# Recent Research

1. Clean Floquet Time Crystals: Models and Realizations in Cold Atoms Time crystals, a phase showing spontaneous breaking of time-translation symmetry, has been an intriguing subject for systems far away from equilibrium. Recent experiments found such a phase both in the presence and absence of localization, while in theories localization by disorder is usually assumed a priori. In this work, we point out that time crystals can generally exist in systems without disorder and is not in a pre-thermal state. A series of clean quasi-one-dimensional models under Floquet driving and non-local interactions are proposed to demonstrate this unexpected result in principle. Robust time crystalline orders are found in the strongly interacting regime due to the emergent integrals of motion in the dynamical system, which can be characterized by the out-of-time-ordered correlators. We propose two cold atom experimental schemes to realize the clean Floquet time crystals, one by making use of dipolar gases and another by synthetic dimensions.

Ref. Phys. Rev. Lett. 120, 110603 (2018)

link: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.120.110603

2. Odd-parity topological superfluidity for fermions in a bond-centered square optical lattice

We propose a physical scheme for the realization of two-dimensional topological odd-parity superfluidity in a spin-independent bond-centered square optical lattice based upon interband fermion pairing. The D4 point-group symmetry of the lattice protects a quadratic band crossing, which allows one to prepare a Fermi surface of spin-up fermions with odd parity close to the degeneracy point. In the presence of spin-down fermions with even parity populating a different energetically well-separated band, odd-parity pairing is favored. Strikingly, as a necessary prerequisite for pairing, both Fermi surfaces can be tuned to match well. As a result, topological superfluid phases emerge in the presence of merely s-wave interaction. Due to the Z2 symmetry of these odd-parity superfluids, we infer their topological features simply from the symmetry and the Fermi-surface topology as confirmed numerically.

Ref. Phys. Rev. A 96, 053607 (2017)

link. https://journals.aps.org/pra/abstract/10.1103/PhysRevA.96.053607

3. Frustrated Magnetism of Dipolar Molecules on a Square Optical Lattice: Prediction of a Quantum Paramagnetic Ground State

Motivated by the experimental realization of quantum spin models of polar molecule KRb in optical lattices, we analyze the spin 1/2 dipolar Heisenberg model with competing anisotropic, longrange exchange interactions. We show that, by tilting the orientation of dipoles using an external electric field, the dipolar spin system on square lattice comes close to a maximally frustrated region similar, but not identical, to that of the J1-J2 model. This provides a simple yet powerful route to potentially realize a quantum spin liquid without the need for a triangular or kagome lattice. The ground state phase diagrams obtained from Schwinger-boson and spin-wave theories consistently show a spin disordered region between the N´eel, stripe, and spiral phase. The existence of a finite quantum paramagnetic region is further confirmed by an unbiased variational ansatz based on tensor network states and a tensor renormalization group

Ref. Phys. Rev. Lett. 119, 050401 (2017)

link. https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.119.050401

4. Theory of interacting fermions in shaken square optical lattice

We develop a theory of weakly interacting fermionic atoms in shaken optical lattices based on the orbital mixing in the presence of time-periodic modulations. Specifically, we focus on fermionic atoms in circularly shaken square lattice with near resonance frequencies, i.e., tuned close to the energy separation between s-band and the p-bands. First, we derive a time-independent four-band effective Hamiltonian in the non-interacting limit. Diagonalization of the effective Hamiltonian yields a quasi-energy spectrum consistent with the full numerical Floquet solution that includes all higher bands. In particular, we find that the hybridized s-band develops multiple minima and therefore non-trivial Fermi surfaces at different fillings. We then obtain the effective interactions for atoms in the hybridized s-band analytically and show that they acquire momentum dependence on the Fermi surface even though the bare interaction is contact-like. We apply the theory to find the phase diagram of fermions with weak attractive interactions and demonstrate that the pairing symmetry is s + d-wave. Our theory is valid for a range of shaking frequencies near resonance, and it can be generalized to other phases of interacting fermions in shaken lattices.

Ref. Arxiv 1703.04074 (2017)

link: https://arxiv.org/pdf/1703.04074.pdf

5. Frustrated magnetism of dipolar molecules on square optical lattice: evidence for a quantum paramagnetic ground state

Motivated by the experimental realization of quantum spin models of polar molecule KRb in optical lattices, we analyze the spin 1/2 dipolar Heisenberg model with competing anisotropic, longrange exchange interactions. We show that by tilting the orientation of dipoles using an external electric field, the dipolar spin system on square lattice come close to a maximally frustrated region similar, but not identical, to that of the J1-J2 model. This provides a simple yet powerful route to potentially realize quantum spin liquid without the need for triangular or kagome lattice. The ground state phase diagrams obtained from Schwinger-boson and spin-wave theories consistently show a spin disordered region between the Neel, stripe, and spiral phase. The existence of a finite quantum paramagnetic region is further confirmed by unbiased variational ansatz based on tensor network states and tensor renormalization group.

Ref. Arxiv 1702.08517 (2017)

link: https://arxiv.org/pdf/1702.08517.pdf

6. Detecting π-phase superfluids with p-wave symmetry in a quasi-one-dimensional optical lattice

We propose an experimental protocol to study p-wave superfluidity in a spin-polarized cold Fermi gas tuned by an s-wave Feshbach resonance. A crucial ingredient is to add a quasi-one-dimensional 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 π-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 with a shallow trap. The π-phase p-wave superfluid is reminiscent of the π state in superconductor-ferromagnet heterostructures but differs in symmetry and physical origin. The spatially varying phases of the superfluid gap provide an approach to synthetic magnetic fields for neutral atoms. It would represent another example of p-wave pairing, first discovered in He3 liquids.

Ref. Phys. Rev. A 94, 031602 (2016)

link: http://journals.aps.org/pra/abstract/10.1103/PhysRevA.94.031602

7. π-Flux Dirac Bosons and Topological Edge Excitations in a Bosonic Chiral p-Wave Superfluid

We study the topological properties of elementary excitations in a staggered px±ipy Bose-Einstein condensate realized in recent orbital optical lattice experiments. The condensate wave function may be viewed as a configuration space variant of the famous px+ipy momentum space order parameter of strontium ruthenate superconductors. We show that its elementary excitation spectrum possesses Dirac bosons with π Berry flux. Remarkably, if we induce a population imbalance between the px+ipy and px−ipy condensate components, a gap opens up in the excitation spectrum resulting in a nonzero Chern invariant and topologically protected edge excitation modes. We give a detailed description of how our proposal can be implemented with standard experimental technology.

Ref: PhysRevLett.117.085301(2016)

link: http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.117.085301

8. 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 (SL) ground states and anyonic excitations. Another example is the geometrically frustrated quantum 120° model on the same lattice whose ground state has not been unambiguously established. To generalize the Kitaev model beyond the exactly solvable limit and connect it with other compass models, we propose a new model, dubbed 'the tripod model', which contains a continuum of compass-type models. It smoothly interpolates the Ising model, the Kitaev model, and the quantum 120° model by tuning a single parameter theta' , the angle between the three legs of a tripod in the spin space. Hence it not only unifies three 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° model has long-range dimer order. Moreover, we find an extended spin-disordered (SL) 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.

Ref. New J. Phys. 18 053040 (2016)

link: http://iopscience.iop.org/article/10.1088/1367-2630/18/5/053040/meta

9. Physics of higher orbital bands in optical lattices: a review

Orbital degree of freedom plays a fundamental role in understanding the unconventional properties in solid state materials. Experimental progress in quantum atomic gases has demonstrated that high orbitals in optical lattices can be used to construct quantum emulators of exotic models beyond natural crystals, where novel many-body states such as complex Bose-Einstein condensation and topological semimetals emerge. A brief introduction of orbital degree of freedom in optical lattices is given and a summary of exotic orbital models and resulting many-body phases is provided. Experimental consequences of the novel phases are also discussed.

link: http://iopscience.iop.org/article/10.1088/0034-4885/79/11/116401

10. Spontaneous quantum Hall effect in an atomic spinor Bose-Fermi mixture

Searching for topological states of matter has become one of the frontier topics in the field of ultracold atomic quantum gases. Tremendous efforts have been made to synthesize effective gauge fields or spin-orbit interactions by complex external manipulations. In contrast, we show that U(1) gauge fields for fermions can be spontaneously generated in an atomic spinor Bose-Fermi mixture (e.g., Rb-87 and Li-6) loaded in a triangular optical lattice. With fermions at 3/4 filling, Fermi surface nesting leads to spontaneous formation of various spin textures of bosons in the ground state, such as collinear, coplanar and even non-coplanar spin orders. Most surprisingly, a non-coplanar spin state is found and it naturally supports a quantum anomalous Hall state of fermions and crystalline superfluidity in bosons, both driven by interaction.

Ref: PhysRevLett.114.125303(2015)

link: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.114.125303

11. Weyl Superfluidity in a Three-dimensional Dipolar Fermi Gas

Weyl superconductivity or superfluidity, a fascinating topological state of matter, features novel phenomena such as emergent Weyl fermionic excitations and anomalies. Here we report that an anisotropic Weyl superfluid state can arise as a low temperature stable phase in a 3D dipolar Fermi gas. A crucial ingredient of our model is a direction-dependent two-body effective attraction generated by a rotating external field. Experimental signatures are predicted for cold gases in radio-frequency spectroscopy. The finite temperature phase diagram of this system is studied and the transition temperature of the Weyl superfluidity is found to be within the experimental scope for atomic dipolar Fermi gases.

Ref: PhysRevLett.114.045302 (2015)

link: http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.114.045302

12.Spin-Orbital Exchange of Strongly Interacting Fermions in the p Band of a Two-Dimensional Optical Lattice

Mott insulators with both spin and orbital degeneracy are pertinent to a large number of transition metal oxides. The intertwined spin and orbital fluctuations can lead to rather exotic phases such as quantum spin-orbital liquids. Here, we consider two-component (spin 1/2) fermionic atoms with strong repulsive interactions on the p band of the optical square lattice. We derive the spin-orbital exchange for quarter filling of the p band when the density fluctuations are suppressed, and show that it frustrates the development of long-range spin order. Exact diagonalization indicates a spin-disordered ground state with ferro-orbital order. The system dynamically decouples into individual Heisenberg spin chains, each realizing a Luttinger liquid accessible at higher temperatures compared to atoms confined to the s band.

Ref:PhysRevLett.114.100406(2015)

link: http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.114.100406