Topological superradiant state in Fermi gases with cavity induced spin–orbit coupling

Abstract

Coherently driven atomic gases inside optical cavities hold great promise for generating rich dynamics and exotic states of matter. It was shown recently that an exotic topological superradiant state exists in a two-component degenerate Fermi gas coupled to a cavity, where local order parameters coexist with global topological invariants. In this work, we characterize in detail various properties of this exotic state, focusing on the feedback interactions between the atoms and the cavity field. In particular, we demonstrate that cavity-induced interband coupling plays a crucial role in inducing the topological phase transition between the conventional and topological superradiant states. We analyze the interesting signatures in the cavity field left by the closing and reopening of the atomic bulk gap across the topological phase boundary and discuss the robustness of the topological superradiant state by investigating the steady-state phase diagram under various conditions. Furthermore, we consider the interaction effect and discuss the interplay between the pairing order in atomic ensembles and the superradiance of the cavity mode. Our work provides many valuable insights into the unique cavity– atom hybrid system under study and is helpful for future experimental exploration of the topological superradiant state.

Keywords

superradiance / topological phase / Fermi gas / cavity QED

References

[1] Y. J.Lin, K.Jiménez-García, and I. B.Spielman, Spin–orbit-coupled Bose–Einstein condensates, Nature471(7336), 83 (2011)

[2] P.Wang, Z. Q.Yu, Z.Fu, J.Miao, L.Huang, S.Chai, H.Zhai, and J.Zhang, Spin–orbit coupled degenerate Fermi gases, Phys. Rev. Lett. 109(9), 095301(2012)

[3] L. W.Cheuk, A. T.Sommer, Z.Hadzibabic,T.Yefsah, W. S.Bakr, and M. W.Zwierlein, Spin-injection spectroscopy of a spin–orbit coupled Fermi gas, Phys. Rev. Lett. 109(9), 095302(2012)

[4] Z. Y.Shi, X. L.Cui, and H.Zhai, Universal trimers induced by spin–orbit coupling in ultracold Fermi gases, Phys. Rev. Lett. 112(1), 013201(2014)

[5] X. L.Cuiand W.Yi, Universal Borromean binding in spin–orbit-coupled ultracold Fermi gases, Phys. Rev. X4(3), 031026(2014)

[6] L.Zhou, X. L.Cui, and W.Yi, Three-component ultracold Fermi gases with spin–orbit coupling, Phys. Rev. Lett. 112(19), 195301(2014)

[7] V.Galitskiand I. B.Spielman, Spin–orbit coupling in quantum gases, Nature494(7435), 49(2013)

[8] N.Goldman, G.Juzeliünas, P.Öhberg, and I. B.Spielman, Light-induced gauge fields for ultracold atoms, Rep. Prog. Phys. 77(12), 126401(2014)

[9] X.Zhou, Y.Li, Z.Cai, and C.Wu, Unconventional states of bosons with the synthetic spin–orbit coupling, J. Phys. At. Mol. Opt. Phys. 46(13), 134001(2013)

[10] H.Zhai, Degenerate quantum gases with spin–orbit coupling: A review, Rep. Prog. Phys. 78(2), 026001(2015)

[11] W.Yi, W.Zhang, and X. L.Cui, Pairing superfluidity in spin–orbit coupled ultracold Fermi gases, Sci. China Phys. Mech. Astron. 58(1), 1 (2015)

[12] J.Zhang, J.Hu, X. J.Liu, and H.Pu, Fermi gases with synthetic spin–orbit coupling, Ann. Rev. Cold At. Mol. 2, 81(2014)

[13] Y.Xuand C.Zhang, Topological Fulde–Ferrell superfluids of a spin–orbit coupled Fermi gas, Int. J. Mod. Phys. B29(01), 1530001(2015)

[14] Y.Zhang, M. E.Mossman, T.Busch, P.Engels, and C.Zhang, Properties of spin–orbit-coupled Bose–Einstein condensates, Front. Phys. 11(3), 118103(2016)

[15] M. Z.HasanandC. L.Kane, Topological insulators, Rev. Mod. Phys. 82(4), 3045(2010)

[16] X. L.Qiand S. C.Zhang, Topological insulators and superconductors, Rev. Mod. Phys. 83(4), 1057(2011)

[17] J.Alicea, New directions in the pursuit of Majorana fermions in solid state systems, Rep. Prog. Phys. 75(7), 076501(2012)

[18] C.Zhang,S.Tewari, R. M.Lutchyn, andS.Das Sarma, p_x+ip_ysuperfluid from s-wave interactions of fermionic cold atoms, Phys. Rev. Lett. 101(16), 160401(2008)

[19] M.Sato,Y.Takahashi, and S.Fujimoto, Non-Abelian topological order in s-wave superfluids of ultracold fermionic atoms, Phys. Rev. Lett. 103(2), 020401(2009)

[20] C.Qu, Z.Zheng, M.Gong, Y.Xu, L.Mao, X.Zou, G.Guo, andC.Zhang, Topological superfluids with finitemomentum pairing and Majorana fermions, Nat. Commun. 4, 2710(2013)

[21] W.Zhangand W.Yi, Topological Fulde–Ferrell– Larkin–Ovchinnikov states in spin–orbit-coupled Fermi gases, Nat. Commun. 4, 2711(2013)

[22] X. J.Liu, Z. X.Liu, and M.Cheng, Manipulating topological edge spins in a one-dimensional optical lattice, Phys. Rev. Lett. 110(7), 076401(2013)

[23] X. J.Liu, K. T.Law, and T. K.Ng, Realization of 2D spin–orbit interaction and exotic topological orders in cold atoms, Phys. Rev. Lett. 112(8), 086401(2014) [Erratum: X. J.Liu, K. T.Law, and T. K.Ng, Phys. Rev. Lett. 113, 059901(2014)]

[24] F.Brennecke, T.Donner, S.Ritter, T.Bourdel, M.Köhl, and T.Esslinger, Cavity QED with a Bose– Einstein condensate, Nature450(7167), 268(2007)

[25] K.Baumann, C.Guerlin, F.Brennecke, and T.Esslinger, Dicke quantum phase transition with a superfluid gas in an optical cavity, Nature464(7293), 1301(2010)

[26] H.Ritsch, P.Domokos, F.Brennecke, and T.Esslinger, Cold atoms in cavity-generated dynamical optical potentials, Rev. Mod. Phys. 85(2), 553(2013)

[27] P.Domokosand H.Ritsch, Collective cooling and selforganization of atoms in a cavity, Phys. Rev. Lett. 89(25), 253003(2002)

[28] F.Dimer, B.Estienne, A. S.Parkins, and H. J.Carmichael, Proposed realization of the Dicke-model quantum phase transition in an optical cavity QED system, Phys. Rev. A75(1), 013804(2007)

[29] D.Nagy, G.Konya, G.Szirmai, and P.Domokos, Dickemodel phase transition in the quantum motion of a Bose–Einstein condensate in an optical cavity, Phys. Rev. Lett. 104(13), 130401(2010)

[30] R.Landig, F.Brennecke, R.Mottl, T.Donner, and T.Esslinger, Measuring the dynamic structure factor of a quantum gas undergoing a structural phase transition, Nat. Commun. 6, 7046(2015)

[31] J.Keeling, M. J.Bhaseen, and B. D.Simons, Fermionic superradiance in a transversely pumped optical cavity, Phys. Rev. Lett. 112(14), 143002(2014)

[32] F.PiazzaandP.Strack, Umklapp superradiance with a collisionless quantum degenerate Fermi gas, Phys. Rev. Lett. 112(14), 143003(2014)

[33] Y.Chen, Z.Yu, and H.Zhai, Superradiance of degenerate Fermi gases in a cavity, Phys. Rev. Lett. 112(14), 143004(2014)

[34] Y.Deng, J.Cheng, H.Jing, and S.Yi, Bose–Einstein condensates with cavity-mediated spin–orbit coupling, Phys. Rev. Lett. 112(14), 143007(2014)

[35] L.Dong, L.Zhou,B.Wu, B.Ramachandhran, and H.Pu, Cavity-assisted dynamical spin–orbit coupling in cold atoms, Phys. Rev. A89, 011602(R)(2014)

[36] J. S.Pan, X. J.Liu, W.Zhang, W.Yi, and G. C.Guo,Topological superradiant states in a degenerate Fermi gas, Phys. Rev. Lett. 115(4), 045303(2015)

[37] L.Dong, C.Zhu, and H.Pu, Photon-induced spin–orbit coupling in ultracold atoms inside optical cavity, Atoms3(2), 182(2015)

[38] C.Kollath, A.Sheikhan, S.Wolff, and F.Brennecke, Ultracold Fermions in a cavity-induced artificial magnetic field, Phys. Rev. Lett. 116(6), 060401(2016)

[39] M.Wang, P.Meystre, W.Zhang, and Q.He, Steadystate atom-light entanglement with engineered spin– orbit coupling, Phys. Rev. A93(4), 042311(2016)

[40] L.Zhouand X. L.Cui, Spin–orbit coupled ultracold gases in optical lattices: High-band physics and insufficiency of tight-binding models, Phys. Rev. B92(14), 140502(2015)

[41] R.Gehr, J.Volz, G.Dubois, T.Steinmetz, Y.Colombe, B. L.Lev, R.Long, J.Estève, andJ.Reichel, Cavitybased single atom preparation and high-fidelity hyperfine state readout, Phys. Rev. Lett. 104(20), 203602(2010)

[42] W.Zhang, G. D.Lin, and L. M.Duan, BCS–BEC crossover of a quasi-two-dimensional Fermi gas: The significance of dressed molecules, Phys. Rev. A77(6), 063613(2008)

[43] W.Zhang, G. D.Lin, and L. M.Duan, Berezinskii– Kosterlitz–Thouless transition in a trapped quasi-twodimensional Fermi gas near a Feshbach resonance, Phys. Rev. A78(4), 043617(2008)

[44] J.-K.Wang, W.Yi, and W.Zhang, Two-body physics in quasi-low-dimensional atomic gases under spin–orbit coupling, Front. Phys. 11(3), 118102(2016)

[45] M.Olshanii, Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons, Phys. Rev. Lett. 81(5), 938(1998)

[46] H.Moritz, T.Stöferle, M.Köhl, and T.Esslinger, Exciting collective oscillations in a trapped 1D gas, Phys. Rev. Lett. 91(25), 250402(2003)

[47] T.Kinoshita, T.Wenger, and D. S.Weiss, Observation of a one-dimensional Tonks–Girardeau gas, Science305(5687), 1125(2004)

[48] B.Paredes, A.Widera,V.Murg, O.Mandel, S.Fölling, I.Cirac, G. V.Shlyapnikov, T. W.Hänsch, and I.Bloch, Tonks–Girardeau gas of ultracold atoms in an optical lattice, Nature429(6989), 277(2004)

[49] X. J.Liu, H.Hu, and P. D.Drummond, Fulde– Ferrell–Larkin–Ovchinnikov states in one-dimensional spin-polarized ultracold atomic Fermi gases, Phys. Rev. A76(4), 043605(2007)

RIGHTS & PERMISSIONS

2018 Higher Education Press and Springer-Verlag Berlin Heidelberg