Fig. 1. Isolators based on Faraday effect

Fig. 2. Magnetic-free nonreciprocity scheme based on spatiotemporal modulation. (a) Indirect interband transition of photons realized by spatiotemporal modulation; (b) nonreciprocity realized by amplitude modulation

Fig. 3. Nonreciprocity induced by thermal motion of atoms^[42]. (a) Energy level structure of atoms; (b) experimental schematic diagram

Fig. 4. Experimental results^[43]. (a) Forward transmission spectra; (b) backward transmission spectra

Fig. 5. Energy level structure of nonreciprocity realized by incoherent pump. (a) Two-level pump structure^[44]; (b) V-type pump structure^[45]

Fig. 6. Nonreciprocal transmission spectra of pumped light at different frequencies (circles and squares in figure are experimental data and solid lines are theoretical fitting results)^[44]. (a) δ_p/2π=-115 MHz; (b) δ_p/2π=0 MHz; (c) δ_p/2π=115 MHz

Fig. 7. Atomic energy levels and experimental results^[45]. (a) V-type structure with multiple energy levels in Rb⁸⁵ atom; (b) nonreciprocal transmission spectra of 795 nm and 780 nm signal light

Fig. 8. Circulators based on hot atoms^[46]. (a) Dispersion and absorption spectra of forward and backward signals; (b) experimental structure diagram; (c) experimental results of circulator

Fig. 9. Unidirectional amplification based on hot atoms^[47]. (a) Energy level structure; (b) experimental results

Fig. 10. Nonreciprocity realized by photothermal nonlinear effect

Fig. 11. Principle of overcoming dynamic reciprocity by atomic thermal motion^[56]. (a) Dynamic reciprocity exists when forward and backward signals interact with atoms without thermal motion; (b) when forward and backward signals interact with atoms with thermal motion, atomic groups of the two are different, which is equivalent to two signals interacting with two nonlinear media respectively, and the dynamic reciprocity is broken

Fig. 12. Transmission spectra with and without "velocity selection nonlinearity" (circle+solid line represents forward signal,and square+solid line represents backward signal)^[56]. In the absence of "velocity selection nonlinearity", forward and backward signals are (a) separately and (b) simultaneously incident; with "velocity selection nonlinearity", forward and backward signals are (c) separately and (d) simultaneously incident