Topological phases in ultracold polar-molecule quantum magnets

Abstract

We show how to use polar molecules in an optical lattice to engineer quantum spin models with arbitrary spin S 1/2 and with interactions featuring a direction-dependent spin anisotropy. This is achieved by encoding the effective spin degrees of freedom in microwave-dressed rotational states of the molecules and by coupling the spins through dipolar interactions. We demonstrate how one of the experimentally most accessible anisotropies stabilizes symmetry protected topological phases in spin ladders. Using the numerically exact density matrix renormalization group method, we find that these interacting phases-previously studied only in the nearestneighbor case-survive in the presence of long-range dipolar interactions. We also show how to use our approach to realize the bilinear-biquadratic spin-1 and the Kitaev honeycomb models. Experimental detection schemes and imperfections are discussed. have spurred tremendous interest in exotic strongly correlated many-body phenomena arising from anisotropic, long-ranged dipole-dipole interactions. The types of anisotropies realizable with these interactions are typically limited to simple changes of the interaction sign and magnitude according to the spherical harmonic Y 2,0 ∝ 1 − 3 cos 2 θ , where (θ,φ) are the spherical coordinates of the vector connecting the two interacting dipoles. 11,13,32,33 In this Rapid Communication we show, in the context of polar molecules, that microwave dressing provides a tremendous degree of simultaneous control over five independent dipoledipole interaction terms whose angular dependences are given by the rank-2 spherical harmonics. This opens the door to simulating well-known models including the spin-1/2 XXZ model with a direction-dependent spin anisotropy, the spin-1 bilinear-biquadratic model, 47 and the Kitaev honeycomb model. 48 Thanks to the use of direct dipole-dipole coupling, the resulting interactions are stronger and hence easier to observe experimentally than other-potentially direction-dependentspin-spin interactions such as superexchange in ultracold atoms 49 or perturbative dipole-dipole-mediated couplings between polar molecules. 16,17 As a specific example demonstrating the reach of our method, we show how to design a spin-1/2 XXZ model with direction-dependent spin anisotropy using a minimal and experimentally reasonable microwave configuration. In a two-legged ladder geometry with nearest-neighbor interactions, this model has been shown to exhibit symmetry protected topological (SPT) phases. 50 These phases are exotic gapped states of matter distinct from trivial gapped phases when specific symmetries are present. A lattice of polar molecules in the XY plane is subjected to a dc electric field alongẑ. We define the xyz coordinate system as the rotation of the XYZ coordinate system around Z by 0 and then aroundŷ by 0 . A vector R with polar coordinates (R, ) in the XY plane has spherical coordinates (R,θ,φ) in the xyz coordinate system. method (DMRG), 64 we compute the phase diagram of the two-legged-ladder model obtai...

Correlations and enlarged superconducting phase of t−J⊥ chains of ultracold molecules on optical lattices

“…At the interface between atomic, molecular, optical, and condensed-matter physics, systems of ultracold polar molecules [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] have caused a great deal of excitement and opened a path for the quantum simulation [21][22][23][24][25][26][27][28][29] of quantum magnetism [30][31][32][33][34][35][36][37][38] and superconductivity [39,40] on optical lattices [41,42]. Intrinsic to these systems are the long-range dipolar-type interactions, which, in contrast to the long-range Coulomb interaction in condensed-matter systems, are not affected by screening.…”

Controllable quantum spin glasses with magnetic impurities embedded in quantum solids

“…(8) can be used to obtain an XXZ model with interactions featuring a direction-dependent spin-anisotropy. This model can be used to study symmetry-protected topological phases on a ladder 69 . Furthermore, the interactions J xx , J yy , and J zz of Eq.…”

“…It would be particularly interesting to follow Refs. 69,[76][77][78][79][80][81][82] and study how all of these spin Hamiltonians and the underlying phase transitions are affected by the long-range nature of the interactions.…”

“…Finally, Eq. (7) can be used to realize the most general spin-1 bilinear-biquadratic model 75 with the Y 2,0 angular dependence 69 . It would be particularly interesting to follow Refs.…”

“…Powerful microwave dressing techniques borrowed from the polar-molecule literature [54][55][56][57][58][59][60][61][62][63][64][65][66][67][68][69][70][71][72][73] can be used to access a great variety of Hamiltonians beyond the one given in Eq. (6) …”