Fermionic transport in a homogeneous Hubbard model: Out-of-equilibrium dynamics with ultracold atoms
Ulrich Schneider, Lucia Hackermüller, Jens Philipp Ronzheimer, Sebastian Will, Simon Braun, Thorsten Best, Immanuel Bloch, Eugene Demler, Stephan Mandt, David Rasch, Achim Rosch
备注：
5 pages, 4 figures +supplementary information, shortened, published version
Transport properties are among the defining characteristics of many important phases in condensed matter physics. In the presence of strong correlations they are difficult to predict even for model systems like the Hubbard model. In real materials they are in general obscured by additional complications including impurities, lattice defects or multi-band effects. Ultracold atoms in contrast offer the possibility to study transport and out-of-equilibrium phenomena in a clean and well-controlled environment and can therefore act as a quantum simulator for condensed matter systems. Here we studied the expansion of an initially confined fermionic quantum gas in the lowest band of a homogeneous optical lattice. While we observe ballistic transport for non-interacting atoms, even small interactions render the expansion almost bimodal with a dramatically reduced expansion velocity. The dynamics is independent of the sign of the interaction, revealing a novel, dynamic symmetry of the Hubbard model.
We investigate long-range pairing interactions between ultracold fermionic atoms confined in an optical lattice which are mediated by the coupling to a cavity. In the absence of other perturbations, we find three degenerate pairing symmetries for a two-dimensional square lattice. By tuning a weak local atomic interaction via a Feshbach resonance or by tuning a weak magnetic field, the superfluid system can be driven from a topologically trivial s-wave to topologically ordered, chiral superfluids containing Majorana edge states. Our work points out a novel path towards the creation of exotic su…
We study finite-temperature magnetic phases of three-component mixtures of ultracold fermions with repulsive interactions in optical lattices with simple cubic or square geometry by means of dynamical mean-field theory (DMFT). We focus on the case of one particle per site (1/3 band filling) at moderate interaction strength, where we observe a sequence of thermal phase transitions into two- and three-sublattice ordered states by means of the unrestricted real-space generalization of DMFT. From our quantitative analysis we conclude that long-range ordering in three-component mixtures should be o…
Hubbard models with ultracold shielded molecules in optical lattices
Institute for Molecules and Materials, Radboud University（分子与材料研究所，拉德堡德大学）；Department of Physics and Astronomy, Rice University（物理与天文系，莱斯大学）；Smalley-Curl Institute, Rice University（斯马利-柯尔研究所，莱斯大学）
Ultracold atomic gases provide a fantastic platform to implement quantum simulators and investigate a variety of models initially introduced in condensed matter physics or other areas. One of the most promising applications of quantum simulation is the study of strongly-correlated Fermi gases, for which exact theoretical results are not always possible with state-of-the-art approaches. Here, we review recent progress of the quantum simulation of the emblematic Fermi-Hubbard model with ultracold atoms. After introducing the Fermi-Hubbard model in the context of condensed matter, its implementat…
We report on the experimental implementation of tunable occupation-dependent tunneling in a Bose-Hubbard system of ultracold atoms via time-periodic modulation of the on-site interaction energy. The tunneling rate is inferred from a time-resolved measurement of the lattice site occupation after a quantum quench. We demonstrate coherent control of the tunneling dynamics in the correlated many-body system, including full suppression of tunneling as predicted within the framework of Floquet theory. We find that the tunneling rate explicitly depends on the atom number difference in neighboring lat…
We study magnetic phases of two-component mixtures of ultracold fermions with repulsive interactions in optical lattices in the presence of hopping imbalance. Our analysis is based on dynamical mean-field theory (DMFT) and its real-space generalization at finite temperature. We study the temperature dependence of the transition into the ordered state as a function of the interaction strength and the imbalance parameter in two and three spatial dimensions. We show that below the critical temperature for Néel order mass-imbalanced mixtures also exhibit a charge-density wave, which provides a dir…
Rapid advancements in the experimental capabilities with ultracold alkaline-earth-like atoms (AEAs) bring to a surprisingly near term the prospect of performing quantum simulations of spin models and lattice field theories exhibiting SU($N$) symmetry. Motivated in particular by recent experiments preparing high density samples of strongly interacting ${}^{87}$Sr atoms in a three-dimensional optical lattice, we develop a low-energy effective theory of fermionic AEAs which exhibits emergent multi-body SU($N$)-symmetric interactions, where $N$ is the number of atomic nuclear spin levels. Our theo…
Exact two-dimensional analytic wave functions for an arbitrary number $N$ of contact-interacting lowest-Landau-level (LLL) spinful fermions are derived with the use of combined numerical and symbolic computational approaches via analysis of exact Hamiltonian numerical diagonalization data. Closed-form analytic expressions are presented for two families of zero-interaction-energy states at given total angular momentum and total spin $0 \leq S \leq N/2$ in the neighborhood of the $ν=1$ filling, covering the range from the maximum density droplet to the first quasihole. Our theoretical prediction…
Understanding the robustness of topological phases of matter in the presence of strong interactions, and synthesising novel strongly-correlated topological materials, lie among the most important and difficult challenges of modern theoretical and experimental physics. In this work, we present a complete theoretical analysis of the synthetic Creutz-Hubbard ladder, which is a paradigmatic model that provides a neat playground to address these challenges. We put special attention to the competition of correlated topological phases and orbital quantum magnetism in the regime of strong interactions…
We describe the formation of fermionic NaLi Feshbach molecules from an ultracold mixture of bosonic 23Na and fermionic 6Li. Precise magnetic field sweeps across a narrow Feshbach resonance at 745 G result in a molecule conversion fraction of 5% for our experimental densities and temperatures, corresponding to a molecule number of 5*10^4. The observed molecular decay ifetime is 1.3 ms after removing free Li and Na atoms from the trap.
We have produced persistent currents of ultracold fermionic atoms trapped in a ring, with lifetimes greater than 10 seconds in the strongly-interacting regime. These currents remain stable well into the BCS regime at sufficiently low temperature. We drive a circulating BCS superfluid into the normal phase and back by changing the interaction strength and find that the probability for quantized superflow to reappear is remarkably insensitive to the time spent in the normal phase and the minimum interaction strength. After ruling out spontaneous current formation for our experimental conditions,…
Quantum simulation with ultracold atoms has become a powerful technique to gain insight into interacting many-body systems. In particular, the possibility to study nonequilibrium dynamics offers a unique pathway to understand correlations and excitations in strongly interacting quantum matter. So far, coherent nonequilibrium dynamics has exclusively been observed in ultracold many-body systems of bosonic atoms. Here we report on the observation of coherent quench dynamics of fermionic atoms. A metallic state of ultracold spin-polarised fermions is prepared along with a Bose-Einstein condensate…
We introduce a density functional formalism to study the ground-state properties of strongly-correlated dipolar and ionic ultracold bosonic and fermionic gases, based on the self-consistent combination of the weak and the strong coupling limits. Contrary to conventional density functional approaches, our formalism does not require a previous calculation of the interacting homogeneous gas, and it is thus very suitable to treat systems with tunable long-range interactions. Due to its asymptotic exactness in the regime of strong correlation, the formalism works for systems in which standard mean-…
We employ metastable ultracold $^{173}$Yb atoms to study dynamics in the 1D dissipative Fermi-Hubbard model experimentally and theoretically, and observe a complete inhibition of two-body losses after initial fast transient dynamics. We attribute the suppression of particle loss to the dynamical generation of a highly entangled Dicke state. For several lattice depths and for two- and six-spin component mixtures we find very similar dynamics, showing that the creation of strongly correlated states is a robust and universal phenomenon. This offers interesting opportunities for precision measurem…
We analyze a ultracold fermionic atom system in a three dimensional optical lattice with a confinement harmonic potential, using the Hubbard model, and time-dependent Gutzwiller variational approach for numerical calculation. Our study is focused on the time evolution of the particle transfer when the lattice potential is modulated by adding a periodic one. The choice of the parameters such as the modulation frequency and amplitude and the particle number affects the particle transfer. We calculate the time evolution of the variance in the particle distribution, and show its dependence on the …
We describe an ultracold fermionic set-up where it is possible to synthesize a superfluid phase with symmetry obtained by locking independent invariance groups of the normal state. In this phase, named two-flavors symmetry-locking phase (TFSL), non-Abelian fractional vortices with semi-integer flux and gapless non-Abelian Goldstone modes localized on them appear. Considerations on the possible experimental realization of the TFSL are also provided.
Advances with trapped ultracold atoms intensified interest in simulating complex physical phenomena, including quantum magnetism and transitions from itinerant to non-itinerant behavior. Here we show formation of antiferromagnetic ground states of few ultracold fermionic atoms in single and double well (DW) traps, through microscopic Hamiltonian exact diagonalization for two DW arrangements: (i) two linearly oriented one-dimensional, 1D, wells, and (ii) two coupled parallel wells, forming a trap of two-dimensional, 2D, nature. The spectra and spin-resolved conditional probabilities reveal for …
We consider the time-reversal-invariant Hofstadter-Hubbard model which can be realized in cold atom experiments. In these experiments, an additional staggered potential and an artificial Rashba--type spin-orbit coupling are available. Without interactions, the system exhibits various phases such as topological and normal insulator, metal as well as semi--metal phases with two or even more Dirac cones. Using a combination of real-space dynamical mean-field theory and analytical techniques, we discuss the effect of on-site interactions and determine the corresponding phase diagram. In particular…
We report on the formation of ultracold fermionic Feshbach molecules of $^{23}$Na$^{40}$K, the first fermionic molecule that is chemically stable in its ground state. The lifetime of the nearly degenerate molecular gas exceeds 100 ms in the vicinity of the Feshbach resonance. The measured dependence of the molecular binding energy on the magnetic field demonstrates the open-channel character of the molecules over a wide field range and implies significant singlet admixture. This will enable efficient transfer into the singlet vibrational ground state, resulting in a stable molecular Fermi gas …
We show that in s-wave superfluids of cold fermionic atoms with laser-field-generated effective spin-orbit interactions, a topological phase with gapless edge states and Majorana fermion quasiparticles obeying the non-Abelian statistics is realized in the case with a large Zeeman magnetic field. Our scenario provides a promising approach for quantum computation manipulating non-Abelian anyons via an s-wave Feshbach resonance.
In a recent work, Murmann {\it et. al.} [Phys. Rev. Lett. {\bf114}, 080402 (2015)] have experimentally prepared and manipulated a double-well optical potential containing a pair of Fermi atoms as a possible building block of Hubbard model. Here, we carry out a detailed theoretical study on the properties of both fermionic and bosonic two-site Hubbard models with a pair of interacting atoms in a trap with a double-well structure along z-axis and a 2D harmonic confinement along the transverse directions. We consider fermions as of two-component type and bosons as of spinless as well as of two sp…
The Hubbard model underlies our understanding of strongly correlated materials. While its standard form only comprises interaction between particles at the same lattice site, its extension to encompass long-range interaction, which activates terms acting between different sites, is predicted to profoundly alter the quantum behavior of the system. We realize the extended Bose-Hubbard model for an ultracold gas of strongly magnetic erbium atoms in a three-dimensional optical lattice. Controlling the orientation of the atomic dipoles, we reveal the anisotropic character of the onsite interaction …
Considering a system of ultracold atoms in an optical lattice, we propose a simple and robust implementation of a quantum simulator for the homogeneous t-J model with a well-controlled fraction of holes x. The proposed experiment can provide valuable insight into the physics of cuprate superconductors. A similar scheme applied to bosons, moreover, allows one to investigate experimentally the subtle role of inhomogeneity when a system passes from one quantum phase to another.
We report on the creation of an ultracold dipolar gas of fermionic $^{23}$Na$^{40}$K molecules in their absolute rovibrational and hyperfine ground state. Starting from weakly bound Feshbach molecules, we demonstrate hyperfine resolved two-photon transfer into the singlet ${\rm X}^1Σ^+ |v{=}0,J{=}0\rangle$ ground state, coherently bridging a binding energy difference of 0.65 eV via stimulated rapid adiabatic passage. The spin-polarized, nearly quantum degenerate molecular gas displays a lifetime longer than 2.5 s, highlighting NaK's stability against two-body chemical reactions. A homogeneous …
We study magnetic phases of two-component mixtures of ultracold fermions with repulsive interactions in optical lattices in the presence of both hopping and population imbalance by means of dynamical mean-field theory (DMFT). It is shown that these mixtures can have easy-axis antiferromagnetic, ferrimagnetic, charge-density wave, and canted-antiferromagnetic order or be unordered depending on parameters of the system. We study the resulting phase diagram in detail and investigate the stability of the different phases with respect to thermal fluctuations. We also perform a quantitative analysis…
Accessing new regimes in quantum simulation requires the development of new techniques for quantum state preparation. We demonstrate the quantum state engineering of a strongly correlated many-body state of the two-component repulsive Fermi-Hubbard model on a square lattice. Our scheme makes use of an ultralow entropy doublon band insulator created through entropy redistribution. After isolating the band insulator, we change the underlying potential to expand it into a half-filled system. The final many-body state realized shows strong antiferromagnetic correlations and a temperature below the…
We show that Majorana fermions (MFs) exist in two- and three-dimensional (2D,3D) fermionic optical lattices with strictly 1D spin-orbit coupling (SOC) which has already been realized in ex- periments. For a quasi-1D topological BCS superfluid, there are multiple MFs at each end which are topologically protected by a chiral symmetry. In the generalization to higher dimensions, the multiple MFs form a zero energy flat band. An additional experimentally tunable in-plane Zeeman field drives the system to a topological Fulde-Ferrell (FF) superfluid phase. We find that even though the multiple MFs a…
We present a calculation of the spectral functions and the associated rf response of ultracold fermionic atoms near a Feshbach resonance. The single particle spectra are peaked at energies that can be modeled by a modified BCS dispersion. However, even at very low temperatures their width is comparable to their energy, except for a small region around the dispersion minimum. The structure of the excitation spectrum of the unitary gas at infinite scattering length agrees with recent momentum-resolved rf spectra near the critical temperature. A detailed comparison is made with momentum integrate…
We show that single-component fermionic polar molecules confined to a 2D geometry and dressed by a microwave field, may acquire an attractive $1/r^3$ dipole-dipole interaction leading to superfluid p-wave pairing at sufficiently low temperatures even in the BCS regime. The emerging state is the topological $p_x+ip_y$ phase promising for topologically protected quantum information processing. The main decay channel is via collisional transitions to dressed states with lower energies and is rather slow, setting a lifetime of the order of seconds at 2D densities $\sim 10^8$ cm$^{-2}$.
We study theoretically many-body equilibrium magnetic phases and corresponding thermodynamic characteristics of ultracold three-component fermionic mixtures in optical lattices described by the SU(3)-symmetric single-band Hubbard model. Our analysis is based on the generalization of the exact diagonalization solver for multicomponent mixtures that is used in the framework of the dynamical mean-field theory. It allows us to obtain a finite-temperature phase diagram with the corresponding transition lines to magnetically ordered phases at filling one particle per site (1/3 band filling) in simpl…
The momentum distribution is one of the most important quantities which provides information about interactions in many-body systems. At the same time it is a quantity that can easily be accessed in experiments on ultracold atoms. In this paper, we consider mixtures of light and heavy fermionic atoms in an optical lattice described effectively by the Falicov-Kimball model. Using a Monte Carlo method, we study how different ordered density-wave phases can be detected by measurement of the momentum distribution of the light atoms. We also demonstrate that ordered phases can be seen in Bragg scat…
We show that atomic Fermi mixtures with density and mass imbalance exhibit a rich diversity of scaling laws for the quasiparticle decay rate beyond the quadratic energy and temperature dependence of conventional Fermi liquids. For certain densities and mass ratios, the decay rate is linear whereas in other cases it exhibits a plateau. Remarkably, this plateau extends from the deeply degenerate to the high temperature classical regime of the light species. Many of these scaling laws are analogous to what is found in very different systems including dirty metals, liquid metals, and high temperat…
We realize and study the ionic Hubbard model using an interacting two-component gas of fermionic atoms loaded into an optical lattice. The bipartite lattice has honeycomb geometry with a staggered energy-offset that explicitly breaks the inversion symmetry. Distinct density-ordered phases are identified using noise correlation measurements of the atomic momentum distribution. For weak interactions the geometry induces a charge density wave. For strong repulsive interactions we detect a strong suppression of doubly occupied sites, as expected for a Mott insulating state, and the externally brok…
We extent the recently developed Multi-Layer Multi-Configuration Time-Dependent Hartree method for Bosons (ML-MCTDHB) for simulating the correlated quantum dynamics of bosonic mixtures to the fermionic sector and establish a unifying approach for the investigation of the correlated quantum dynamics of mixture of indistinguishable particles, be it fermions or bosons. Relying on a multi-layer wave-function expansion, the resulting Multi-Layer Multi-Configuration Time-Dependent Hartree method for Mixtures (ML-MCTDHX) can be adapted to efficiently resolve system-specific intra- and inter-species c…
Ultracold atoms in optical lattices have great potential to contribute to a better understanding of some of the most important issues in many-body physics, such as high-$T_c$ superconductivity. The Hubbard model describes many of the features shared by the copper oxides, including an interaction-driven Mott insulating state and an antiferromagnetic (AFM) state. Optical lattices filled with a two-spin-component Fermi gas of ultracold atoms can faithfully realise the Hubbard model with readily tunable parameters, and thus provide a platform for the systematic exploration of its phase diagram. Re…
We characterize the Mott insulating regime of a repulsively interacting Fermi gas of ultracold atoms in a three-dimensional optical lattice. We use in-situ imaging to extract the central density of the gas, and to determine its local compressibility. For intermediate to strong interactions, we observe the emergence of a plateau in the density as a function of atom number, and a reduction of the compressibility at a density of one atom per site, indicating the formation of a Mott insulator. Comparisons to state-of-the-art numerical simulations of the Hubbard model over a wide range of interacti…
We study a two-leg fermionic Hubbard ladder model with a state-dependent hopping. We find that, contrary to the case without a state-dependent hopping, for which the system has a superfluid nature regardless of the sign of the interaction at incommensurate filling, in the presence of such a hopping a spin-triplet superfluid, spin- density wave and charge-density wave phases emerge. We examine our results in the light of recent experiments on periodically-driven optical lattices in cold atoms. We give protocols allowing us to realize the spin-triplet superfluid elusive in the cold atoms.
Understanding quantum many-body states of correlated electrons is one main theme in modern condensed matter physics. Given that the Fermi-Hubbard model, the prototype of correlated electrons, has been recently realized in ultracold optical lattices, it is highly desirable to have controlled numerical methodology to provide precise finite-temperature results upon doping, to directly compare with experiments. Here, we demonstrate the exponential tensor renormalization group (XTRG) algorithm [Phys. Rev. X 8, 031082 (2018)], complemented with independent determinant quantum Monte Carlo (DQMC) offe…
We study finite-temperature properties of ultracold four-component mixtures of alkaline-earth-like atoms in optical lattices that can be effectively described by the two-band spin-$1/2$ Hubbard model including the Hund's exchange coupling term. Our main goal is to investigate the effect of exchange interactions on finite-temperature magnetic phases for a wide range of lattice fillings. We use the dynamical mean-field theory approach and its real-space generalization to obtain finite-temperature phase diagrams including transitions to magnetically-ordered phases. It allows to determine optimal …
We present our experimental setup to produce ultracold strongly correlated fermionic superfluids made of a two-component spin-mixture of $^6$Li atoms. Employing standard cooling techniques, we achieve quantum degeneracy in a single-beam optical dipole trap. Our setup is capable of generating spin-balanced samples at temperatures as low as $T/T_F = 0.1$ containing up to $5 \times 10^4$ atomic pairs. We can access different superfluid regimes by tuning the interparticle interactions close to a broad magnetic Feshbach resonance. In particular, we are able to explore the crossover from the molecul…
We propose a minimal theoretical model for the description of a two-dimensional (2D) strongly interacting Fermi gas confined transversely in a tight harmonic potential, and present accurate predictions for its equation of state and breathing mode frequency. We show that the minimal model Hamiltonian needs at least two independent interaction parameters, the 2D scattering length and effective range of interactions, in order to quantitatively explain recent experimental measurements at nonzero filling factor $N/N_{2D}$, where $N$ is the total number of atoms and $N_{2D}$ is the threshold number …
We study a class of SU(N) Heisenberg models, describing Mott insulators of fermionic ultra-cold alkaline earth atoms on the three-dimensional simple cubic lattice. Based on an earlier semiclassical analysis, magnetic order is unlikely, and we focus instead on a solvable large-N limit designed to address the competition among non-magnetic ground states. We find a rich phase diagram as a function of the filling parameter k, composed of a variety of ground states spontaneously breaking lattice symmetries, and in some cases also time reversal symmetry. One particularly striking example is a state …
We study Mott insulators of fermionic alkaline earth atoms, described by Heisenberg spin models with enhanced SU(N) symmetry. In dramatic contrast to SU(2) magnetism, more than two spins are required to form a singlet. On the square lattice, the classical ground state is highly degenerate and magnetic order is thus unlikely. In a large-N limit, we find a chiral spin liquid ground state with topological order and Abelian fractional statistics. We discuss its experimental detection. Chiral spin liquids with non-Abelian anyons may also be realizable with alkaline earth atoms.
We present a pairing fluctuation theory which self-consistently incorporates finite momentum pair excitations in the context of BCS--Bose-Einstein condensation (BEC) crossover, and we apply this theory to high $T_c$ superconductors and ultracold Fermi gases. There are strong similarities between Fermi gases in the unitary regime and high Tc superconductors. Here we address key issues of common interest, especially the pseudogap. In the Fermi gases we summarize recent experiments including various phase diagrams (with and without population imbalance), as well as evidence for a pseudogap in the…
Wave-function microscopy: Derivation and anatomy of exact algebraic spinful wave functions and full Wigner-molecular spectra of a few highly correlated rapidly rotating ultracold fermionic atoms
We study a 1D Fermi gas with attractive short range-interactions in a disordered potential by the density matrix renormalization group (DMRG) technique. This setting can be implemented experimentally by using cold atom techniques. We identify a region of parameters for which disorder enhances the superfluid state. As disorder is further increased, global superfluidity eventually breaks down. However this transition occurs before the transition to the insulator state takes place. This suggests the existence of an intermediate metallic `pseudogap' phase characterized by strong pairing but no qua…
Recent experimental advances in the cooling and manipulation of bialkali dimer molecules have enabled the production of gases of ultracold molecules that are not chemically reactive. It has been presumed in the literature that in the absence of an electric field the low-energy scattering of such nonreactive molecules (NRMs) will be similar to atoms, in which a single $s$-wave scattering length governs the collisional physics. However, in Ref. [1], it was argued that the short-range collisional physics of NRMs is much more complex than for atoms, and that this leads to a many-body description i…
Identification and understanding of the evolution of interference patterns in two-particle momentum correlations as a function of the strength of interatomic interactions are important in explorations of the nature of quantum states of trapped particles. Together with the analysis of two-particle spatial correlations, they offer the prospect of uncovering fundamental symmetries and structure of correlated many-body states, as well as opening vistas into potential control and utilization of correlated quantum states as quantum information resources. With the use of the second-order density matr…
