Bound states and universality in layers of cold polar molecules

Abstract

Abstract. -The recent experimental realization of cold polar molecules in the rotational and vibrational ground state opens the door to the study of a wealth of phenomena involving longrange interactions. By applying an optical lattice to a gas of cold polar molecules one can create a layered system of planar traps. Due to the long-range dipole-dipole interaction one expects a rich structure of bound complexes in this geometry. We study the bilayer case and determine the two-body bound state properties as a function of the interaction strength. The results clearly show that a least one bound state will always be present in the system. In addition, bound states at zero energy show universal behavior and extend to very large radii. These results suggest that non-trivial bound complexes of more than two particles are likely in the bilayer and in more complicated chain structures in multi-layer systems.Introduction. -Quantum gases of polar atoms and molecules in their rovibrational ground-state represent a unique opportunity to study the interplay of long-and short-range interactions in the highly controllable trapped gas environment. Early experiments used magnetic dipolar atoms [1-4] which have observable effects in spite of intrinsically weak dipole moments. Recently, heteronuclear molecules with very large electric dipole moments have been realized by a number of groups [5][6][7][8][9]. The goal of a quantum degenerate system of polar molecules with strong 1/r 3 long-range dipole-dipole forces therefore seems close at hand.The attractive force of polar molecules in the headto-tail configuration can lead to collapse of the system [10]. However, as suggested by Wang et al. [11], a onedimensional optical lattice that creates a multilayered stack of pancake systems can stabilize the situation. If we apply a field to polarize the dipoles perpendicular to the layers then the intralayer interaction will be purely repulsive, whereas the interlayer part will be attractive but with the optical lattices separating the dipoles in different layers. This setup is presently being implemented experimentally. As discussed in [11], the dipole-dipole force forms bound chains and the system effectively behaves as a liquid of chains with resemblance to rheological fluids.

Density waves in layered systems with fermionic polarmolecules

“…In the strong-coupling limit, a single layer of dipoles can also form a Wigner crystal with a symmetry which depends on how the dipoles are aligned with respect to the plane [14,15,16,35]. The presence of bound states in single and multilayer configuration of both fermionic and bosonic dipoles has also been given a great deal of attention recently [20,36,37,38,39,40,41]. For strong coupling, chains of multiple dipoles in bound states could be the relevant degree of freedom in the system and the effective interaction of such constituents should determine the ground-state, and could be very different for odd fermionic chains as opposed to even bosonic ones.…”

Model Independence in Two Dimensions and Polarized Cold Dipolar Molecules

“…Novel superfluid and density-wave instabilites have been proposed in this geometry [13]. However, very little is known about few-body bound states in the system, particularly in the experimentally relevant weak coupling limit, where universal features emerge independent of specific models, and previous works have only considered the case of perpendicular polarization [14][15][16]. We shall compare analytic and numerical results and investigate the approach towards the universal limit.…”

“…The energy very close to threshold is exponential in U 2 , as seen in Eq. (14), and determined by the polarization angle through A 0 . The first order terms, (A 1 , B 1 ), in U exhibit the difference in approach to threshold for the different signs of the strength, U .…”

Correlation effects and collective excitations in bosonic bilayers: Role of quantum statistics, superfluidity, and the dimerization transition

“…The intralayer and interlayer correlations play here a dominant role and determine the character of the static response and the screening properties. The interlayer attractive dipolar interaction, in the bilayer (or multilayer) case, results in a variety of interesting physical phenomena, which include a peculiar behavior of the scattering cross-section and bound states, [1][2][3][4] interlayer pairing and superfluidity. [5][6][7] Even more intriguing is the behavior of the collective modes as they can be directly detected with experimental probes that couple to the particle density operators.…”