Cross Modulation of Two Laser Beams at the Individual-Photon Level

Deterministic photon-photon interactions are a long-standing goal in optical science. Using an atomic ensemble inside a cavity, we demonstrate the mutual cross modulation of two continuous light beams at the level of individual photons. The originally uncorrelated beams derived from independent lasers become anticorrelated, as evidenced by an equal-time cross-correlation function $g^{(2)}=0.89(1)$, showing that one photon in one beam extinguishes a photon in the other beam with a probability of 11(1)%. With further technical improvements, our approach should enable the nondestructive continuous detection of traveling optical photons.

Figure 1

Cross modulation of two laser beams at the level of individual photons. (a) Experimental setup and (b) atomic level scheme. An ensemble of laser-cooled atoms is trapped inside a high-finesse optical resonator and prepared in state $|f⟩$. The ensemble and the coupling beam (resonant with the $|c⟩\to |d⟩$ transition) mediate interactions between signal ($|f⟩\to |d⟩$) and cavity photons ($|c⟩\to |e⟩$): Signal photons travel through the medium as slow-light polaritons whose atomic excitation component in the state $|c⟩$ blocks the transmission through the cavity. Photons are measured with photon counters $D_s$ and $D_c$.

Figure 2

Switching of cavity photons by signal light. Fractional cavity transmission is plotted versus average signal photon number per EIT lifetime $⟨n_s⟩=R_s\mathrm{\Gamma }/{\mathrm{\Omega }}^2$. The measurement was performed with $⟨n_c⟩{|}_{n_s=0}=2.7$ and ${\mathrm{\Omega }}^2/\mathrm{\Gamma }=1.4(1)\mu {\mathrm{s}}^{-1}$. The expected transmission (solid curve) is the calculated cavity blocking (see the text). Inset: Illustration of cavity transmission reduction (red curve) due to signal photons as a function of light cavity detuning $\mathrm{\Delta }$. Error bars are $\pm 1$ s.d.

Figure 3

Switching of signal photons by cavity light. (a) Representative EIT spectra as a function of signal detuning for $⟨n_c⟩{|}_{n_s=0}=0$ (black curve, high transmission) and 11.5 (red curve, low transmission) cavity photons. (b) EIT decoherence rates are plotted versus cavity photon number for ${\mathrm{\Omega }}^2/\mathrm{\Gamma }=1.4(1)\mu {\mathrm{s}}^{-1}$. A fit (solid line) gives a cavity-light-induced decoherence rate of ${\gamma }_c/(2\pi n_c)=70(25)\mathrm{kHz}$. Error bars are $\pm 1$ s.d.

Figure 4

Mutual photon-photon interaction between continuous laser beams. The second-order cross-correlation function $g^{(2)}(\tau )$ versus time separation $\tau =t_s-t_c$ for different coupling beam powers: ${\mathrm{\Omega }}^2/\mathrm{\Gamma }=$ (a) $0.5(1)\mu {\mathrm{s}}^{-1}$, (b) $1.4(1)\mu {\mathrm{s}}^{-1}$, and (c) $4.0(1)\mu {\mathrm{s}}^{-1}$. Fits of the data to the model (see the text) yield (a) $\{g^{(2)}(0),{\kappa }_{<}/\mu {\mathrm{s}}^{-1},{\kappa }_{>}/\mu {\mathrm{s}}^{-1}\}=\{0.91(1),1.6(2),1.4(2)\}$, (b) $\{0.89(1),1.5(1),2.4(3)\}$, and (c) $\{0.90(1),1.6(1),3.9(3)\}$. (d) Fitted rate constants ${\kappa }_{\gtrless }$ versus the EIT linewidth ${\mathrm{\Omega }}^2/\mathrm{\Gamma }$. The positive-time rate constant fits to ${\kappa }_{>}=a{\mathrm{\Omega }}^2/\mathrm{\Gamma }+b$ with slope $a=0.7(1)$ and $y$-axis intercept $b=1.2(2)\mu {\mathrm{s}}^{-1}$. The negative-time rate constant ${\kappa }_{<}=1.6(1)\mu {\mathrm{s}}^{-1}$ is independent of ${\mathrm{\Omega }}^2$. Here, ${\mathrm{\Omega }}^2/\mathrm{\Gamma }$ was independently determined from separately measured EIT spectra. The measurements were performed at photon numbers $⟨n_c⟩\approx 0.2$ and $⟨n_s⟩\approx 0.2$ when integrated over time windows $1/{\kappa }_{<}$ and $1/{\kappa }_{>}$, respectively.