High-contrast transparency comb of the electromagnetically-induced-transparency memory

Quantum interface of coherent optical field and atomic excitations plays an important role in quantum metrology and quantum information science. The electromagnetically-induced-transparency (EIT) technique has shown versatile and powerful capability in many applications during the last decades. By using efficient EIT-based memory, we directly observed single-photon-level Ramsey interference and also high-contrast spectral transparency comb with a visibility up to about 0.81 at around the resonant line in cold atoms. The interference fringes are mainly influenced by the pulse repetition period, the waveform overlap of the slowed and retrieved signal pulses, and the coherent lifetime of the EIT memory. All these factors have been investigated in detail. Such high-contrast interference fringe may offer us methods for precision measurement and potential applications in areas of atomic clock and magnetometry.

Figure 1

(a) Experiment scheme and energy structure of the ${}^{87}\mathrm{Rb}$ atoms. All the atoms are initially in the ground state $|5S_{1/2},F=1\rangle$. The control (${\mathrm{\Omega }}_c$) and signal (${\widehat{\mathcal{E}}}_p$) fields are right circularly polarized (${\sigma }^{+}$), and resonant of the $D1$-line transition of $|F=2\rangle \to |F^{\prime }=2\rangle$ and $|F=1\rangle \to |F^{\prime }=2\rangle$, respectively. The transparent signal pulses are measured by a single-photon detector (APD), after passing through a Fabry-Perot cavity filter and an atomic filter successively. (b) Time sequence for the two-pulse EIT-Ramsey interference. Pulse width of the control field is 800 ns, and pulse width of the signal field is 300 ns. (c) Time sequence for the multipulse EIT-combed interference. Both the signal and control pulses are 200-ns width and are synchronously repeated hundreds of times after preparation of the atoms.

Figure 2

Envelope of the slowed (black solid) and retrieved (red dashed) signal pulses, and the relative overlap parameter ${\eta }_{\mathrm{vis}}$ (blue dotted) between them. Pulse width of the incident signal field is 300 ns. Storage time of the retrieved signal pulse is $200\mathrm{ns}$. Average of ${\eta }_{\mathrm{vis}}$ over the whole 800-ns duration is about 0.59.

Figure 3

The two-pulse EIT-Ramsey interference with a pulse separation of 0.5 and $1.0\mu \mathrm{s}$. (a) and (b) The normalized interference amplitude $\mathcal{A}$ for different signal pulse detuning $\delta$. Calculations are performed within a 100-ns duration around the crossing point of the slowed and retrieved pulses (Fig. 2). The dark black data (red line fitting) is the interference amplitude of the two signal pulses ($n_{s,r}$) while the shallow gray one (white line fitting) is the oscillation envelope of $\pm 2\sqrt{n_s{n}_r}$. Normalization of $\mathcal{A}$ is corresponding to the value of $2\sqrt{n_s{n}_r}$ where $\delta =0\text{MHz}$. (c) The central peak position ${\delta }_0$ for a different counting interval of the signal photons, where duration of the photon count for each data is $100\mathrm{ns}$. (d) The interference visibility ${\eta }_{\mathrm{vis}}$ of it. $t$ in the $x$ axis is the middle time instant of the analysis region.

Figure 4

The EIT-based transparency comb of the signal photons for a different pulse repetition period of $T=\{1,2,8\}\mu \mathrm{s}$ from top to bottom. The $x$ axis is detuning of the signal photons. The right subgraphs are enlargement of the central 1-MHz interval of the left. Photon counts are recorded over the whole signal pulse; the transparency rate $\mathcal{T}(\%)$ in the $y$ axis is relative to a reference signal pulse without atoms.

Figure 5

The interference visibility ${\eta }_{\mathrm{vis}}$ of the EIT-combed transparency for different repetition period $T$. The red value of ${\eta }_{\mathrm{vis}}(\delta \simeq 0\mathrm{MHz})=\{0.81\left(0\right),0.68\left(2\right),0.26\left(3\right)\}$ is related to the central peak shown in Fig. 4. Theoretical calculation of ${\eta }_{\mathrm{vis}}$ for the EIT-Ramsey (orange dashed) and EIT-combed (blue solid) schemes is also presented. The $x$ axis is in units of the coherence lifetime $\tau \simeq 2.8\mu \mathrm{s}$.