Session N40: Dipolar Gases and Rydberg Atoms

Time-reversal-breaking and $d$-wave superfluidity of ultracold dipolar fermions in optical lattices

We describe possible superfluid phases of ultracold dipolar fermions in optical lattices for two-dimensional systems. Considering the many-body screening of dipolar interactions at larger filling factors, we show that several superfluid phases with distinct pairing symmetries naturally emerge in the singlet channel: local $s$-wave $(sl)$, extended $s$-wave $(se)$, $d$-wave $(d)$ or time-reversal-symmetry breaking $(sl + se \pm id)$-wave. The temperature versus filling factor phase diagram indicates that $d$-wave is favored near half-filling, that $(sl + se)$-wave is favored near zero or full filling, and that time-reversal-breaking $(sl + se \pm id)$-wave is favored in between. When a harmonic trap is included a sequence of phases can exist in the cloud depending on the filling factor at the center of the trap. Most notably in the region where the $(sl + se \pm id)$-wave superfluid exists, spontaneous currents are generated, and may be detected using velocity sensitive Bragg spectroscopy.   

Dipolar Fermions in Quasi-Two-Dimensional Square Lattice

Motivated by recent experimental realization of quantum degenerate dipolar Fermi gas, we study a system of ultralcold single- and two-species polar fermions in a double layer two-dimensional square lattice. The long-range anisotropic nature of dipole-dipole interaction has shown a rich phase diagram on a two dimensional square lattice*. We investigate how the interlayer coupling affects the monolayer system. Our study focuses on the regime where the fermions are closed to half-filling, which is when lattice effects play an important role. We find several correlated phases by using a functional renormalization group technique, which also provides estimates for the critical temperature of each phase. [*] S. G. Bhongale et. al. arXiv:1209.2671 and Phys. Rev. Lett. 108 145301 (2012).   

Orbital coupled dipolar fermions in an asymmetric optical ladder

We study a quantum ladder of dipolar atoms/molecules with coupled $s$ and $p$ orbitals. The interaction of such a system can be controlled with dipole moments being aligned by an external field. The two orbital components have distinct hoppings. The tunneling between them is equivalent to a partial Rashba spin-orbital coupling when the orbital space ($s$, $p$) is identified as spanned by pseudo-spin 1/2 states. A rich phase diagram is established. In particular a superconducting phase is found for repulsive fermions and a plaquette phase is found for bosons at 1/4 filling.   

Emergence of unconventional spin density waves in dipolar Fermi gases

Motivated by experiments on Fermi gases of dipolar molecules and dysprosium, we study the competing quantum phases of two- component (pseudo-spin 1/2) dipolar fermions on a two-dimensional optical lattice. The anisotropic, long-range dipole-dipole interaction leads to the occurrence of numerous exotic many-body states, e.g. supersolid, nematic, and topological superfluid. Here, using unbiased functional renormalization group approach, we discover that another quantum phase of matter, spin density wave (SDW) with p-wave orbital symmetry, emerges in this system when the dipoles are tilted at intermediate angles with respect to the lattice plane. This phase can be viewed as the particle-hole analogue of p-wave superconductors. We present the phase diagram of the system and show that the order parameter of the unconventional SDW is a vector quantity in spin space, and, moreover, is defined on lattice bonds rather than on lattice sites.   

Topological phases in polar-molecule quantum magnets

We show that ultracold polar molecules pinned in an optical lattice and interacting via dipolar interactions can be used to implement a huge variety of exotic quantum magnets. These can be used to realize, for example, fractional Chern insulators, symmetry protected topological phases, the bilinear-biquadratic spin-1 Hamiltonian, and the Kitaev honeycomb model. [References for some of the results: arXiv:1207.4479, arXiv:1210.5518]   

Symmetry Protected Topological Phases in Polar Molecule Spin Ladder Systems

We show how to use polar molecules in an optical lattice to engineer quantum spin models with arbitrary spin $S \geq 1/2$ 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 phases -- previously studied only in the nearest-neighbor 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.   

Realizing Fractional Chern Insulators with Dipolar Spins

Strongly correlated quantum systems can exhibit exotic behavior that is determined and controlled by topology. Such topological systems are of interest because they constitute fundamentally new states of matter exhibiting fractionalized excitations and robust chiral edge modes. We theoretically predict that the nu = 1/2 fractional Chern insulator, a recently proposed topological state of lattice bosons, arises naturally in a two-dimensional array of driven, dipolar-interacting spins.   

Preparation and detection of dipolar fractional Chern insulators

We describe schemes for preparation and detection of fractional Chern insulators as arise in driven dipolar spin systems. Such topological phases generically compete with superfluid and crystalline orders. We discuss the nature of the phase transitions and describe a dynamical preparation procedure. Prospects for measuring the properties of these topological phases using cold atomic techniques are considered.   

Parafermion excitations in superfluid of quasi-molecular chains formed by dipolar molecules or indirect excitons

We study a quantum phase transition in a system of dipoles confined in a stack of $N$ identical 1D lattices (tubes) polarized perpendicularly to the lattices. The dipoles may represent polar molecules or indirect excitons. The transition separates two phases; in one of them superfluidity takes place in each individual lattice, in the other (chain superfluid) the order parameter is the product of bosonic operators from all lattices. We argue that in the presence of finite inter-lattice tunneling the transition belongs to the universality class of the $q=N$ two-dimensional classical Potts model. For $N=2,3,4$ the corresponding low energy field theory is the model of Z$_N$ parafermions perturbed by the thermal operator. Results of Monte Carlo simulations are consistent with these predictions. The detection schemes for the chain superfluid of dipolar molecules and indirect excitons are outlined.   

Collective excitations of quasi-two-dimensional trapped dipolar fermions

We study the collective excitations of quasi-two-dimensional fermions with dipole-dipole interactions in an isotropic harmonic trap by solving the collisional Boltzmann-Vlasov equation. Except for the scaling monopole mode which exhibits a negligible damping, the other collective modes undergo a transition from the collisionless regime to a highly dissipative crossover regime and finally to the hydrodynamic regime upon increasing the dipolar interaction strength. In the 2D limit, we predict the existence of a temperature window within which the characteristics of the collective modes become temperature independent.   

Unconventional triplet pairing state in a polarized dipolar Fermi gas

We theoretically discuss the possibility of a triplet superfluid state in a polarized dipolar Fermi gas. In this system, it is usually believed that a high-energy cutoff is necessary in solving the superfluid BCS gap equation, reflecting the non-convergent behavior of a dipole-dipole interaction in the high-momentum limit. Because of this, the superfluid theory for a dipolar Fermi gas is believed to need a regularization for the angular-dependent dipole-dipole interaction as in the case of the s-wave interaction. In this talk, we show that such a renormalization is actually unnecessary, when one carefully includes the detailed structure of a dipolar molecule. We present a superfluid theory for a dipolar Fermi gas where the dipole-dipole interaction is only described by the two physical parameters, dipole size and dipole-dipole coupling constant. Using this, we discuss the possibility of a triplet pairing state, as well as superfluid properties, of this system. Since our theory only involves observable physical parameters, it would be useful in quantitatively evaluating superfluid properties of a dipolar Fermi gas, such as the superfluid phase transition temperature.   

P-wave superfluid in a quasi-two-dimensional dipolar Bose-Fermi quantum gas mixture

The $p$-wave ($p_{x} + i p_{y})$ superfluid has attracted significant attention in recent years mainly because its vortex core supports a Majorana fermion which, due to its non-Abelian statistics, can be explored for implementing topological quantum computation (TQC). Mixing in bosons may lead to $p$-wave pairing in a Fermi gas. In a dipolar condensate, the dipole-dipole interaction represents a control knob inaccessible to nondipolar Bosons. Thus, mixing dipolar bosons with fermions opens up new possibilities. We consider a mixture of a spin-polarized Fermi gas and a dipolar Bose-Einstein condensate in a quasi-two-dimensional trap setting. We take the Hartree-Fock-Bogoliubov mean-field approach and develop a theory for studying the stability of the mixture and estimating the critical temperature of the $p$-wave superfluid. We use this theory to identify the experimentally accessible parameter space in which the mixture is stable against phase separation and the $p$-wave superfluid pairing can be resonantly enhanced. An enhanced $p$-wave superfluid order parameter can make the fault tolerant TQC less susceptible to thermal fluctuations. This work aims to stimulate experimental activity in creating dipolar Bose-Fermi mixtures.   

Superfluidity of atomic Fermi gases with dipolar interactions

While quantum degenerate dipolar Fermi gases have been made available in experiment, the superfluidity in such Fermi gases has been of very high interest. In this talk, we study the superfluidity and associated BCS-BEC crossover behavior of a two-component atomic Fermi gases in three dimensions in the presence of dipole-dipole interactions, such as polar molecules $^{40}$K$^{87}$Rb and magnetic atoms $^{161}$Dy, using a pairing fluctuation theory. The relative interaction strength can be tuned via the atomic number. Various geometric configurations will be explored. We show that in certain configurations, the superfluidity may disappear altogether for a narrow range of interaction strength, and the Tc curve throughout the BCS-BEC crossover exhibits a reentrant behavior. We argue that such disappearance of the superfluidity is associated with the long range nature of the dipole-dipole interaction. A pseudogap develops naturally as the relative interaction becomes strong.   

Superfluid Pairing and Majorana Zero Mode in an Ultracold Rydberg Fermi Gas

We systematically calculate the p-wave superfluid phase of spin polarized Fermi gases in a Rydberg state. The mutual interaction between atoms are dressed by external fields and show nonlocal attractive 1/(a$+$r6) interaction. Different from the p-wave pairing phase of regular atoms near p-wave Feshbach resonance, the obtained p-wave superfluid phase can be stable away from three-body collision and has intrinsic nontrivial nodes in the momentum space. The critical temperature and order parameter for various interaction parameters have been calculated analytically and numerically, both in the 2D and 3D free space. When loading into optical lattice, we also show the proximity effect of Tc near half filling. Finally, when considering the harmonic confinement potential, we obtain the gapless Majorana Fermions confined to the boundary via self-consistently solving the DBG equation. We will discuss how to experimentally prepare and measure these Majorana states in Rydberg atoms.   

Supersolid phases of two-species Rydberg-dressed Bose-Einstein condensates

We investigate the supersolid ground states of a binary Rydberg-dressed BEC system. From a many-body perturbation expansion, both intra- and inter-species long-range dressed interactions are derived, which are essential for the study of the ground-state manifold of the binary Rydberg-dressed BEC system. Due to the long-range interactions, five distinct phases of the supersolid ground states are identified, which are experimentally observable.