Entanglement of Light-Shift Compensated Atomic Spin Waves with Telecom Light

Entanglement of a 795 nm light polarization qubit and an atomic Rb spin-wave qubit for a storage time of 0.1 s is observed by measuring the violation of Bell’s inequality ($S=2.65\pm 0.12$). Long qubit storage times are achieved by pinning the spin wave in a 1064 nm wavelength optical lattice, with a magic-valued magnetic field superposed to eliminate lattice-induced dephasing. Four-wave mixing in a cold Rb gas is employed to perform light qubit conversion between near infrared (795 nm) and telecom (1367 nm) wavelengths, and after propagation in a telecom fiber, to invert the conversion process. Observed Bell inequality violation ($S=2.66\pm 0.09$), at 10 ms storage, confirms preservation of memory-light entanglement through the two stages of light qubit frequency conversion.

Figure 1

Left side: A write laser ($270\mu \mathrm{m}$ mode waist) generates spin waves in atomic ${}^{87}\mathrm{Rb}$, confined in a 1D lattice with magnetically compensated clock transition light shifts. Estimated trap depth $U_0=56\mu \mathrm{K}$, trap frequencies $[{\omega }_x/(2\pi ),{\omega }_y/(2\pi ),{\omega }_z/(2\pi )]=(8100,116,10)\mathrm{Hz}$. The experimental protocol is based on a sequence of write-clean pulses, terminated by photodetection of the signal field at $D1$ or $D2$ [2, 6]. After a storage period, the stored spin-wave qubit is converted by the read laser to idler field qubit and polarization measurement of the latter is performed. Signal and idler fields intersect at the center of the trap at an angle of $\pm 0.9°$ with respect to the $z$ axis, and have waist size of $120\mu \mathrm{m}$. Two signal (idler) paths are overlapped on PBS1 (PBS2). The interferometric path length difference is stabilized so that the signal-idler polarization state at the output of PBS1 and PBS2 has the form $\propto (|H{⟩}_s|H{⟩}_i+|V{⟩}_s|V{⟩}_i)$. An auxiliary laser at 767 nm (not shown), intensity stabilized and frequency locked to the potassium $D_2$ line, is used for that purpose. Right side: Successive frequency down- and up-conversion of the signal field qubit is realized by four-wave mixing in cold ${}^{87}\mathrm{Rb}$. A polarizing beam splitter separates the $H$ and $V$ components of the signal field and the latter is delayed by an optical fiber (step 1). In step 2, the write signal and pump fields generate the telecom signal ($e\to d$ transition), which is directed through a 100 m standard telecommunication fiber back to the atomic sample. In step 3 the telecom signal is up-converted to the NIR signal ($a\leftrightarrow c$ transition). After its two polarization components are temporally overlapped (step 4) using the same interferometric arrangement used to separate the incoming NIR signal, a polarization measurement is performed. High-efficiency detection is achieved by the Si single-photon detectors, $D{1}^{\prime }$ and $D{2}^{\prime }$. The inset shows the $\Lambda$-type atomic levels used for the DLCZ scheme (left) and the cascade configurations used for wavelength conversion (right): $|a⟩=|5S_{1/2}F=1⟩$, $|b⟩=|5S_{1/2}F=2⟩$, $|c⟩=|5P_{1/2}F=2⟩$, $|d⟩=|5P_{3/2}F=2⟩$, $|e⟩=|6S_{1/2}F=1⟩$, ${\Delta }_s=-2\pi \times 17\mathrm{MHz}$, ${\Delta }_I=2\pi \times 41\mathrm{MHz}$, ${\Delta }_{II}=2\pi \times 6\mathrm{MHz}$.

Figure 2

Measured values of the correlation function $E({\theta }_s,{\theta }_i)$ as a function of ${\theta }_i$ for 1 ms storage. Circles are for ${\theta }_s=0$, squares are for ${\theta }_s=\pi /4$. The curves are sinusoidal fits to the data.

Figure 3

Measured correlation function $E({\theta }_s,{\theta }_i)$ when the 795 nm signal field is first converted to telecom wavelength, passed through a 100 m telecom fiber, and converted back to 795 nm field, for $1\mu \mathrm{s}$ storage. Circles are for ${\theta }_s=0$, squares are for ${\theta }_s=\pi /4$. The curves are sinusoidal fits to the data.