1. State Key Laboratory of Mesoscopic Physics, School of Physics, Peking University, Beijing 100871, China 2. Department of Physics, Renmin University of China, Beijing 100872, China 3. Collaborative Innovation Center of Quantum Matter, Beijing 100871, China 4. Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China 5. Beijing Key Laboratory of Opto-electronic Functional Materials and Micro-nano Devices, Renmin University of China, Beijing 100872, China
We study the pairing states in a largely imbalanced two-component Fermi gas loaded in an anisotropic two-dimensional optical lattice, where the spin-up and spin-down fermions are filled to the s- and px-orbital bands, respectively. We show that owing to the relative inversion of the band structures of the s and px orbitals, the system favors pairing between two fermions on the same side of the Brillouin zone, leading to a large stable regime for states with a finite center-of-mass momentum, i.e., the Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) state. In particular, when two Fermi surfaces are close in momentum space, a nesting effect stabilizes a special type of π-FFLO phase with a spatial modulation of πalong the easily tunneled x direction. We map out the zero-temperature phase diagrams within the mean-field approach for various aspect ratios within the two-dimensional plane and calculate the Berezinskii–Kosterlitz–Thouless (BKT) transition temperatures TBKT for different phases.
Y. A.Liao, A. S. C.Rittner, T.Paprotta, W.Li, G. B.Partridge, R. G.Hulet, S. K.Baur, and E. J.Mueller, Spin-imbalance in a one-dimensional Fermi gas, Nature467(7315), 567 (2010) https://doi.org/10.1038/nature09393
G.Sarma, On the influence of a uniform exchange field acting on the spins of the conduction electrons in a superconductor, J. Phys. Chem. Solids24(8), 1029 (1963) https://doi.org/10.1016/0022-3697(63)90007-6
D. E.Sheehy and L.Radzihovsky, BEC–BCS crossover, phase transitions and phase separation in polarized resonantly-paired superfluids, Ann. Phys. 322(8), 1790 (2007) https://doi.org/10.1016/j.aop.2006.09.009
H.Hu, X. J.Liu, and P. D.Drummond, Phase diagram of a strongly interacting polarized Fermi gas in one dimension, Phys. Rev. Lett. 98(7), 070403 (2007) https://doi.org/10.1103/PhysRevLett.98.070403
12
W.Zhang and W.Yi, Topological Fulde–Ferrell– Larkin–Ovchinnikov states in spin–orbit-coupled Fermi gases, Nat. Commun. 4, 2711 (2013) https://doi.org/10.1038/ncomms3711
13
W.Yi, W.Zhang, and X. L.Cui, Pairing superfluidity in spin–orbit coupled ultracold Fermi gases, Sci. China Phys. Mech. Astron. 58(1), 014201 (2015) https://doi.org/10.1007/s11433-014-5609-8
14
T. K.Koponen,T.Paananen, J. P.Martikainen, M. R.Bakhtiari, and P.Törmä, FFLO state in 1-, 2- and 3-dimensional optical lattices combined with a nonuniform background potential, New J. Phys. 10(4), 045014 (2008) https://doi.org/10.1088/1367-2630/10/4/045014
15
Z.Cai, Y.Wang, and C.Wu, Stable Fulde–Ferrell– Larkin–Ovchinnikov pairing states in two-dimensional and three-dimensional optical lattices, Phys. Rev. A83(6), 063621 (2011) https://doi.org/10.1103/PhysRevA.83.063621
16
Z.Zhang, H. H.Hung, C. M.Ho, E.Zhao, and W. V.Liu, Modulated pair condensate of p-orbital ultracold fermions, Phys. Rev. A82(3), 033610 (2010) https://doi.org/10.1103/PhysRevA.82.033610
17
S.Yin,J. E.Baarsma, M. O. J.Heikkinen, J. P.Martikainen, and P.Törmä, Superfluid phases of fermions with hybridized s and porbitals, Phys. Rev. A92(5), 053616 (2015) https://doi.org/10.1103/PhysRevA.92.053616
18
B.Liu, X.Li, R. G.Hulet, and W. V.Liu, Detecting pphase superfluids with p-wave symmetry in a quasi-onedimensional optical lattice, Phys. Rev. A94, 031602(R) (2016)
19
A. I.Buzdin, Proximity effects in superconductorferromagnet heterostructures, Rev. Mod. Phys. 77(3), 935 (2005) (and references therein) https://doi.org/10.1103/RevModPhys.77.935
20
C.Bernhard, J. L.Tallon, C.Niedermayer, T.Blasius, A.Golnik, E.Brücher, R. K.Kremer, D. R.Noakes, C. E.Stronach, and E. J.Ansaldo, Coexistence of ferromagnetism and superconductivity in the hybrid ruthenate-cuprate compound RuSr2GdCu2O8 studied by muon spin rotation and dc magnetization, Phys. Rev. B59(21), 14099 (1999) https://doi.org/10.1103/PhysRevB.59.14099
21
A. C.McLaughlin, W.Zhou, J. P.Attfield, A. N.Fitch, and J. L.Tallon, Structure and microstructure of the ferromagnetic superconductor RuSr2GdCu2O8, Phys. Rev. B60(10), 7512 (1999) https://doi.org/10.1103/PhysRevB.60.7512
22
O.Chmaissem, J. D.Jorgensen, H.Shaked, P.Dollar, and J. L.Tallon, Crystal and magnetic structure of ferromagnetic superconducting RuSr2GdCu2O8, Phys. Rev. B61(9), 6401 (2000) https://doi.org/10.1103/PhysRevB.61.6401
23
I.Zapata, B.Wunsch, N. T.Zinner, and E.Demler, p-phases in balanced fermionic superfluids on spindependent optical lattices, Phys. Rev. Lett. 105(9), 095301 (2010) https://doi.org/10.1103/PhysRevLett.105.095301
24
I. E.Mooij,T. P.Orlando, L.Levitov,L.Tian, C. H.van der Wal, and S.Lloyd, Josephson persistent-current qubit, Science285(5430), 1036 (1999) https://doi.org/10.1126/science.285.5430.1036
25
L. B.Ioffe, V. B.Geshkenbein, M. V.Feigel’man, A. L.Fauchère, and G.Blatter, Environmentally decoupled sds-wave Josephson junctions for quantum computing, Nature398(6729), 679 (1999) https://doi.org/10.1038/19464
26
T.Müller, S.Fölling, A.Widera, and I.Bloch, State preparation and dynamics of ultracold atoms in higher lattice orbitals, Phys. Rev. Lett. 99(20), 200405 (2007) https://doi.org/10.1103/PhysRevLett.99.200405
27
G.Wirth, M.Ölschläger, and A.Hemmerich, Evidence for orbital superfluidity in the P-band of a bipartite optical square lattice, Nat. Phys. 7(2), 147 (2011)
28
P.Soltan-Panahi, D. S.Lühmann, J.Struck, P.Windpassinger, and K.Sengstock, Quantum phase transition to unconventional multi-orbital superfluidity in optical lattices, Nat. Phys. 8(1), 71 (2011)
J. P.Kestner and L. M.Duan,Effective low-dimensional Hamiltonian for strongly interacting atoms in a transverse trap, Phys. Rev. A76(6), 063610 (2007) https://doi.org/10.1103/PhysRevA.76.063610
31
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) https://doi.org/10.1103/PhysRevA.77.063613
32
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) https://doi.org/10.1103/PhysRevA.78.043617
V. L.Berezinskii, Destruction of long-range order in one-dimensional and two-dimensional systems having a con-tinuous symmetry group (I): Classical systems, Sov. Phys. JETP32, 493 (1971)
35
J. M.Kosterlitz andD.Thouless, Long range order and metastability in two dimensional solids and superfluids. (Application of dislocation theory), J. Phys. C: Solid State Phys. 5, L124 (1972) https://doi.org/10.1088/0022-3719/5/11/002
