Session B4: Focus Session: Dipolar Quantum Gases

Rotational Frenkel excitons in optical lattices with polar molecules

Ultracold polar molecules trapped in an optical lattice may form crystal-like structures with unique properties. Here, I will discuss a Mott insulator phase of ultracold molecules with one molecule per lattice site under conditions that can be realized in ongoing experiments with optical lattices. I will show that dipole-dipole interactions between molecules in different lattice sites give rise to collective excitations, such as Frenkel excitons, characteristic of solid-state molecular crystals. Due to the perturbative nature of the intermolecular interactions, the collective excitations in this system can be controlled by an external electric field. This can be used to realize Frenkel excitons in the presence of dynamically tunable disorder or an ensemble of Frenkel excitons with tunable exciton - exciton interactions. An external electric field can thus be used to induce strong localization or delocalization of Frenkel excitons as well as bi-exciton annihilation. The latter can be used to produce dark exciton states and entangled exciton pairs. The complicated quantum statistics of excitons leads to kinematic interactions. Our results show that the kinematic interactions can be eliminated by varying an external electric field, effectively leading to a system of quantum quasi-particles with tunable quantum statistics. \\[4pt] [1] ``Tunable disorder in a crystal of cold polar molecules,'' Felipe Herrera, Marina Litinskaya, Roman V. Krems, Phys. Rev. A {\bf 82}, 033428 (2010).   

Optimizing the entangling power of Rydberg quantum gates

Optimal control is a versatile tool for quantum information processing since it allows for implementing a desired operation with extremely high fidelity. It can also be used to determine the minimum required gate operation time. In an implementation of quantum information processing based on trapped neutral atoms or molecules as qubit carriers, the main difficulty is encountered in realizing an entangling two-qubit operation such as a controlled NOT. In an optimal control approach, implementation of a CNOT gate can be achieved by maximizing the projection of the actual evolution onto CNOT as a functional of a control such as a laser field. However, for a given encoding of qubits in a physical system, it is a priori not clear whether CNOT is the two-qubit gate that can best be implemented or whether a gate that is equivalent to CNOT up to local, i.e. single-qubit, operations would be a more suitable choice. We have developed a new optimization functional that maximizes the entangling power of a desired two-qubit gate rather than the gate itself. We can thus optimize for all gates that are locally equivalent to the desired two-qubit operation. We apply this new functional to the implementation of fast two-qubit gates with dipolar systems.   

Ultracold polar KRb molecules

Ultracold polar molecules in the quantum degenerate regime open the possibility of realizing quantum gases with long-range, and spatially anisotropic, interparticle interactions. Currently, we can create a gas of ultracold fermionic ground-state KRb molecules in with a peak density of 10$^{12}$ cm$^{-3}$ and a temperature just 1.4 times the Fermi temperature. We will report on efforts to further cool this gas of molecules. One possibility is to evaporatively cool a spin-polarized molecular Fermi gas confined in quasi-2D, where we would rely on dipole-dipole interactions for rethermalization.   

The Efimov effect for three dipoles

The hyperspherical adiabatic representation is used to numerically solve the three-dipole problem. We show that this gives the characteristic Efimov potential in the limit of a zero-energy two-body bound state. Near such a dipole-dipole resonance, the infinite series of three-dipole Efimov states can strongly affect three-dipole collisions. A major finding is that the long-range dipolar interaction is particularly beneficial for the study of Efimov physics, in the following sense: In contrast to the usual Efimov effect, the 3-body bound and scattering properties are found to be universally determined by the $s$-wave scattering length and by the dipole length, i.e. they are insensitive to any three-body parameter. Moreover, the lifetime of Efimov states is found to increase with dipole moment. The universal scaling of the adiabatic hyperspherical potentials further implies scaling laws for the three-body recombination rates. Another result is that an effective repulsive interaction appears between a deeply-bound two-dipole molecule and a free dipole, which can stabilize an ultracold two-dipole dimer against collisional decay.   

Quantum Magnetism with Polar Alkali Dimers

We show that ultracold polar alkali dimers in optical lattices can be used to realize a highly tunable generalization of the $t-J$ model, which we refer to as the $t-J-V-W$ model. The model features long-range dipolar interactions of XXZ type ($J_z$ and $J_\perp$) and of density-density type ($V$), as well as a novel density-spin interaction $W$. The interaction terms can all be controlled in both magnitude and sign independently of each other and of the tunneling $t$. The ``spin" is encoded in the rotational degree of freedom of the molecules, while the interactions are controlled by applied static electric and continuous-wave microwave fields. Furthermore, we show that nuclear spins of the molecules can be used to implement an additional, orbital, degree of freedom that is coupled to the original rotational degree of freedom in a tunable way. We expect the competition between the different types of interaction to stabilize exotic phases. In particular, we carry out a Density Matrix Renormalization Group calculation to study the phase diagram in 1D for the special experimentally relevant case $J_z = V = W = 0$ and find that superconductivity is enhanced relative to the usual $t-J$ model.   

Electric and magnetic long-range interactions between two Erbium atoms

Lanthanides have recently attracted a lot of interest in the field of laser-cooling and trapping. Their high magnetic dipole moment - seven Bohr magnetons for Erbium - opens new prospects for the precise control of their mutual interactions. As they are also characterized by a high orbital angular momentum, they also interact through their permanent electric quadrupole moments. We have studied the combined effects of the magnetic-dipole and electric-quadrupole interaction as functions of the distance R between two atoms of Erbium. Although they scale as R-3 and R-5 respectively, we have shown that the two types of interaction can compete with each other in a wide range of interatomic distances. This is due to the weakness of magnetic forces compared to electric ones. For example, we observe long-range wells, which could drastically influence the collisional properties of the atoms. Our calculations can be generalized to other lanthanides, like Dysprosium.   

Narrow-line cooling and the optical dipole trapping of dysprosium

Highly magnetic atoms such as dysprosium offer the ability to create strongly correlated matter in both atomic physics and quantum optics settings. In addition, these atoms will form the key ingredient in novel devices possessing unsurpassed sensitivity and resolution for the microscopy of condensed matter materials. We present results on the narrow-line cooling of Dy to sub-10 $\mu$K temperatures and the subsequent optical dipole trapping of Dy. Progress toward ultracold collisional measurements and evaporative cooling will be discussed.