Session F24: Quantum Gases in Optical Lattices

Microscopic studies of doped cold-atom Fermi-Hubbard antiferromagnets

The experimental platform of ultracold fermionic atoms in optical lattices offers new perspectives for studying the physics of strongly correlated materials. We use this platform to implement the Fermi-Hubbard model, a paradigmatic model thought to capture the physics of high-temperature superconductivity, the pseudogap, and other phenomena containing longstanding open questions. The additional tool of quantum gas microscopy enables site-resolved readout and access to projections of the many-body wavefunction in the Fock basis. I will report on our most recent studies of doped antiferromagnets, where there is no universally agreed-upon mechanism for the interplay between hole motion and antiferromagnetic order.   

Toward low-entropy states in the Fermi-Hubbard model with quantum gas microscopy

Ultracold atoms in optical lattices are a powerful platform for studying strongly correlated quantum systems. We study the repulsive Fermi-Hubbard model through quantum gas microscopy with fermionic Lithium-6 atoms in a square lattice. This technique allows for single-site resolved readout and manipulation, and has enabled us to achieve long-range antiferromagnetic order across our entire sample by performing entropy redistribution. Accessing intriguing phases in the Fermi-Hubbard model, requires development of new techniques for low-entropy quantum state preparation. Here we report on our low-noise interfering optical lattice, which offers dynamically tunable lattice geometry and allows for studies of the Fermi-Hubbard model in dimerized, honeycomb, and triangular lattices. This tunability can alternatively facilitate an adiabatic ramp from an ultra-low entropy initial state, prepared through entropy redistribution, toward strongly-correlated quantum phases. Another possible application of this interfering lattice is to provide simultaneous readout of both spin species.   

Photoemission spectroscopy of a Fermi-Hubbard system with a quantum gas microscope

Strongly correlated systems with superconducting ground states, including the high-temperature superconducting cuprates and the unitary fermi gas, exhibit normal state precursors to the superconducting gap in their single-particle excitations. A quantitative understanding of these so called pseudogap regimes may elucidate details of the ground states, but developing this is difficult in real materials because the parameters of the microscopic Hamiltonian are not known. In cold atom experiments the development of fermionic quantum gas microscopes has enabled high-precision studies of fermions in optical lattices. The Hamiltonian parameters of these systems can be calculated from first principles, and good agreement between theory and experiment has been reported in recent studies of equal-time spin and density correlations. In this talk I will report on the development of angle-resolved photoemission spectroscopy (ARPES) compatible with quantum gas microscopy and its application to studying pseudogap physics in an attractive Fermi-Hubbard system across the BEC-BCS crossover, setting the stage for future studies of the pseudogap regime in repulsive Hubbard systems.   

Progress toward a dipolar quantum gas microscope with an expandable lattice

Highly dipolar atoms present an exciting opportunity to extend previous experiments to more complex systems influenced by long range, anisotropic interactions. Erbium, with its large dipole moment, numerous isotopes, and rich Feshbach spectrum, is an excellent element for such research. We present on current progress toward the construction of a novel optical lattice expandable in all three dimensions. This expandable lattice gives us tunability of the lattice spacing by a factor of 20. This allows for short spacing lattice that maximizes the strength of the dipole-dipole interaction, and then allows for in situ imaging in a larger spacing lattice with higher fidelity.   

Progress toward an Erbium Dipolar Quantum Gas Microscope

Quantum gas microscopy provides an exciting platform for the study of in situ atom-atom interactions. Recent advances in quantum gas microscopy have allowed probing of the Bose-Hubbard and Fermi-Hubbard Hamiltonian. We are currently extending these platforms with the introduction of an Erbium Dipolar Quantum Gas Microscope allowing us to study dipole-dipole interactions in a lattice. Erbium has several exciting properties, which increase the control and flexibility of these systems. These include stable bosonic and fermionic isotopes, a large magnetic dipole moment (7uB), a large spin value (J=6 and F=19/2 for bosonic and fermionic isotopes), a rich Feshbach spectrum, and several broad and narrow atomic transitions. Here we are presenting our recent progress toward an Erbium Quantum Gas Microscope. This features the integration of several unique systems, such as a high-resolution reflective objective, an accordion lattice for imaging, and a low disorder optical lattice. These developments will allow us to benefit from the long-range interaction of Erbium and probe the Extended Bose-Hubbard and Extended Fermi-Hubbard Hamiltonian to an unprecedented degree.   

Antiferromagnetic Order and Non-Equilibrium Distributions in the Floquet-Engineered Hubbard Model

The periodically driven half-filled two-dimensional Hubbard model is studied via a saddle point plus fluctuations analysis of the Keldysh action. The drive is implemented as an alternating electric field, and the system is coupled to a metallic substrate in thermal equilibrium to allow for a non-equilibrium steady state synchronized to the drive. For drive frequencies below the equilibrium gap, and strong enough drive amplitudes, the mean-field equation has multiple solutions with a substantial time-dependent component. Even for "Magnus" drive frequencies much larger than the equilibrium gap, a one-loop analysis around the mean-field solution shows that even if no real electron-hole pairs are excited, the ac drive produces a highly excited, generically non-thermal distribution of fluctuations, which can affect the physics significantly, for example destroying zero-temperature long-ranged antiferromagnetic order for large enough drive amplitudes.   

Strong correlations in magic-angle semimetals

In magic-angle graphene, Moiré patterns lead to an enlarged unit cell, mini-Brillouin zone, and strongly correlated phases (as shown experimentally). We generalize this behavior to a whole class of semimetallic models from one- to three-dimensions, and we show that the key ingredients are (1) an “untwisted” semimetallic band structure and (2) a spatially quasiperiodic structure (e.g., a “twist”) [1]. As the quasiperiodic structure is enhanced, the velocity of the effective low-energy semimetal decreases until it vanishes at a quantum phase transition. The magic-angle phenomena are associated with this eigenstate phase transition which is a unique type of “Anderson delocalization” transition in momentum space. Further, it is accompanied with flat-bands and behaves universally across models. Lastly, we build effective Hubbard models on the new bands by computing Wannier states. The interactions in these Hubbard models are strongly enhanced at this transition, indicating the existence of strongly correlated phases. All ingredients to realize our proposal are available in present-day cold-atomic laboratories for which the magic-angle effect can be exploited to induce strong correlations in quantum degenerate gases.

[1] Fu, Yixing et al., arXiv:1809.04604 (2018).   

Enhancement and destruction of superfluidity: Unusual effects of population imbalance of atomic Fermi gases on a 1D optical lattice

We study the superfluid behavior of population imbalanced ultracold atomic Fermi gases with a short range attractive interaction on a 1D optical lattice, using a pairing fluctuation theory. Due to the lattice-continuum mixing in a 1D optical lattice, population imbalance now has highly unusual effects. While the transition Tc in the balanced case decreases and scales as k_Fa in the BEC regime, it approaches a constant BEC asymptote in imbalanced case. Therefore, population
imbalance may strongly enhance the superfluidity by raising Tc to the constant BEC asymptote. In addition to the destruction of superfluidity in some range of intermediate pairing strengths, the BEC regime may also become inaccessible when the lattice spacing d and the population imbalance p become large, and/or the lattice hopping integral t becomes small, in contrast to the 3D continuum or dilute 3D lattice case, for which the BEC regime is always accessible. Furthermore, even when the BEC regime is accessible, not all minority atoms are paired up in the BEC limit. Upon destruction of the superfluidity due to increasing (d,p) or decreasing t, only 50% of the minority atoms form pairs.   

Harmonic potential effect on the ground state of the “g-e” model

Alkaline-earth fermionic atoms confined in one-dimensional optical lattices can be described by the so-called "g-e" model [Nat. Phys. 6, 289 (10)], which at half filling shows four interesting insulating phases (CDW, Orbital density wave (ODW), Spin Haldane (SH) and Spin-Peierls) [PRB 91, 075121(15)]. However, the confining potential has not been considered so far, for this reason we explore an extended "g-e" model where a harmonic potential for both ¹S₀ (g) and ³P₀ (e) atoms was considered. Using the density-matrix renormalization group method, we found that diverse insulating phase coexist in the ground state and that the spin Haldane and the spin Peierls phases disappear with the confining potential, meaning that these phases will not be observed in the experiments. The evolution of the CDW and the ODW phases around the middle of the trap was studied for different parameters. This work is motivated by recent experimental results about ¹⁷¹Yb atoms confined in optical lattices [Arxiv:1810.00536v1].   

Light-cone like spreading of correlations in the Bose Hubbard model at strong coupling

We study the spreading of correlations in space and time after a quantum quench in the Bose Hubbard model. We derive equations of motion for the single-particle Green's function within the contour-time formalism, allowing us to study dynamics in the strong coupling regime. We discuss the numerical solutions of these equations and calculate the single-particle density matrix for quenches in the Mott phase. We demonstrate light-cone like spreading of correlations in the Mott phase in one, two, and three dimensions and calculate propagation velocities in each dimension. Our results show excellent agreement with existing results in one dimension and demonstrate the anisotropic spreading of correlations in higher dimensions.

  

Rigorous Results for the Ground States of the Spin-2 Bose-Hubbard Model

In this work, we prove rigorous theorems for the ground states of the spin-2 Bose-Hubbard model, concerning the magnetic properties, degeneracies and forms of the wave functions. The theorems are highly universal in the sense that they do not depend on the lattice structure (including spatial dimension), particle number and spin-independent interaction.

The spin-2 Bose-Hubbard model is a model for ultracold f = 2 spinor bosonic atoms in optical lattices. We prove that, with c₁ and c₂ being the coefficients of the two spin-dependent interaction terms of the Hamiltonian, the ground state has a maximum total spin when c₁ < 0 and c₂ ≧ 5c₁, while tends to be a singlet if c₁ = 0 and c₂ < 0. When c₁ = c₂ = 0, the model has SU(5) symmetry. Furthermore, the ground-state degeneracies and the forms of wave function are also exactly determined in each coefficient region. Our approach takes the advantage of the symmetry of the Hamiltonian and employs sophisticated mathematical tools including the Perron-Frobenius theorem and the min-max theorem, as well as the representation theory of so(5) Lie algebra.

References
[1] Hong Yang and Hosho Katsura. arXiv:1803.09441 (2018).
[2] M. Koashi and M. Ueda, Phys. Rev. Lett. 84, 1066 (2000).
[3] M. Ueda and M. Koashi, Phys. Rev. A 65, 063602 (2002).   

Metal-Insulator-Superconductor Transition in Two-Channel Interacting Many-Body Systems

Using a slave-rotor approach within a mean-field theory, we study two-channel interacting systems to investigate the competition of metallic, Mott-insulating, and superconducting phases. Considering spin-3/2 cold atoms on optical lattices as a model system and treating a spin-3/2 atom as a bound state of a charge and a spin, we uncover a novel form of matter due to the competition between metal and superconducting phase. This novel unconventional phase emerges as a result of the global U(1) broken symmetries with respect to both roton and spinon fields. Further, we argue that the emergence of this unconventional phase is a generic phenomenon associates with many body systems where there are competing interactions. As such, we show that this unconventional phase can exist in rubidium doped fullerides under pressure.
  

Quantum Joule expansions in one-dimensional lattices

We discuss the expansion dynamics of nonintegrable systems that contain bosons or fermions in one-dimensional lattices. The particles are initially confined in half of the system with a thermal state described by the canonical ensemble. At short times after we remove the barrier before the front hits the other boundary of the lattice, the radial velocity of the expansion is a constant. The center of mass is accelerated with a constant acceleration. At long times, local observables can be approximated by a thermal expectation of another canonical ensemble with an effective temperature. The weights for the diagonal ensemble and the canonical ensemble match well for high initial temperatures that correspond to negative effective final temperature after the expansion. The negative effective temperature for finite systems goes to positive inverse temperatures in the thermodynamic limit for bosons but is a true thermodynamic effect for fermions. We also compare the thermal entanglement entropy and density distribution in momentum space for the canonical ensemble, diagonal ensemble and instantaneous long-time states calculated by exact diagonalization.