Shaping Quantum Pulses of Light Via Coherent Atomic Memory

We describe proof-of-principle experiments demonstrating a novel approach for generating pulses of light with controllable photon numbers, propagation direction, timing, and pulse shapes. The approach is based on preparation of an atomic ensemble in a state with a desired number of atomic spin excitations, which is later converted into a photon pulse. Spatiotemporal control over the pulses is obtained by exploiting long-lived coherent memory for photon states and Electromagnetically Induced Transparency in an optically dense atomic medium. Using photon counting experiments, we observe Electromagnetically Induced Transparency based generation and shaping of few-photon sub-Poissonian light pulses.

Figure 1

Experimental procedure and apparatus. (a) ${}^{87}\mathrm{R}\mathrm{b}$ levels used in the experiments ($D_1\mathrm{\text{line}}$): $|g⟩=|5^2{S}_{1/2},F=1⟩$, $|s⟩=|5^2{S}_{1/2},F=2⟩$, and $|e⟩$ corresponds to $|5^2{P}_{1/2},F^{\prime }=1⟩$ and $|5^2{P}_{1/2},F^{\prime }=2⟩$. The write (retrieve) laser and Stokes (anti-Stokes) beam are labeled ${\Omega }_W$ (${\Omega }_R$) and ${\epsilon }_{\mathrm{S}}$ (${\epsilon }_{\mathrm{A}\mathrm{S}}$), respectively. The write (retrieve) laser has a waist of $100\mu \mathrm{m}$ (1 mm). ${\Delta }_W\approx 1\mathrm{G}\mathrm{H}\mathrm{z}$. (b) After the optical pumping pulse (provided by the retrieve laser), the $1.6\mu s$-long write pulse is followed by the retrieve pulse after a controllable delay ${\tau }_d$. (c) Schematic of the experimental setup. The write and retrieve lasers overlap at a small angle ($\sim 10\mathrm{m}\mathrm{r}\mathrm{a}\mathrm{d}$) inside a magnetically-shielded ${}^{87}\mathrm{R}\mathrm{b}$ vapor cell held at $\approx 75°\mathrm{C}$. AOM is acousto-optical modulator. PBS is polarizing beam splitter. S1, S2 (AS1, AS2) are avalanche photodetectors (APDs) for the Stokes (anti-Stokes) channel.

Figure 2

Stokes and anti-Stokes pulse shapes. (a) Experimentally measured and theoretically calculated values of the Stokes photon flux $d{n}_S/dt$. For each plot, $n_S=\int dtd{n}_S/dt$ represents the total number of photons emitted from the cell. Write laser power was varied from $25\mu \mathrm{W}$ to $100\mu \mathrm{W}$. (b) Experimentally measured (left) and theoretically calculated (right) values of the anti-Stokes photon flux $d{n}_{AS}/dt$. The experimental pulse shapes correspond to a Stokes pulse with $n_S\approx 3$ photons, and the theoretical curves assume an initial spin-wave with $n_{spin}=3$ excitations and an optical depth of $\simeq 20$. Each curve is labeled with the power of the retrieve laser. (b and inset) Theoretical calculation of the number of flipped spins per unit length $d{n}_{spin}/dz$ (${\mathrm{c}\mathrm{m}}^{-1}$) for $n_{spin}=3$. (c) Measured anti-Stokes pulse width (full-width at half-max) and total photon number as a function the retrieve laser intensity.

Figure 3

Observation of nonclassical correlations. Normalized variance $V$ (diamonds) and mean number of anti-Stokes photons (triangles) versus delay time ${\tau }_d$. The open and filled symbols represent two experimental runs with similar experimental parameters. The dashed line is an exponential fit (characteristic time $\sim 3\mu \mathrm{s}$) to the mean number of anti-Stokes photons. The solid line is the result of a theoretical model described in the text.

Figure 4

Conditional nonclassical state generation. Diamonds show experimentally measured values $g^{(2)}(AS)=⟨A{S}_1·A{S}_2⟩/⟨A{S}_1⟩⟨A{S}_2⟩$ [see Fig. 1c] as a function of the number of detected Stokes photons. The measured mean photons numbers were ${\overline{n}}_S=1.06$ and ${\overline{n}}_{AS}=0.36$. The solid line shows the result of a theoretical model [26]. (Inset) Measured mean anti-Stokes number ${\overline{n}}_{n_S}^{AS}$ conditioned on the Stokes photon-number $n_S$. The solid line represents ${\overline{n}}_{n_S}^{AS}$ as predicted by the model.