Realization of Nonlinear Optical Nonreciprocity on a Few-Photon Level Based on Atoms Strongly Coupled to an Asymmetric Cavity

Optical nonreciprocity is important in photonic information processing to route the optical signal or prevent the reverse flow of noise. By adopting the strong nonlinearity associated with a few atoms in a strongly coupled cavity QED system and an asymmetric cavity configuration, we experimentally demonstrate the nonreciprocal transmission between two counterpropagating light fields with extremely low power. The transmission of 18% is achieved for the forward light field, and the maximum blocking ratio for the reverse light is 30 dB. Though the transmission of the forward light can be maximized by optimizing the impedance matching of the cavity, it is ultimately limited by the inherent loss of the scheme. This nonreciprocity can even occur on a few-photon level due to the high optical nonlinearity of the system. The working power can be flexibly tuned by changing the effective number of atoms strongly coupled to the cavity. The idea and result can be applied to optical chips as optical diodes by using fiber-based cavity QED systems. Our work opens up new perspectives for realizing optical nonreciprocity on a few-photon level based on the nonlinearities of atoms strongly coupled to an optical cavity.

Figure 1

Scheme of the ONR model. A cavity QED system with multiple two-level atoms strongly coupled to an asymmetric cavity is adopted. The coupling efficiencies of the cavity mirrors fulfill the relation ${\kappa }_1>{\kappa }_2$, which means that the intracavity atoms reach saturation easier for the incident light field in mode $a$ (the forward direction) than that in mode $b$ (the backward direction) along with the increase in incident power. Consequently, the light field in mode $a$ can transmit, whereas the light field in mode $b$ is blocked under certain powers.

Figure 2

Bistability of the light fields with an effective atom number $N_{\mathrm{eff}}=12.8\pm 0.4$ as the power in mode $a$ and $b$ increases. (a) The theoretical results given by the semiclassic method; (b) the experimental results. The blue (red) curve and data points are for the forward (backward) light field in mode $a$ ($b$). The shaded area in both figures, with lower and upper bounds marked by $P_l$ and $P_u$, indicates the ONR working window, in which the light field in mode $a$ transmits, whereas the light field in mode $b$ is blocked. In (b), the top horizontal and right vertical axes show the input photon rate and the mean photon numbers in the cavity, deduced by the output of the forward light field, respectively.

Figure 3

Performance of the ONR with atom number $N_{\mathrm{eff}}=12.8\pm 0.4$. The samples of the working power are selected in between 30 and 110 pW. The red and blue data points are the experimental results for transmission in mode $a$ and the blocking ratio of the backward light field, respectively. The red-solid and blue-dashed curves are the theoretical expectations.

Figure 4

Performance of the nonlinear ONR for different effective atom numbers. (a) The measured bistability for the two counterpropagating light fields under different atom numbers. The blue and red points are for the light fields in modes $a$ and $b$, respectively. Each data point is the average of 20 measurements. The inset gives the map of the ONR working window associated with the corresponding atom numbers. The right vertical axis of the inset shows the corresponding mean photon number of the cavity for the forward light field. The solid curves and shaded area are the theoretical expectations, and the points are experimental data. (b) The average blocking ratios and transmissions of the ONR in the corresponding working window. Please see the Supplemental Material [60] for the extra data. The meaning of the points and the curves is the same as that in Fig. 3.