“…Traditionally, magneto-optical media are used to break the time-reversal symmetry with the Faraday rotation effect, which requires however bulky magnets making against real applications involving integrated photonic devices [5][6][7][8]. Hence, significant efforts have been made recently to develop the magnet-free optical non-reciprocity by exploring different mechanisms, including nonlinear effects [9][10][11][12][13][14][15][16][17], spatiotemporal modulations [18][19][20][21][22], optomechanical interactions [23][24][25][26][27][28], moving atomic lattices [29][30][31], chiral quantum systems [32][33][34][35][36], and atomic thermal motions [37][38][39][40][41][42][43][44][45][46]. Note also that nonreciprocal amplification has aroused particular interests and achieved significant progresses since it can facilitate the optical read-out of sensitive signals and simplify the construction of complex optical networks by avoiding the amplification of undesired reflections [46]<...…”