed as a resonator for both the field of signal and idler. In this section, we first consider a χ⁽²⁾-medium inside the optical cavity with the experimental scheme which shown in Fig.2.1. In order to picture the interaction inside the medium, we then write down the interaction Hamiltonian of SPDC. Final, we introduce the field operator further to depict the behavior of light in the optical resonator.