Three-body interactions with cold polar molecules

Abstract

We show that polar molecules driven by microwave fields give naturally rise to strong three-body interactions, while the two-particle interaction can be independently controlled and even switched off. The derivation of these effective interaction potentials is based on a microscopic understanding of the underlying molecular physics, and follows from a well controlled and systematic expansion into many-body interaction terms. For molecules trapped in an optical lattice, we show that these interaction potentials give rise to Hubbard models with strong nearest-neighbor two-body and three-body interaction. As an illustration, we study the one-dimensional Bose-Hubbard model with dominant three-body interaction and derive its phase diagram.Fundamental interactions between particles, such as the Coulomb law, involves pairs of particles, and our understanding of the plethora of phenomena in condensed matter physics rests on models involving effective twobody interactions. On the other hand, exotic quantum phases, such as topological phases or spin liquids, are often identified as ground states of Hamiltonians with three or more body terms. While the study of these phases and properties of their excitations is presently one of the most exciting developments in theoretical condensed matter physics, it is difficult to identify real physical systems exhibiting such properties -a noticeable exception being the Fractional Quantum Hall effect. Here we show that polar molecules in optical lattices driven by microwave fields give naturally rise to Hubbard models with strong nearest-neighbor three-body interactions, while the twobody terms can be tuned (even switched off) with external fields.The many-body Hamiltonians underlying condensed matter physics are derived within an effective low energy theory, obtained by integrating out the high energy excitations. In general, this gives rise to interaction termswhere V (r) describes the two-particle interaction depending only on the separation between the particles. The second term W (r i , r j , r k ) is the three-body interaction, which depends on the distance and orientation of three particles, and vanishes if one particle is far apart from the other two. The ellipsis denotes possible higher many-body term terms. While for Helium atoms in the context of superfluidity the two-particle interaction dominates and determines the ground state properties with the three-body interactions providing small corrections, 1 model Hamiltonians with strong three-body interactions have attracted a lot of interest in the search for microscopic Hamiltonians exhibiting exotic ground state properties. Well known examples are the fractional quantum Hall states described by the Pfaffian wave functions which appear as ground states of a Hamiltonian with three-body interaction. 2,3,4 These topological phases admit anyonic excitations with non-abelian braiding statistic. Of special interest are also spin systems and bosonic Hamiltonians with complex many-body interactions, such as ring exchange model, whic...

Atomic quantum simulation of a three-dimensional U(1) gauge-Higgs model

“…(D2) We adjust the parameters J ab and V ab so that the conditions for the groups (i), (ii), (iv), and (v) are satisfied. In fact, Rydberg atoms trapped on the optical lattice [55] may have an isotropic interaction with a 1/r 3 -type potential under a certain external electric field [56]. This long-range interaction is expected to satisfy the condition in the groups (i, ii).…”

d-wave superfluidity in optical lattices of ultracold polar molecules

“…The amplitudes and signs of J ⊥ , J z , V , and W can be tuned independently [30] by tuning the external dc electric field and applying external microwave fields [17][18][19][21][22][23][24][25]29,[42][43][44][45][46]. The tunneling amplitude t (assumed to be positive throughout the paper) can be tuned by adjusting the depth of the optical lattice.…”

“…This system can be used to implement lattice Hamiltonians based on rotational states of polar molecules [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32]. Specifically, two rotational states of the molecules can be used as an effective spin-1/2 degree of freedom, while dipole-dipole interactions mediate "spin"-dependent coupling between molecules.…”

Controllable quantum spin glasses with magnetic impurities embedded in quantum solids

“…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) …”