[1] A. Einstein. On the quantum theory of radiation. Phys. Z., 18, 121(1917).
[2] M. Scully, M. Zubairy. Quantum Optics(1997).
[3] A. Metelmann, A. A. Clerk. Nonreciprocal photon transmission and amplification via reservoir engineering. Phys. Rev. X, 5, 021025(2015).
[4] K. Fang, J. Luo, A. Metelmann, M. Matheny, F. Marquardt, A. Clerk, O. Painter. Generalized non-reciprocity in an optomechanical circuit via synthetic magnetism and reservoir engineering. Nat. Phys., 13, 465-471(2017).
[5] X.-W. Xu, Y. Li. Optical nonreciprocity and optomechanical circulator in three-mode optomechanical systems. Phys. Rev. A, 91, 053854(2015).
[6] X.-W. Xu, Y. Li, A.-X. Chen, Y.-X. Liu. Nonreciprocal conversion between microwave and optical photons in electro-optomechanical systems. Phys. Rev. A, 93, 023827(2016).
[7] A. Metelmann, A. A. Clerk. Nonreciprocal quantum interactions and devices via autonomous feedforward. Phys. Rev. A, 95, 013837(2017).
[8] L. Tian, Z. Li. Nonreciprocal quantum-state conversion between microwave and optical photons. Phys. Rev. A, 96, 013808(2017).
[9] F. Ruesink, M.-A. Miri, A. Alù, E. Verhagen. Nonreciprocity and magnetic-free isolation based on optomechanical interactions. Nat. Commun., 7, 13662(2016).
[10] G. A. Peterson, F. Lecocq, K. Cicak, R. W. Simmonds, J. Aumentado, J. D. Teufel. Demonstration of efficient nonreciprocity in a microwave optomechanical circuit. Phys. Rev. X, 7, 031001(2017).
[11] N. Bernier, L. D. Toth, A. Koottandavida, M. Ioannou, D. Malz, A. Nunnenkamp, A. Feofanov, T. Kippenberg. Nonreciprocal reconfigurable microwave optomechanical circuit. Nat. Commun., 8, 604(2017).
[12] S. Barzanjeh, M. Wulf, M. Peruzzo, M. Kalaee, P. Dieterle, O. Painter, J. Fink. Mechanical on-chip microwave circulator. Nat. Commun., 8, 953(2017).
[13] J. Koch, A. A. Houck, K. L. Hur, S. M. Girvin. Time-reversal-symmetry breaking in circuit-QED-based photon lattices. Phys. Rev. A, 82, 043811(2010).
[14] R. O. Umucalılar, I. Carusotto. Artificial gauge field for photons in coupled cavity arrays. Phys. Rev. A, 84, 043804(2011).
[15] Y.-P. Wang, W. Wei, Z.-Y. Xue, W. L. Yang, Y. Hu, Y. Wu. Realizing and characterizing chiral photon flow in a circuit quantum electrodynamics necklace. Sci. Rep., 5, 8352(2015).
[16] F. X. Sun, D. Mao, Y. T. Dai, Z. Ficek, Q. Y. He, Q. H. Gong. Phase control of entanglement and quantum steering in a three-mode optomechanical system. New J. Phys., 19, 123039(2017).
[17] S. J. M. Habraken, K. Stannigel, M. D. Lukin, P. Zoller, P. Rabl. Continuous mode cooling and phonon routers for phononic quantum networks. New J. Phys., 14, 115004(2012).
[18] A. Seif, W. DeGottardi, K. Esfarjani, M. Hafezi. Thermal management and non-reciprocal control of phonon flow via optomechanics. Nat. Commun., 9, 1207(2017).
[19] M. Rechtsman, J. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, A. Szameit. Photonic Floquet topological insulators. Nature, 496, 196-200(2013).
[20] M. Schmidt, S. Kessler, V. Peano, O. Painter, F. Marquardt. Optomechanical creation of magnetic fields for photons on a lattice. Optica, 2, 635-641(2015).
[21] V. Peano, C. Brendel, M. Schmidt, F. Marquardt. Topological phases of sound and light. Phys. Rev. X, 5, 031011(2015).
[22] V. Peano, M. Houde, F. Marquardt, A. A. Clerk. Topological quantum fluctuations and traveling wave amplifiers. Phys. Rev. X, 6, 041026(2016).
[23] V. Peano, M. Houde, C. Brendel, F. Marquardt, A. Clerk. Topological phase transitions and chiral inelastic transport induced by the squeezing of light. Nat. Commun., 7, 10779(2015).
[24] M. Minkov, V. Savona. Haldane quantum hall effect for light in a dynamically modulated array of resonators. Optica, 3, 200-206(2016).
[25] C. Brendel, V. Peano, O. Painter, F. Marquardt. Snowflake phononic topological insulator at the nanoscale. Phys. Rev. B, 97, 020102(2018).
[26] M. Hafezi, E. Demler, M. Lukin, J. Taylor. Robust optical delay lines via topological protection. Nat. Phys., 7, 907-912(2011).
[27] K. Fang, Z. Yu, S. Fan. Realizing effective magnetic field for photons by controlling the phase of dynamic modulation. Nat. Photonics, 6, 782-787(2012).
[28] L. Tzuang, K. Fang, P. Nussenzveig, S. Fan, M. Lipson. Non-reciprocal phase shift induced by an effective magnetic flux for light. Nat. Photonics, 8, 701-705(2014).
[29] K. M. Sliwa, M. Hatridge, A. Narla, S. Shankar, L. Frunzio, R. J. Schoelkopf, M. H. Devoret. Reconfigurable Josephson circulator/directional amplifier. Phys. Rev. X, 5, 041020(2015).
[30] R. Sarma, L. Ge, J. Wiersig, H. Cao. Rotating optical microcavities with broken chiral symmetry. Phys. Rev. Lett., 114, 053903(2015).
[31] J. F. Poyatos, J. I. Cirac, P. Zoller. Quantum reservoir engineering with laser cooled trapped ions. Phys. Rev. Lett., 77, 4728-4731(1996).
[32] X. Xu, T. Purdy, J. M. Taylor. Cooling a harmonic oscillator by optomechanical modification of its bath. Phys. Rev. Lett., 118, 223602(2017).
[33] D. Kienzler, H.-Y. Lo, B. Keitch, L. Clercq, F. Leupold, F. Lindenfelser, M. Marinelli, V. Negnevitsky, J. Home. Quantum harmonic oscillator state synthesis by reservoir engineering. Science, 347, 53-56(2014).
[34] A. Miranowicz, J. C. V. Bajer, M. Paprzycka, Y.-X. Liu, A. M. Zagoskin, F. Nori. State-dependent photon blockade via quantum-reservoir engineering. Phys. Rev. A, 90, 033831(2014).
[35] C.-J. Yang, J.-H. An, W. Yang, Y. Li. Generation of stable entanglement between two cavity mirrors by squeezed-reservoir engineering. Phys. Rev. A, 92, 062311(2015).
[36] X.-B. Yan. Enhanced output entanglement with reservoir engineering. Phys. Rev. A, 96, 053831(2017).
[37] P. Rabl, A. Shnirman, P. Zoller. Generation of squeezed states of nanomechanical resonators by reservoir engineering. Phys. Rev. B, 70, 205304(2004).
[38] M. J. Woolley, A. A. Clerk. Two-mode squeezed states in cavity optomechanics via engineering of a single reservoir. Phys. Rev. A, 89, 063805(2014).
[39] C. Ockeloen-Korppi, E. Damskägg, J.-M. Pirkkalainen, M. Asjad, A. Clerk, F. Massel, M. Woolley, M. Sillanpää. Stabilized entanglement of massive mechanical oscillators. Nature, 556, 478-482(2018).
[40] L. Zhou, L.-P. Yang, Y. Li, C. P. Sun. Quantum routing of single photons with a cyclic three-level system. Phys. Rev. Lett., 111, 103604(2013).
[41] Z. H. Wang, L. Zhou, Y. Li, C. P. Sun. Controllable single-photon frequency converter via a one-dimensional waveguide. Phys. Rev. A, 89, 053813(2014).
[42] X.-W. Xu, A.-X. Chen, Y. Li, Y.-X. Liu. Single-photon nonreciprocal transport in one-dimensional coupled-resonator waveguides. Phys. Rev. A, 95, 063808(2017).
[43] X.-W. Xu, A.-X. Chen, Y. Li, Y.-X. Liu. Nonreciprocal single-photon frequency converter via multiple semi-infinite coupled-resonator waveguides. Phys. Rev. A, 96, 053853(2017).
[44] P. Král, M. Shapiro. Cyclic population transfer in quantum systems with broken symmetry. Phys. Rev. Lett., 87, 183002(2001).
[45] P. Král, I. Thanopulos, M. Shapiro, D. Cohen. Two-step enantio-selective optical switch. Phys. Rev. Lett., 90, 033001(2003).
[46] Y. Li, C. Bruder, C. P. Sun. Generalized Stern-Gerlach effect for chiral molecules. Phys. Rev. Lett., 99, 130403(2007).
[47] W. Z. Jia, L. F. Wei. Probing molecular chirality by coherent optical absorption spectra. Phys. Rev. A, 84, 053849(2011).
[48] D. Patterson, J. M. Doyle. Sensitive chiral analysis via microwave three-wave mixing. Phys. Rev. Lett., 111, 023008(2013).
[49] D. Patterson, M. Schnell, J. Doyle. Enantiomer-specific detection of chiral molecules via microwave spectroscopy. Nature, 497, 475-477(2013).
[50] S. Eibenberger, J. Doyle, D. Patterson. Enantiomer-specific state transfer of chiral molecules. Phys. Rev. Lett., 118, 123002(2017).
[51] C. Ye, Q. Zhang, Y. Li. Real single-loop cyclic three-level configuration of chiral molecules. Phys. Rev. A, 98, 063401(2018).
[52] Y.-X. Liu, J. Q. You, L. F. Wei, C. P. Sun, F. Nori. Optical selection rules and phase-dependent adiabatic state control in a superconducting quantum circuit. Phys. Rev. Lett., 95, 087001(2005).
[53] J. Mooij, T. Orlando, L. Levitov, L. Tian, C. van der Wal, S. Lloyd. Josephson persistent-current qubit. Science, 285, 1036(1999).
[54] A. Barfuss, J. Kölbl, L. Thiel, J. Teissier, M. Kasperczyk, P. Maletinsky. Phase-controlled coherent dynamics of a single spin under closed-contour interaction. Nat. Phys., 14, 1087-1091(2018).
[55] J. R. Maze, A. Gali, E. Togan, Y. Chu, A. Trifonov, E. Kaxiras, M. D. Lukin. Properties of nitrogen-vacancy centers in diamond: the group theoretic approach. New J. Phys., 13, 025025(2011).
[56] V. Dobrovitski, G. Fuchs, A. Falk, C. Santori, D. Awschalom. Quantum control over single spins in diamond. Annu. Rev. Condens. Matter Phys., 4, 23-50(2013).
[57] E. R. MacQuarrie, T. A. Gosavi, N. R. Jungwirth, S. A. Bhave, G. D. Fuchs. Mechanical spin control of nitrogen-vacancy centers in diamond. Phys. Rev. Lett., 111, 227602(2013).
[58] A. Barfuss, J. Teissier, E. Neu, A. Nunnenkamp, P. Maletinsky. Strong mechanical driving of a single electron spin. Nat. Phys., 11, 820-824(2015).
[59] F. Ripka, H. Kübler, R. Löw, T. Pfau. A room-temperature single-photon source based on strongly interacting Rydberg atoms. Science, 362, 446-449(2018).
[60] A. Rosario Hamann, C. Müller, M. Jerger, M. Zanner, J. Combes, M. Pletyukhov, M. Weides, T. M. Stace, A. Fedorov. Nonreciprocity realized with quantum nonlinearity. Phys. Rev. Lett., 121, 123601(2018).
[61] M. Johnson, M. Amin, S. Gildert, T. Lanting, F. Hamze, N. Dickson, R. Harris, A. Berkley, J. Johansson, P. Bunyk, E. Chapple, C. Enderud, J. Hilton, K. Karimi, E. Ladizinsky, N. Ladizinsky, T. Oh, I. Perminov, C. Rich, G. Rose. Quantum annealing with manufactured spins. Nature, 473, 194-198(2011).
[62] S. E. Harris. Lasers without inversion: interference of lifetime-broadened resonances. Phys. Rev. Lett., 62, 1033-1036(1989).
[63] M. O. Scully, S.-Y. Zhu, A. Gavrielides. Degenerate quantum-beat laser: lasing without inversion and inversion without lasing. Phys. Rev. Lett., 62, 2813-2816(1989).
[64] O. Kocharovskaya, P. Mandel, Y. V. Radeonychev. Inversionless amplification in a three-level medium. Phys. Rev. A, 45, 1997-2005(1992).
[65] W. Z. Jia, L. F. Wei. Gains without inversion in quantum systems with broken parities. Phys. Rev. A, 82, 013808(2010).
[66] R. Huang, A. Miranowicz, J.-Q. Liao, F. Nori, H. Jing. Nonreciprocal photon blockade. Phys. Rev. Lett., 121, 153601(2018).
[67] X. Xu, Y. Zhao, H. Wang, H. Jing, A. Chen. Quantum nonreciprocality in quadratic optomechanics. Photon. Res., 8, 143-150(2020).
[68] B. Li, R. Huang, X. Xu, A. Miranowicz, H. Jing. Nonreciprocal unconventional photon blockade in a spinning optomechanical system. Photon. Res., 7, 630-641(2019).
[69] M. Z. Hasan, C. L. Kane. Colloquium: topological insulators. Rev. Mod. Phys., 82, 3045-3067(2010).
