Bose-Hubbard models with synthetic spin-orbit coupling: Mott insulators, spin textures, and superfluidity.

Motivated by the experimental realization of synthetic spin-orbit coupling for ultracold atoms, we investigate the phase diagram of the Bose-Hubbard model in a non-Abelian gauge field in two dimensions. Using a strong coupling expansion in the combined presence of spin-orbit coupling and tunable interactions, we find a variety of interesting magnetic Hamiltonians in the Mott insulator (MI), which support magnetic textures such as spin spirals and vortex and Skyrmion crystals. An inhomogeneous mean-field treatment shows that the superfluid (SF) phases inherit these exotic magnetic orders from the MI and display, in addition, unusual modulated current patterns. We present a slave-boson theory which gives insight into such intertwined spin-charge orders in the SF, and discuss signatures of these orders in Bragg scattering, in situ microscopy, and dynamic quench experiments.

[1]  M. Lewenstein,et al.  Quantum phase transition of ultracold bosons in the presence of a non-Abelian synthetic gauge field , 2011 .

[2]  Ashvin Vishwanath,et al.  Subject Areas : Strongly Correlated Materials A Viewpoint on : Topological semimetal and Fermi-arc surface states in the electronic structure of pyrochlore iridates , 2011 .

[3]  C. Gardiner,et al.  Cold Bosonic Atoms in Optical Lattices , 1998, cond-mat/9805329.

[4]  V. Galitski,et al.  Spin-orbit coupled Bose-Einstein condensates , 2007, 0712.2256.

[5]  Ian Mondragon-Shem,et al.  Unconventional Bose—Einstein Condensations from Spin-Orbit Coupling , 2008, 0809.3532.

[6]  P Zoller,et al.  Cold atoms in non-Abelian gauge potentials: from the Hofstadter "moth" to lattice gauge theory. , 2005, Physical review letters.

[7]  T. Corcovilos,et al.  Detecting antiferromagnetism of atoms in an optical lattice via optical Bragg scattering , 2009, 0910.2450.

[8]  M. Lukin,et al.  Controlling spin exchange interactions of ultracold atoms in optical lattices. , 2002, Physical review letters.

[9]  I. B. Spielman,et al.  Synthetic magnetic fields for ultracold neutral atoms , 2009, Nature.

[10]  Alexei Kitaev,et al.  Anyons in an exactly solved model and beyond , 2005, cond-mat/0506438.

[11]  X. Qi,et al.  Topological insulators and superconductors , 2010, 1008.2026.

[12]  G. Jackeli,et al.  Mott insulators in the strong spin-orbit coupling limit: from Heisenberg to a quantum compass and Kitaev models. , 2008, Physical review letters.

[13]  T. Moriya.  Anisotropic Superexchange Interaction and Weak Ferromagnetism , 1960 .

[14]  Chuanwei Zhang,et al.  Mean-field dynamics of spin-orbit coupled Bose-Einstein condensates. , 2011, Physical review letters.

[15]  C. Kane,et al.  Topological Insulators , 2019, Electromagnetic Anisotropy and Bianisotropy.

[16]  Leon Balents,et al.  Mott physics and band topology in materials with strong spin-orbit interaction , 2009, 0907.2962.

[17]  A. Hemmerich,et al.  Staggered-vortex superfluid of ultracold bosons in an optical lattice. , 2007, Physical review letters.

[18]  Fisher,et al.  Boson localization and the superfluid-insulator transition. , 1989, Physical review. B, Condensed matter.

[19]  Hui Zhai,et al.  Spin-orbit coupled spinor Bose-Einstein condensates. , 2010, Physical review letters.

[20]  S. Sachdev.  Quantum Phase Transitions: A first course , 1999 .

[21]  Immanuel Bloch,et al.  Single-spin addressing in an atomic Mott insulator , 2011, Nature.

[22]  A. Paramekanti,et al.  Bose-Hubbard model in a strong effective magnetic field: Emergence of a chiral Mott insulator ground state , 2011, 1109.5703.

[23]  T. Ozawa,et al.  Ground-state phases of ultracold bosons with Rashba-Dresselhaus spin-orbit coupling , 2011, 1109.4954.

[24]  A. Paramekanti,et al.  Use of quantum quenches to probe the equilibrium current patterns of ultracold atoms in an optical lattice , 2012, 1204.5184.

[25]  Shizhong Zhang,et al.  Bose-Einstein condensates with spin-orbit interaction. , 2011, Physical review letters.

[26]  V. Galitski,et al.  Exotic quantum spin models in spin-orbit-coupled Mott insulators. , 2012, Physical review letters.

[27]  W. Phillips,et al.  Bose-Einstein condensate in a uniform light-induced vector potential. , 2008, Physical review letters.

[28]  Hui Hu,et al.  Spin-orbit coupled weakly interacting Bose-Einstein condensates in harmonic traps. , 2012, Physical review letters.

[29]  T. Hänsch,et al.  Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms , 2002, Nature.

[30]  I. Dzyaloshinsky.  A thermodynamic theory of “weak” ferromagnetism of antiferromagnetics , 1958 .

[31]  Mikhail D. Lukin,et al.  Phase diagram of two-component bosons on an optical lattice , 2003 .

[32]  I. B. Spielman,et al.  Spin–orbit-coupled Bose–Einstein condensates , 2011, Nature.

[33]  H. R. Krishnamurthy,et al.  Superfluid and insulating phases in an interacting-boson model: mean-field theory and the RPA , 1993 .

[34]  Naoto Nagaosa,et al.  Doping a Mott insulator: Physics of high-temperature superconductivity , 2004, cond-mat/0410445.