Fig. 3. Few-photon nonreciprocity.

a Isolation ratio versus the effective coupling strength $g$ and the detuning frequency between the frequency $\omega$ of the probe field and the frequency ${\omega }_o$ of the cavity mode with $⟨n_a⟩\approx 3$. b Isolation ratio versus effective coupling strength $g/\kappa$ and the average photon numbers $⟨n_a⟩$ inside the cavity with $\left(\omega -{\omega }_0\right)/2\pi \approx 2.7$MHz. c Comparison of forward (blue, $1\to 4$ in Fig. 1a) and backward (red, $3\to 2$ in Fig. 1a) transmission rates in the weak-coupling regime. d Same as c in the strong-coupling regime. The transmission rates in c and d are defined as $10\log \left(V_{\mathrm{out}}^2/V_{\mathrm{in}}^2\right)$ and have been normalized, where $V_{\mathrm{in}}$ and $V_{\mathrm{out}}$ are the input and output complex amplitudes of the probing fields. e The forward output power versus the average photon numbers $⟨n_a⟩$ with $\left(\omega -{\omega }_0\right)/2\pi \approx 2.7$ MHz. The red circle data are measured with effective coupling strength $g/\kappa \approx 2.70$. The blue triangle data are measured with coupling strength $g/\kappa \approx 0.09$. The sweep direction for a–e is from low frequency to high frequency, from forward to backward, and from low power to high power.