Quantum interference of stored dual-channel spin-wave excitations in a single tripod system

We present an experimental demonstration of dual-channel memory in a single tripod atomic system. The total readout signal exhibits either constructive or destructive interference when the dual-channel spin-wave excitations (SWEs) are retrieved by two reading beams with a controllable relative phase. When the two reading beams have opposite phases, the SWEs will remain in the medium, which can be retrieved later with two in-phase reading beams. Such a phase-sensitive storage and retrieval scheme can be used to measure and control the relative phase between the two SWEs in the memory medium, which may find applications in quantum-information processing.

Figure 1

(a) Experimental setup. EOM: electronic optical modulator. BD1 and BD2: beam displacing polarizers. PBS1–PBS3: polarization beam splitters, the angle of the orientation of PBS3 from the horizontal ($p$) direction (same as the orientation of PBS1 and PBS2) is ${45}^{°}$; APD1 and APD2: avalanche photodetectors. The symbols “…,” “$\Vert$,” “$//$,” “,“ and ““ denote the vertical, horizontal, ${45}^{°}$-angle-to-horizontal, left- and right-circular polarizations, respectively. The polarization of PBS3 is along the orientation with (or at) ${45}^{°}$ angle to the horizontal polarization. (b) The scheme of a four-level tripod system of ${}^{87}\mathrm{Rb}$ atom. $|a\rangle$ is the $|5S_{1/2},F=1,m=+1\rangle$ state; $|b\rangle$ and $|c\rangle$ are the $|5S_{1/2},F=2,m=+1\rangle$ and $|5S_{1/2},F=2,m=-1\rangle$ states, respectively; and $|e\rangle$ is the $|5P_{1/2},F^{\prime }=1,m=0\rangle$ state.

Figure 2

Retrieval signal for different storage and retrieval configurations. (a) One-channel storage and retrieval. The stored SWE (${\sigma }_{\mathit{ca}}$) in one (left) channel has been retrieved by the reading beam R+ at 380 ns, and no clear signal is retrieved again by the $p$-polarized writing beam at 3.4 μs. (b) Dual-channel storage and only one (right) channel (${\sigma }_{\mathit{ba}}$) retrieval. The stored SWE in the right channel (${\sigma }_{\mathit{ba}}$) was first retrieved by the reading beam $R^{-}$ at 380 ns. At 3.4 μs, a small optical signal [with ∼13% of the full-scale readout in Fig. 2(f)] is retrieved by the $p$-polarized writing beam from the remaining SWE (${\sigma }_{\mathit{ca}}$). (c) Dual-channel storage and only one- (left-) channel retrieval. The stored SWE in the left channel (${\sigma }_{\mathit{ca}}$) was first retrieved by the reading beam $R^{+}$ at 380 ns. At 3.4 μs, a small optical signal [with ∼20% of the full-scale readout in Fig. 2(f)] is retrieved by the $p$-polarized writing beam from the remaining SWE (${\sigma }_{\mathit{ba}}$). (d) Dual-channel storage and dual-channel retrieval with in-phase reading beams at 380 ns. There is no retrieved signal by the $p$-polarized writing beam at 3.4 μs. (e) Dual-channel storage and dual-channel retrieval with out-of-phase reading beams at 380 ns, and reading again at 3.4 μs with the writing beams. (f) Dual-channel storage and retrieval by reading with two writing beams at 3.4 μs only. (g) Left-channel storage and right-channel retrieval. At 380 ns, only a small optical signal [about 7% of the full-scale readout in Fig. 2(f)] is retrieved by the $R^{-}$ reading beam. At 3.4 μs, an optical signal [about 21% of the full-scale readout in Fig. 2(f)] is retrieved by the $p$-polarized writing beam. (h) Right-channel storage and left-channel retrieval. At 380 ns, only a small optical signal [about 9% of the full-scale readout in Fig. 2(f)] is retrieved by the $R^{+}$ reading beam. At 3.4 μs, an optical signal [about 20% of the full-scale readout in Fig. 2(f)] is retrieved by the $p$-polarized writing beam. In Figs. 2(a)–2(h), the retrieved signals at 380 ns have a broad offset background, which comes from the leakage of the reading beams.

Figure 3

Retrieval efficiency as a function of the relative phase ${\delta }_R$. Blue square points are the total retrieved efficiency at 380 ns storage time for different $\Delta$. The solid blue line is the fit to the data. The red circular points are the retrieved efficiency at 3.4 μs storage time after the system has been first read at 380 ns with a pair of reading beams.

Figure 4

Retrieval efficiency and compensation of Larmor precession. Black circular points: retrieval efficiency as a function of storage time. Curve (a) (red curve): fitting to the function $R_e=A\cos {}^2({\Omega }_{L}t-\varphi /2)e^{-t/t_0}$, where the fitting parameters are $A$ $=$0.1, ${\Omega }_L=2\pi \times 0.21\hspace{0.5em}\mathrm{MHz}$, $\varphi =0.3\pi$(initial phase), and the lifetime $t_0\approx 90\hspace{0.5em}\mu \mathrm{s}$. Curve (b) (with blue squares): the results with compensated Larmor precession by adjusting the relative phase ${\delta }_R$.