Narrowband four-photon states from spontaneous four-wave mixing

Abstract

We observe time-correlated four photons within a correlation window of 20ns from spontaneous four-wave mixing via a double-Lambda scheme in a cold cloud of Rb-87 atoms. In contrast to high-power pulsed pumping of chi^(2) nonlinear processes in crystals, our scheme generates correlated four-photon states by direct continuous-wave pumping at nominal powers. We verify the presence of genuinely correlated four-photon states over accidentals by higher-order intensity cross-correlation measurements and accidental subtraction. We infer a time-correlated four-photon generation rate of 2.5(4)x10^6 counts per second close to saturation. The photons produced are near-resonant with atomic transitions, and have a bandwidth in the order of MHz, making them readily compatible with quantum networking applications involving atoms.

Figures (5)

• Figure 1: (a) Energy levels involved in the Double-$\Lambda$ spontaneous four-wave mixing in $^{87}$Rb. Solid blue and red arrows indicate cw pump and coupling fields, respectively. Wiggly blue and red arrows indicate generated Stokes and anti-Stokes fields. Black dots indicate initialization of atoms in the $F=1$ hyperfine ground level. (b) Schematic of experimental setup. The pump and coupling beams have a waist of $\approx0.85$ mm. The collection spatial mode is focused on the atomic ensemble with a waist of $175\,\mu\text{m}$. Detectors D1 and D2 detect the Stokes field, and D3 and D4 the anti-Stokes fields in a Hanbury-Brown and Twiss like setup. $\lambda/2$: half-wave plate, $\lambda/4$: quarter-wave plate, PBS: polarizing beamsplitter, D1-D4: single photon detectors.
• Figure 2: Normalized second-order correlation measurements. Main figure: Stokes---anti-Stokes cross-correlation as a histogram of coincidences for various detection delays $\tau$, normalized to the Stokes and anti-Stokes singles rates for a 2 ns bin size and an integration time of 150 s. Results averaged over 17 measurements. Oscillations are caused by the coupling field that drives the $|2\rangle \rightarrow |3\rangle$ transition at an effective Rabi frequency of $2\pi \times 55\, \text{MHz}\,$. Insets: Unheralded autocorrelation measurements of Stokes photons (blue) with peak $g^{(2)}_{s,s}(0) = 2.07 \pm 0.02$ and anti-Stokes photons (red) with peak $g^{(2)}_{a,a}(0)=2.02 \pm 0.07$ (jointly labeled $g^{(2)}_{\text{auto}}(\tau)$).
• Figure 3: Normalized third-order correlation. (a) Normalized triple coincidences $g^{(3)}_{a,a,s}$ for various delays $\tau_{3s}$ and $\tau_{4s}$ between a detection in D3 and D4,respectively, and a heralding Stokes photon in either of D1 or D2. Coincidences analyzed from data acquired over a measurement duration $T_m$ of 0.7 h, normalized by the accidental triplet rate $R_{s}R_{3}R_{4}\delta t^{2}T_{m}$, where the time bin $\delta t =2\, \text{ns}$, and $R_i$ is the single count in detector D$i$. The $g^{(3)}_{a,a,s}$ peak value of 18 indicates strongly correlated triplets. (b) Comparison of the vertical ridge with $g^{(2)}_{a,s}$. Red dots: $g^{(3)}_{a,a,s}$ results averaged over $\tau_{4s}$ from 20 ns to 60 ns. Solid line: normalized cross-correlation $g^{(2)}_{a,s}(\tau_{3s})$ between a Stokes detection in D1 or D2 and an anti-Stokes detection in D3. (c) Peak to ridge ratio. Blue dots: Trace at $\tau_{3s} = 10\,\mathrm{ns}$, normalized by average value at $\tau_{3s} = 10$ ns and $\tau_{4s }= 20$ to $60$ ns, i.e., at long delays. The peak is close to 4 times the mean value in the ridge.
• Figure 4: Quadruple-coincidence detection. Each slice shows unnormalized four-fold coincidences from a detection in each of D1 to D4 for a fixed delay $\tau_{12}$ with a 2 ns time bin, and a range of delays $\tau_{31}$ and $\tau_{41}$. Data acquired over a measurement duration of 0.7 h. The coincidences are peaked for $\tau_{12}=0\pm 2$ ns and $\tau_{31}$ and $\tau_{41}= 8 \pm 2$ ns.
• Figure 5: Top: Detection rates as a function of pump power. (a) Single count rates (right axis) of Stokes (blue circles) and anti-Stokes photons (red circles), and photon pair rate (green squares, left axis) as functions of pump power. (b) Total photon triplet rates (magenta triangles, left axis) and photon quadruplet rate (black diamonds, right axis) as functions of pump power. Bottom: Ratio of pairs, triplets and quadruplets to singles. The photon pair rate $R_{p}$ (green squares), photon triplet rate $R_{t}$ (magenta triangles), and photon quadruplet rate $R_{q}$ (black diamonds) from data in plots (a) and (b) represented in log-scale relative to the singles count rate $R_{\text{s}}$ in Stokes mode (c) and single count rate the anti-Stokes $R_{\text{a}}$ (d). The change in single count rates is achieved by varying the pump power while keeping all other parameters constant. The detuning of the pump is 40 MHz, while the coupling field is resonant with a fixed power of 10 mW. The atomic cloud has an OD $\approx$ 30.