Dependence of retrieval efficiency on the waist ratio of read beam and anti-Stokes photon modes in cavity-enhanced quantum memory

Quantum communication holds promise for absolutely secure information transmission. However, the direct transmission distance of quantum states is limited by the no-cloning theorem and transmission loss. To overcome these problems, Duan et al. proposed a promising quantum repeater scheme, DLCZ protocol (for Duan, Lukin, Cirac, and Zoller, in 2001), in which linear optics and atomic ensembles are used to combine entanglement generation and quantum memory into a single node. A quantum memory with highly retrieval efficiency is beneficial to increase the rate of entanglement swapping, achieving high-speed entanglement distribution. Up to now, high-efficiency quantum memories have been realized using high-optical-depth atomic ensembles or by coupling atomic ensembles with a medium-finesse optical cavity. However, the effect of the waist ratio of read beam and anti-Stokes photon modes on intrinsic retrieval efficiency has not been studied in detail. Here, we study the dependence of intrinsic retrieval efficiency on the waist ratio of read beam and anti-Stokes photon modes in cavity-enhanced quantum memory.In this work, a 87Rb atomic ensemble, that is placed at the center of a passively stabilized polarization interferometer (BD1,2), is used as quantum memory. Firstly, the ensemble is captured through magneto-optical trapping (MOT) and prepared to the Zeeman sub-level of ground state $|5{S_{1/2}},F = 1,m = 0\rangle$. Then, a weak write pulse, with frequency red-detuned from the $|5{S_{1/2}},F = 1,m = 0\rangle$$ \to |5{P_{1/2}},F' = 1,m = 1\rangle $ transition by 110 MHz, illuminates the atoms and induces spontaneous Raman scattering out a Stokes photon. In this regime of weak excitation, the detection of a Stokes photon heralds the storage of a single spin wave $|5{S_{1/2}},F = 1,m = 0\rangle$$ \leftrightarrow |5{S_{1/2}},F = 2,m = 0\rangle $ ($|5{S_{1/2}},F = 1,m = 0\rangle$$\leftrightarrow |5{S_{1/2}},F = 2,m = 2\rangle $) distributed among the whole ensemble. After a programmable delay, a read pulse, red-detuned from the $|5{S_{1/2}},F = 2,m = 0\rangle \to |5{P_{1/2}},F' = 2,m = - 1\rangle $ transition by 110MHz, transfer this spin wave into an anti-Stokes photon. We detect the Stokes photons and anti-Stokes photons with polarization ${\sigma ^ + }$, which means all the spin-wave are stored in a magnetic-field-insensitive state to reduce the decoherence caused by the stray magnetic fields. In order to increase the intrinsic retrieval efficiency, the atomic ensemble is placed in a ring cavity. The cavity length is 4 m, the finesse is measured to be ~15, and the escape efficiency of ring cavity is 52.9%. Both Stokes and anti-Stokes photon qubits are required to resonate with the ring cavity. To meet this requirement, a cavity-locking beam is injected into the cavity to stabilize the cavity length using a Pound-Drever-Hall locking scheme. Finally, we fixed the Stokes (anti-Stokes) photon modes waist and changed the waist ratio by changing the write beam (read beam) waist.The experiment result show that when the waist ratio of read beam and anti-Stokes photon modes is 3, the intrinsic retrieval efficiency is up to 68.9±1.6% and normalized cross-correlation function g(2) reaches 26.5±1.9. We built a theoretical model, the intrinsic retrieval efficiency increases with the rise of the waist ratio, which show that the intrinsic retrieval efficiency is up to the peak when the waist ratio is 3, and the intrinsic retrieval efficiency tends to be stable when the waist ratio continues to increase. The experiment agrees with the theory. In the future, we will improve the intrinsic retrieval efficiency by enhance the fineness of the optical cavity with optimizing the cavity parameters.