Session M9: Novel Phases and Ordering in Fermi Gases

Detecting $\pi$-phase superfluids with $p$-wave symmetry in a quasi-1D optical lattice

We propose an experimental protocol to create a $p$-wave superfluid in a spin-polarized cold Fermi gas tuned by an $s$-wave Feshbach resonance. A crucial ingredient is to add an anisotropic 3D optical lattice and tune the fillings of two spins to the $s$ and $p$ band, respectively. The pairing order parameter is confirmed to inherit $p$-wave symmetry in its center-of-mass motion. We find that it can further develop into a state of unexpected $\pi$-phase modulation in a broad parameter regime. Experimental signatures are predicted in the momentum distributions, density of states and spatial densities for a realistic experimental setup. The $\pi$-phase $p$-wave superfluid is reminiscent of the $\pi$-state in superconductor-ferromagnet heterostructures but differs in symmetry and physical origin. The spatially-varying phases of the superfluid gap provide a novel approach to synthetic magnetic fields for neutral atoms. It would represent another example of $p$-wave pairing, first discovered in He-3 liquids.   

Experimental realization of the ionic Hubbard model on a honeycomb lattice with ultracold fermions

Ultracold atoms in optical lattices constitute a tool of choice to realize the Fermi-Hubbard model. There, the on-site interaction energy opens a gap in the charge excitation spectrum, leading to a Mott insulating ground state. However, in the ionic Hubbard model, the addition of a staggered energy offset on each lattice site also leads to an insulating ground state with charge-density-wave ordering, even in the absence of inter-particle interactions. In our experiment we realize the Ionic Hubbard model on a honeycomb lattice by loading a two-component interacting Fermi gas into an optical lattice with a staggered energy offset on alternating sites. The underlying density order of the ground state is revealed through the correlations in the noise of the measured momentum distribution. For a large energy offset, we observe a charge density-wave ordering, which is suppressed as the on-site interactions are increased. To further elucidate the nature of the ground state, we measure the double occupancy of lattice sites and the charge excitation spectrum for a wide range of parameters.   

A long-lived spin-orbit-coupled dipolar Fermi gas

We report on the demonstration of spin-orbit coupling in a quantum degenerate dipolar Fermi gas of dysprosium. The $T/T_F = 0.4$ gas has a lifetime as large as 0.4 s under Raman dressing at densities exceeding $10^{13}$ cm$^{-3}$. The lifetime is limited not by spontaneous emission but by dipolar relaxation loss, and the effect of the dipolar interaction is also observed in the dephasing of Rabi oscillations. This spin-orbit-coupled dipolar gas will allow future studies of fermionic systems in the presence of synthetic gauge fields wherein long lifetimes are essential to observing collective effects.   

A continuum of compass spin models on the honeycomb lattice

Quantum spin models with spatially dependent interactions, known as compass models, play an important role in the study of frustrated quantum magnetism. One example is the Kitaev model on the honeycomb lattice with spin-liquid ground states. Another example is the geometrically frustrated quantum $120^\circ$ model whose ground state has not been unambiguously established. To generalize the Kitaev model beyond the exactly solvable limit and connect it with other models, we propose a new model, dubbed ``the tripod model," which contains a continuum of compass-type models. It not only unifies paradigmatic spin models, but also enables the study of their quantum phase transitions. We obtain the phase diagram of the tripod model numerically by tensor networks in the thermodynamic limit. We show that the ground state of the quantum $120^\circ$ model has long-range dimer order. Moreover, we find an extended spin-disordered (spin-liquid) phase between the dimer phase and an antiferromagnetic phase. The unification and solution of a continuum of frustrated spin models as outline here may be useful to exploring new domains of other quantum spin or orbital models.   

Exotic topological density waves in cold atomic Rydberg fermions

Versatile controllability of interactions in ultracold atomic and molecular gases has now reached an era where quantum correlations and unconventional many-body phases can be studied with no corresponding analogues in solid-state systems. Recent experiments in Rydberg atomic gases have achieved exquisite control over non-local interactions, allowing novel quantum phases unreachable with the usual local interactions in atomic systems. Here I will discuss Rydberg-dressed atomic fermions in a three-dimensional optical lattice where we predict the existence of hitherto unheard-of exotic mixed topological density wave phases. By varying the spatial range of the non-local interaction, we find various chiral density waves with spontaneous time-reversal symmetry breaking, whose quasiparticles form three-dimensional quantum Hall and Weyl semimetal states. Remarkably, certain density waves even exhibit mixed topologies beyond the existing topological classification. Our results suggest gapless sermonic states with long-range interactions could exhibit far richer topology than previously expected. Reference: Xiaopeng Li, S. Das Sarma, Nat. Comms. 6:7137 (2015)   

Analog simulation of Weyl particles with cold atoms

The high degree of control of the properties of ultracold gases offers the possibility to study experimentally unconventional many-body systems. An example is given by massless relativistic Weyl fermions, which are of particular interest in high energy and condensed matter physics, where they emerge in the form of low energy excitations of exotic compounds like TaAs. The particular case of harmonically trapped Weyl particles can be mimicked by a laser-cooled cloud of $^6\rm{Li}$ trapped in a magnetic quadrupole potential. The non-separability of this particular potential enables a quasi-thermalization of the single particle distribution function even in the absence of interactions. Surprisingly, the dynamics features an effective decoupling between the strong trapping axis and the weak trapping plane. We studied both, numerically and experimentally, the relaxation of the excited cloud towards its equilibrium distribution, mapping this dynamics directly to the case of non-interaction massless particles in a harmonic potential. D.~Suchet, M.~Rabinovic, T.~Reimann, et al.\emph{submitted} (2016).   

Chiral magnetism and spin liquid Mott insulators induced by synthetic gauge fields

Recent experiments using Raman-assisted tunneling or lattice-shaking have realized synthetic gauge fields and optical lattice bands with nontrivial band topology. Here we examine the effect of particle interactions in such bands, focussing on two-component fermions with local Hubbard repulsion. We show that interactions can drive the integer quantum Hall insulator into Mott insulating states which possess noncoplanar chiral magnetic textures and even chiral spin liquids with many-body topological order. We establish our results using a combination of mean field theory, strong coupling expansions, numerical exact diagonalization and DMRG methods. We also discuss possible signatures of such non-coplanar orders in Bragg scattering and noise measurements.   

Pairing of Fermions with Unequal Effective Charges in an Artificial Magnetic Field

Artificial magnetic fields (AMFs) created for ultracold systems depend sensitively on the internal structure of the atoms. In a mixture, each component couples to the AMF with a different charge. This enables the study of Bardeen-Cooper-Schrieffer pairing of fermions with unequal effective charges [1]. We investigate the superconducting (SC) transition of a system formed by such pairs as a function of the field strength. We consider a homogeneous two-component Fermi gas of unequal charges but equal densities with attractive interactions. We find that the phase diagram is altered drastically compared to the usual equal charge case. First, for some AMFs there is no SC transition and isolated SC phases are formed, reflecting the discrete Landau level (LL) structure. SC phases become reentrant both in AMF and temperature. For extremely high fields where both components are confined to their lowest LLs, the effect of the charge imbalance is suppressed. Charge asymmetry reduces the critical temperature even in the low-field semiclassical regime. We discuss a pair breaking mechanism due to the unequal Lorentz forces acting on the components of the Cooper pairs to identify the underlying physics. [1] F. Nur \"{U}nal and M. \"{O}. Oktel, Phys. Rev. Lett. 116, 045305 (2016).   

Three-component Fulde-Ferrell superfluids in a two-dimensional Fermi gas with spin-orbit coupling

We investigate the pairing physics of a three-component spin-orbit coupled (SOC) Fermi gas in two spatial dimensions. The three atomic hyperfine states of the system are coupled by the recently realized synthetic SOC, which mixes different hyperfine states into helicity branches in a momentum-dependent manner. As a consequence, the interplay of SOC and the hyperfine-state dependent interactions leads to the emergence of Fulde-Ferrell (FF) pairing states with finite center-of-mass (COM) momenta even in the absence of the Fermi-surface asymmetry that is usually mandatory to stabilize an SOC-induced FF state. We show that, for different combinations of spin-dependent interactions, the ground state of the system can either be the conventional BCS pairing state with zero COM momentum or be the FF pairing states. Of particular interest here is the existence of a three-component FF pairing state in which every two out of the three components form FF pairing. We map out the phase diagram of the system and characterize the properties of the three-component FF state, such as the order parameters, the gapless contours and the momentum distributions. Based on these results, we discuss possible experimental detection schemes for the interesting pairing states in the system.