Controlled-not gate with orbital angular momentum in a rare-earth-ion-doped solid
Introduction
Recently, the experimental investigation of the interaction between vortex beams carrying orbital angular momentum (OAM) and the atomic ensemble has attracted much attention [[1], [2], [3]]. It is well known that Laguerre-Gaussian (LG) mode field is one important family of these vortex beams [4]. Generally, LG-mode fields with helical phase front carry an OAM per photon in units of , where is a topological charge and represents an azimuthal angle [5]. Usually, each photon carries a quantum bit if the information is encoded in a two-dimensional state, for example, orthogonal polarization states of a photon [6,7]. If the photon is encoded in high-dimensional state (OAM space of the inherent infinite dimension), the information carried by each photon can be significantly increased, and the channel capacity of the network can also be greatly improved [8,9]. Compared with a two-dimensional state, high-dimensional states allow for more efficient quantum information processing [10]. Therefore, the information processing based on OAM states has become a hot topic and has earned much interest.
The future network of quantum information needs the distribution of quantum information over channels between different nodes [11,12]. To overcome the error rate with the long channel distance, the concept of quantum repeater or quantum memory should be introduced to extend the achievable distance of network communication [13]. Some important progresses have been made towards the realization of coherent and reversible information memory. It is found that EIT, as a quantum interference phenomenon, is a powerful method to store and manipulate light field [14]. EIT is widely used to investigate the light-matter interaction. Enhanced optical nonlinearity and light storage have been successfully demonstrated in experiment via EIT technique [[15], [16], [17], [18]]. Especially, there is an increasing interest to use EIT method to manipulate vortex beams carrying OAM. The coherent storage of OAM has been demonstrated in atomic vapors [[19], [20], [21], [22]]. FWM using vortex beams with OAM has been discussed in atomic gases [23,24]. The OAM transfer has been investigated in EIT atomic system [25]. The arithmetic of OAM has been experimentally obtained in EIT-based FWM [26]. CNOT gate based on OAM has been demonstrated in FWM process of rubidium vapor [27].
EIT-related phenomena can be realized in different physical systems, such as atomic ensembles [15] or solid systems [28]. Developing the interaction between OAM and different mediums is very important for further applications. The solid-state medium is preferred for practical applications compared with atomic gases [28]. In this paper, we experimentally investigate CNOT gate with vortex beams carrying OAM via EIT-based storage in an EIT solid medium. By applying the vortex probe field with OAM, we realize the storage and retrieval of OAM in EIT single lambda system. Using the double lambda system to control the retrieval process, the stored information is transferred into a new information channel. The generation of the new signal satisfies the condition of phase matching and OAM conservation. The topological charge of the newly-generated signal field is determined by the applied light fields. By imposing different OAMs into the control and probe fields, we experimentally obtain a CNOT gate with OAM. This demonstration of CNOT gate with OAM could be useful for information processing and quantum computing.
Section snippets
Experimental configuration
Pr3+: Y2SiO5 (Pr:YSO) crystal is used as the experimental medium to perform CNOT gate with OAM. As shown in Fig. 1, the optical transition of is chosen to the coupling of EIT system. The center wavelength of the involved transition is about 606 nm. The ground state and excited state each has three hyperfine levels. The ground-state transition has long coherence lifetime, thus the phenomena of atomic coherence can be effectively demonstrated in this crystal. The inhomogeneous
Experimental results and discussions
Firstly, we perform OAM storage using EIT. The experimental pulse sequences are shown in Fig. 2(a). The probe field is a Gaussian-shaped pulse of 43. After the probe pulse enters the medium, the first control field is switched off, and the probe pulse is mapped into spin coherence. The probe pulse is remitted when the first control field is switched back on. This EIT storage is explained with the dark-state polariton [31], which includes the components of the probe field and spin coherence.
Conclusions
We experimentally demonstrate the CNOT gate with OAM through EIT-based storage in a solid. Using the probe field of vortex beam carrying OAM, we perform the reversible storage of OAM. By controlling the reading control field in the retrieval process, the stored OAM is transferred into a new information channel. Furthermore, we impose OAMs into both the probe field and the first control field, and investigate the spatial structure of the newly-generated signal field. We show that EIT storage
Credit author statement
Lei Wang: Conceptualization, Data curation, Writing-Original Draft. Xiaojun Zhang: Methodology, Formal analysis. Aijun Li: Formal analysis, Investigation. Zhihui Kang: Investigation, Data curation. Haihua Wang: Conceptualization, Writing-Original Draft, Supervision. Jinyue Gao: Funding acquisition, Project administration.
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
The authors acknowledge the financial support from the National Basic Research Program, China (Grant No.2011CB921603), the National Natural Science Foundation of China, China (Grant Nos. 61590930, 11374126, 11404336), Science and Technology Development Plan of Jilin Province , China (20180414010 GH, 20190201133JC).
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