Summary and Outlook

<sec>Long-distance entanglement distribution is an important task for quantum communication, but difficult to achieve due to the loss of photons in optical fiber transmission. Quantum repeater is a scheme to solve this problem. In this scheme, the long distance of entanglement distribution is divided into several small parts, the entanglement is established first at both ends of each part, then, the entanglement distance is extended through the entanglement exchange of adjacent interval parts, in order to achieve the long distance entanglement distribution. Of them, the Duan-Lukin-Cirac-Zoller (DLCZ) protocol based on the cold atom ensemble and the linear optics which can generate and store entanglement, is regarded as one of the most potential schemes. In the process of DLCZ, retrieval efficiency is an important index of the quantum repeater, because it will influence each entanglement exchange operation between adjacent quantum repeater nodes. Generally, the retrieval efficiency is improved by optimizing the reading pulse, increasing the optical depth (OD) of the atomic ensemble and the cavity enhancement. The ring cavity constrains the light field to increase the intensity of the interaction between light and atoms, and effectively improve the retrieval efficiency of the quantum memory.</sec><sec>In this work, atomic ensembles are placed in a ring cavity. The cavity length is 3.3 m and the fineness is 13.5. The optical loss of all ring cavity is 21%, mainly including 15% loss of other optical elements and 6% loss of the cell. In order to increase the retrieval efficiency, we need to ensure the mode resonance of read-out photon, write-out photon and locking. The cavity needs two input beams of light: one comes from the path of read-out photon and the other from the path of write-out photon in the reverse direction. The two beams are locked at the same frequency as the write-out photon and the read-out photon respectively. The cavity length is adjusted by moving the cavity mirrors’ positions through translating the frame, to make two light modes resonate. The acousto-optic modulator (AOM) is inserted into the path of the locking to control the frequency of the locking. By adjusting the AOM to change the frequency of the locking, the locking can be coincident with the write-out and read-out cavity modes. Then, the three-mode resonance can be achieved</sec><sec>When the cavity mode resonates with the atomic line, it will lead the atomic formants to split. thereby affecting the enhancement effect of retrieval efficiency. In the experiment, the detuning of the read light will affect the frequency of the read-out photon, and further affect the detuning of the cavity mode with the resonance line of the atom. Thus, by increasing the detuning between the reading light and the atomic transition line, the frequency splitting between the two modes can be reduced, then enhance the retrieval efficiency. We study the relation between the enhancement factor of the retrieval efficiency and the detuning amount of the reading light relative to the atomic resonance line. The results show that when the detuning amount of reading light is 80 MHz, the intrinsic readout efficiency is 45%, and the readout efficiency is enhanced by 1.68 times.</sec>

Quantum memory is one of key ingredients consisting of quantum networks, therefore storing light at single photon level is an important step for realizing quantum networks. A photon, encoded in a high-dimensional state, can significantly increase the information capacity that a photon can carry. Furthermore, quantum memories with the ability to store multiple optical modes offer advantages in speed and robustness over single mode memories in quantum communication and computation. So far, there is no any report about the storage and retrieval of multiple mode images at single photon level. Here, we give a first experimental demonstration to our best knowledge, that two spatial probe fields at single photon level, each imprinted a real image, can be stored and retrieved with a considerable visibility and similarity through electromagnetically induced transparency in cold atomic ensemble. The accomplishment of multiple modes quantum image memory would move closer towards high dimensional quantum networks.

In quantum information science, photons are the best candidate for transmitting information, and atoms are the best candidate for storing information. The combination of these two systems provides a fascinating future for practical applications of the quantum information concepts. The work presented in this thesis mainly consists of two parts. The first part is about manipulation of entangled photons, including the demonstration of a nondestructive CNOT gate, the creation of narrowband entangled photons through cavity-enhanced spontaneous parametric down-conversion, and the realization of interference between narrowband photon sources. The second part is about manipulation of atomic ensembles. The main purpose for this part is to extend the quantum communication distance using the concept of quantum repeater. Within this part, the experimental work includes, the extension of storage lifetime of quantum memories to 1 ms by increasing the wavelength of stored spinwave, the realization of entanglement assisted spinwave interferometer, the demonstration of efficient entanglement swapping with quantum memories, and the realization of quantum teleportation between atomic ensembles.

Quantum networks are composed of quantum nodes which coherently interact by way of quantum channels. They offer powerful capabilities for quantum computation, communication, and metrology. A generic requirement for these realizations is the capability to generate and store quantum states among multiple quantum nodes, and to disseminate these resources throughout the network via the quantum channels. In this thesis, I describe a series of experiments whereby single excitations in atomic ensembles are strongly coupled to optical modes and provide efficient means for the coherent control of entangled states between matter and light. By following the seminal proposal by Duan et al., we have generated measurement-induced entanglement of an excitation between two cold atomic ensembles. Using this system, we investigated the relationship for the global bipartite entanglement and local correlations in its subsystems. In addition, we achieved functional quantum nodes for entanglement distribution. Two pairs of remote ensembles at two quantum nodes were prepared into entangled states in a heralded and asynchronous fashion by the conditional controls of the entanglement. The quantum states of the ensembles were then distributed into polarization entangled states of photons. We also prepared an analogous quantum state and transferred the nonlocal coherence between two pairs of heralded entangled atomic ensembles, providing a step towards entanglement connection. Beyond such probabilistic approaches, we demonstrated an experiment where entanglement between two quantum memories is created by the reversible and deterministic mapping of an entangled state of light via dynamic electromagnetically induced transparency. This experiment opens novel prospects of integrating hybrid quantum systems by way of reversible quantum interfaces between light and matter. Then, we extended our work to multipartite quantum systems. We theoretically investigated the characterization of multipartite mode-entangled states by way of quantum uncertainty relations, and introduced theoretical tools to verify the entanglement orders in multipartite systems. In particular, we achieved entanglement for one delocalized photon among multiple optical modes (N > 2). Finally, we have achieved measurement-induced entanglement of spin waves among four quantum memories. The individual atomic components for the entangled W state of the four ensembles were then coherently converted into four propagating entangled beams of light via superradiant emissions. We observed the statistical and dynamic transitions for the multipartite entangled spin waves. Experiments described in this thesis thereby represent significant advances of experimental and theoretical capabilities to generate, store, transfer, and characterize entanglement of matter and light over quantum networks.

The reversible transfer of a high-dimensional quantum state between a true single photon, an information carrier, and a matter used as a quantum memory with high fidelity and reliability could enhance the channel capacity significantly in addition to overcoming distance limitations of quantum communication schemes through transmission losses. In the Chap. 2, we have introduced how we demonstrated single photon storage encoded with two-dimensional OAM degree of freedom. Due to the infinity Hilbert space spanned by OAM degree of freedom, photon encoded in OAM space can extend to high-dimensional state. Quantum memories have been realized with different physical systems, such as atomic ensembles and solid systems etc., many of them only realize the storage and retrieval of the single photons spanned in a two-dimensional space for example, orthogonal polarizations, therefore only a quantum bit could be stored there. In this Chapter, I will introduce an experimental realization of a quantum memory storing a heralded photon lived in a three-dimensional space spanned by OAM via EIT in a cold atomic ensemble. We reconstruct the storage process density matrix with fidelity of \(85.3\% \) by the aid of a 4-F imaging system experimentally. The ability to store a high-dimensional quantum state with high fidelity is very promising for building a high-dimensional quantum network.

A single-photon source is realized with a cold atomic ensemble (87Rb atoms). A single excitation, written in an atomic quantum memory by Raman scattering of a laser pulse, is retrieved deterministically as a single photon at a predetermined time. It is shown that the production rate of single photons can be enhanced considerably by a feedback circuit while the single-photon quality is conserved. Such a single-photon source is well suited for future large-scale realization of quantum communication and linear optical quantum computation.

In this paper, we propose a slow light-enhanced quantum memory with high efficiency based on atomic frequency comb (AFC) in ion-doped photonic crystal waveguide (PCW). The performance of the quantum memory is investigated theoretically, considering the impact of the signal bandwidth. Both the forward and backward retrieval schemes are analyzed. In the forward retrieval scheme, the analysis shows that a moderate slow light effect can improve the retrieval efficiency to above 50% with very high fidelity, even when the intrinsic optical depth is very low and the signal bandwidth is comparable with the AFC bandwidth. In the backward retrieval scheme, retrieval efficiency larger than 90% can be obtained and fidelity can remain above 90% for signal with bandwidth much narrower than AFC bandwidth, when moderate slow light is introduced into waveguide with low intrinsic optical depth. Although the phase mismatching effect limits the slow light enhancement on retrieval efficiency and decreases the fidelity for signal with bandwidth approaching AFC bandwidth, we design a modified atomic frequency comb structure (MAFC) based on which a moderate slow light can make the retrieval efficiency larger than 85% and keep the fidelity above 80%. Our calculations show that the proposed scheme provides a promising way to realize high efficiency on-chip quantum memory.

We investigate the non-stationary and relaxation phenomena in cavity-assisted quantum memories for light. As a storage medium we consider an ensemble of cold atoms with standard Lambda-scheme of working levels. Some theoretical aspects of the problem were treated previously by many authors, and recent experiments stimulate more deep insight into the ultimate ability and limitations of the device. Since quantum memories can be used not only for the storage of quantum information, but also for a substantial manipulation of ensembles of quantum states, the speed of such manipulation and hence the ability to write and retrieve the signals of relatively short duration becomes important. In our research we do not apply the so-called bad cavity limit, and consider the memory operation of the signals whose duration is not much larger than the cavity field lifetime, accounting also for the finite lifetime of atomic coherence. In our paper we present an effective approach that makes it possible to find the non-stationary amplitude and phase behavior of strong classical control field, that matches the desirable time profile of both the envelope and the phase of the retrieved quantized signal. The phase properties of the retrieved quantized signals are of importance for the detection and manipulation of squeezing, entanglement, etc by means of optical mixing and homodyning.

The physical platform being used in this thesis is the cold atomic ensemble. Several quantum memory protocols can be implemented, including electromagnetically induced transparency (EIT) [1], Duan-Lukin-Cirac-Zoller (DLCZ) [2] scheme, and also controlled reversible inhomogeneous broadening inversion (CRIB) [3], and photonic gradient echo memory (GEM) [4]. In this chapter, we will introduce the first two protocols, which will be experimentally realized in the following chapters. In addition, we will also briefly introduce some basics of the Rydberg interaction [5], which was utilized to tackle the higher-order excitation problem in the ensemble-based quantum memories.

Quantum storage and distribution of entanglement are the key ingredients for realizing a global quantum internet. Compatible with existing fiber networks, telecom-wavelength entangled photons and corresponding quantum memories are of central interest. Recently, 167Er3+ ions have been identified as a promising candidate for an efficient telecom quantum memory. However, to date, no storage of entangled photons, the crucial step of quantum memory using these promising ions, 167Er3+, has been reported. Here, we demonstrate the storage and retrieval of the entangled state of two telecom photons generated from an integrated photonic chip. Combining the natural narrow linewidth of the entangled photons and long storage time of 167Er3+ ions, we achieve storage time of 1.936 μs, more than 387 times longer than in previous works. Successful storage of entanglement in the crystal is certified using entanglement witness measurements. These results pave the way for realizing quantum networks based on solid-state devices.

An efficient multimode quantum memory is a crucial resource for long-distance quantum communication based on quantum repeaters. We propose a quantum memory based on spectral shaping of an inhomogeneously broadened optical transition into an atomic frequency comb (AFC). The spectral width of the AFC allows efficient storage of multiple temporal modes without the need to increase the absorption depth of the storage material, in contrast to previously known quantum memories. Efficient readout is possible thanks to rephasing of the atomic dipoles due to the AFC structure. Long-time storage and on-demand readout is achieved by use of spin states in a lambda-type configuration. We show that an AFC quantum memory realized in solids doped with rare-earth-metal ions could store hundreds of modes or more with close to unit efficiency, for material parameters achievable today.

Quantum communication provides an absolute security advantage, and it has been widely developed over the past 30years. As an important branch of quantum communication, quantum secure direct communication (QSDC) promotes high security and instantaneousness in communication through directly transmitting messages over a quantum channel. The full implementation of a quantum protocol always requires the ability to control the transfer of a message effectively in the time domain; thus, it is essential to combine QSDC with quantum memory to accomplish the communication task. In this Letter, we report the experimental demonstration of QSDC with state-of-the-art atomic quantum memory for the first time in principle. We use the polarization degrees of freedom of photons as the information carrier, and the fidelity of entanglement decoding is verified as approximately 90%. Our work completes a fundamental step toward practical QSDC and demonstrates a potential application for long-distance quantum communication in a quantum network.

(English) Future networks for quantum communication will require a new form of technology in order to operate over long distances. The no-cloning theorem precludes the use of amplification, so quantum repeater schemes have been proposed to achieve long-distance quantum communication through the distribution of entanglement. A key device for this setup is a quantum memory, which is required in order to store entanglement and synchronise its distribution. Among the many physical systems than can be used as a quantum memory, rare-earth ion-doped crystals stand out due to their long coherence times and potential for multiplexing and integration. This thesis reports the use of one such system, Pr3+:Y2SiO5, as a quantum memory using the atomic frequency comb (AFC) protocol. Building on previous work, we improved the performance of the memory to be able to demonstrate light-matter entanglement with a telecommunications wavelength photon and the quantum memory, for both a bulk memory and an integrated version. To measure light-matter entanglement, we use photon pairs generated through cavity-enhanced spontaneous parametric down conversion, where one photon (the signal) is stored in the memory and the other (the idler) is at a telecommunications wavelength. These photon pairs exhibit energy-time entanglement, which we analyse in the time basis using fibre- and AFC-based Mach-Zehnder interferometers. In the first experiment, we demonstrate light-matter entanglement where the bulk quantum memory is used with on-demand retrieval via storage in a spin-wave. We measure interference fringes with average visibilities of 89(2)% for AFC storage, and 70(3)% for spin-wave storage, sufficient to demonstrate entanglement. This is the first such demonstration using an on-demand multimode solid-state memory and telecom photon. We show that entanglement is maintained for up to 47.7 µs of storage. These results were made possible through improvements in the AFC efficiency and the noise filtering. Furthermore, we perform on-demand storage and retrieval of up to 30 temporal modes. We take the next step towards implementing our system in a real world scenario by measuring entanglement over a distance. To do so, we send the idler photons through both optical fibre spools and deployed fibre in the metropolitan area of Barcelona, Spain, while the photon detection still occurs in the same lab. The resulting visibilities (80% or higher) demonstrate that the photonic qubit does not decohere during transmission through the optical fibre. We then decouple the photon creation and detection by measuring non-classical correlations between signal photons detected in the lab, and idler photons detected 16 km away (44 km in fibre) in a different location. The final experiment uses a fibre-integrated memory for light-matter entanglement. We use a Pr3+:Y2SiO5 crystal containing a Type I laser-written waveguide, interfaced directly with optical fibre. The fibre-integration allows for improved transmission and AFC efficiency compared to a free-space coupled waveguide memory. To analyse the performance of the memory, we demonstrate non-classical correlations for storage times up to 28 µs. We perform qubit tomography in the time basis for storage times of 3 and 10 µs, measuring two-qubit fidelities of 86(2)% and 86(4)%, respectively, demonstrating storage of entanglement. These experiments demonstrate the potential of our system for use as part of a quantum repeater, with many opportunities for further improvement to the storage time, efficiency, and multiplexing capability.

Coherently converting the frequency and temporal waveform of single and entangled photons will be crucial to interconnect the various elements of future quantum information networks. Of particular importance is the quantum frequency conversion of photons emitted by material systems able to store quantum information, so-called quantum memories. There have been significant efforts to implement quantum frequency conversion using nonlinear crystals, with non-classical light from broadband photon-pair sources and solid-state emitters. However, solid state quantum frequency conversion has not yet been achieved with long-lived optical quantum memories. Here we demonstrate an ultra-low-noise solid state photonic quantum interface suitable for connecting quantum memories based on atomic ensembles to the telecommunication fibre network. The interface is based on an integrated-waveguide nonlinear device. We convert heralded single photons at 780 nm from a rubidium-based quantum memory to the telecommunication wavelength of 1,552 nm, showing significant non-classical correlations between the converted photon and the heralding signal.

Feasible distribution of quantum entanglement over long distances remains a fundamental step towards quantum secure communication and quantum network implementations. Quantum repeater nodes based on quantum memories promise to overcome exponential signal decay inherent to optical implementations of quantum communication. While performance of current quantum memories hinders their practical application, multimode solutions with multiplexing can offer tremendous increase in entanglement distribution rates. We propose to use a wavevector-multiplexed atomic quantum memory (WV-MUX-QM) as a fundamental block of a multiplexed quantum repeater architecture. We show the WV-MUX-QM platform to provide quasi-deterministic entanglement generation over extended distances, mitigating the fundamental issue of optical loss even with currently available quantum memory devices, and exceeding performance of repeaterless solutions as well as other repeater-based protocols such as temporal multiplexing. We establish the entangled-bit (ebit) rate per number of employed nodes as a practical figure of merit reflecting the cost-efficiency of larger inter-node distances.