Detection of spatial correlations in an ultracold gas of fermions

Spatial correlations are observed in an ultracold gas of fermionic atoms close to a Feshbach resonance. The correlations are detected by inducing spin-changing rf transitions between pairs of atoms. We observe the process in the strongly interacting regime for attractive as well as for repulsive atom-atom interactions and both in the regime of high and low quantum degeneracy. The observations are compared with a two-particle model that provides theoretical predictions for the measured rf transition rates.     

Signature of Mott-insulator transition with ultracold fermions in a one-dimensional optical lattice

Using the exact Bethe ansatz solution of the Hubbard model and Luttinger liquid theory, we investigate the density profiles and collective modes of one-dimensional ultracold fermions confined in an optical lattice with a harmonic trapping potential. We determine a generic phase diagram in terms of a characteristic filling factor and a dimensionless coupling constant. The collective oscillations of the atomic mass density, a technique that is commonly used in experiments, provide a signature of the quantum phase transition from the metallic phase to the Mott-insulator phase. A detailed experimental implementation is proposed.     

Noise correlations in one-dimensional systems of ultracold fermions

Time of flight images reflect the momentum distribution of the atoms in the trap, but the spatial noise in the image holds information on more subtle correlations. Using bosonization, we study such correlations in generic 1D systems of ultracold fermions. We show how pairing as well as spin and charge density wave correlations may be identified and extracted from time of flight images. These incipient orders manifest themselves as power-law singularities in the noise correlations, that depend on the Luttinger parameters, which suggests a general experimental technique to obtain them.     

Hofstadter's butterfly energy spectrum of ultracold fermions on the two-dimensional triangular optical lattice

We study the energy spectrum of ultracold fermionic atoms on the two-dimensional triangular optical lattice subjected to a perpendicular effective magnetic field, which can be realized with laser beams. We derive the generalized Harper's equations and numerically solve them, then we obtain the Hofstadter's butterfly-like energy spectrum, which has a novel fractal structure. The observability of the Hofstadter's butterfly spectrum is also discussed.     

Staggered-vortex superfluid of ultracold bosons in an optical lattice

We show that the dynamics of cold bosonic atoms in a two-dimensional square optical lattice produced by a bichromatic light-shift potential is described by a Bose-Hubbard model with an additional effective staggered magnetic field. In addition to the known uniform superfluid and Mott insulating phases, the zero-temperature phase diagram exhibits a novel kind of finite-momentum superfluid phase, characterized by a quantized staggered rotational flux. An extension for fermionic atoms leads to an anisotropic Dirac spectrum, which is relevant to graphene and high-T(c) superconductors.     

Probing non-abelian statistics of Majorana fermions in ultracold atomic superfluid

We propose an experiment to directly probe the non-abelian statistics of Majorana fermions by braiding them in an s-wave superfluid of ultracold atoms. We show that different orders of braiding operations give orthogonal output states that can be distinguished through Raman spectroscopy. Realization of Majorana states in an s-wave superfluid requires strong spin-orbital coupling and a controllable Zeeman field in the perpendicular direction. We present a simple laser configuration to generate the artificial spin-orbital coupling and the required Zeeman field in the dark-state subspace.     

Stability of superflow for ultracold fermions in optical lattices

We investigate the stability of superflow of paired fermions in an optical lattice. We show that there are two distinct dynamical instabilities which limit the superflow in this system. One dynamical instability occurs when the superfluid stiffness becomes negative; this evolves, with increasing pairing interaction, from the fermion pair breaking instability to the well-known dynamical instability of lattice bosons. The second, more interesting, dynamical instability is marked by the emergence of a transient atom density wave. Both dynamical instabilities can be experimentally accessed by tuning the pairing interaction and the fermion density.     

光晶格中非相干超冷原子的密度关联效应

陷俘于光晶格中的Mott绝缘体态原子是非相干物质波波源. 这种物质波从光晶格释放后不会出现一阶干涉现象,但是存在二阶干涉(密度关联)效应. 针对这一现象,理论上给出了自由膨胀超冷原子气体的密度关联函数,该函数表现出清晰的干涉峰,其条纹结构与光栅衍射谱类似. 进一步研究表明,密度关联函数的峰值结构与两探测器的相对位置有关,出现了物质波的"亚波长干涉"现象. 关键词： 光晶格 密度关联函数 两粒子干涉     

Probing many-body interactions in an optical lattice clock

We present a unifying theoretical framework that describes recently observed many-body effects during the interrogation of an optical lattice clock operated with thousands of fermionic alkaline earth atoms. The framework is based on a many-body master equation that accounts for the interplay between elastic and inelastic p$p$-wave and s$s$-wave interactions, finite temperature effects and excitation inhomogeneity during the quantum dynamics of the interrogated atoms. Solutions of the master equation in different parameter regimes are presented and compared. It is shown that a general solution can be obtained by using the so called Truncated Wigner Approximation which is applied in our case in the context of an open quantum system. We use the developed framework to model the density shift and decay of the fringes observed during Ramsey spectroscopy in the JILA ⁸⁷${}^{87}$Sr and NIST ¹⁷¹${}^{171}$Yb optical lattice clocks. The developed framework opens a suitable path for dealing with a variety of strongly-correlated and driven open-quantum spin systems.     

Superexchange-mediated magnetization dynamics with ultracold alkaline-earth atoms in an optical lattice

Superexchange and inter-orbital spin-exchange interactions are key ingredients for understanding(orbital) quantum magnetism in strongly correlated systems and have been realized in ultracold atomic gases.Here we study the spin dynamics of ultracold alkaline-earth atoms in an optical lattice when the two exchange interactions coexist.In the superexchange interaction dominating regime,we find that the time-resolved spin imbalance shows a remarkable modulated oscillation,which can be attributed to the interplay between local and nonlocal quantum mechanical exchange mechanisms.Moreover,the filling of the long-lived excited atoms affects the collapse and revival of the magnetization dynamics.These observations can be realized in state-dependent optical lattices combined with the state-of-the-art advances in optical lattice clock spectroscopy.     

Light-induced unconventional Landau levels of ultracold fermions in a trilayer honeycomb lattice

The spectrum of cold fermionic atoms is studied in a trilayer honeycomb optical lattice subjected to a perpendicular effective magnetic field,which is created with optical means. In the low energy approximation,the spectrum shows unconventional Landau levels,which are proportional to the 3/2 power of integer numbers. The zoro modes exist and the quasiparticles are chiral. It is also proposed to identify the unconventional Landau levels via probing the dynamic structure factor of the system with Bragg spectr...     

SU(3) spin-orbit coupled fermions in an optical lattice

We propose a scheme to realize the SU(3)spin-orbit coupled three-component fermions in an one-dimensional optical lattice.The topological properties of the single-particle Hamiltonian are studied by calculating the Berry phase,winding number and edge state.We also investigate the effects of the interaction on the ground-state topology of the system,and characterize the interaction-induced topological phase transitions,using a state-of-the-art density-matrix renormalization-group numerical method.Finally,we show the typical features of the emerging quantum phases,and map out the many-body phase diagram between the interaction and the Zeeman field.Our results establish a way for exploring novel quantum physics induced by the SOC with SU(N)symmetry.     

Effective Hamiltonian for fermions in an optical lattice across a Feshbach resonance

We derive the Hamiltonian for cold fermionic atoms in an optical lattice across a broad Feshbach resonance, taking into account both multiband occupations and neighboring-site collisions. Under typical configurations, the resulting Hamiltonian can be dramatically simplified to an effective single-band model, which describes a new type of resonance between the local dressed molecules and the valence bond states of fermionic atoms at neighboring sites. On different sides of such a resonance, the effective Hamiltonian is reduced to either a t-J model for the fermionic atoms or an XXZ model for the dressed molecules. The parameters in these models are experimentally tunable in the full range, which allows for observation of various phase transitions.     

Quantum correlations of spin-1 atoms in an optical lattice

In this work, we investigate the system of cold spin-1 atoms in a one dimensional optical lattice in relation with squeezing and entanglement. By using the corresponding Bose-Hubbard Hamiltonian, both superfluid and Mott-insulator phases are studied by using numerical methods in the mean-field approximation. To observe the presence of entanglement, we used a squeezing measure as a criterion for quantum correlations. We further investigate the two interaction regimes, namely ferromagnetic and antiferromagnetic in the case of zero and nonzero but very small angle between the counterpropagating laser beams that form the optical lattice. States in the superfluid phase are calculated analytically by using the perturbation theory.     

Quantum simulation of the Hubbard model with ultracold fermions in optical lattices

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 implementation in ultracold atom systems, and its phase diagram, we review landmark experimental achievements, from the early observation of the onset of quantum degeneracy and superfluidity to the demonstration of the Mott insulator regime and the emergence of long-range anti-ferromagnetic order. We conclude by discussing future challenges, including the possible observation of high-$T_{\mathrm{c}}$ superconductivity, transport properties, and the interplay of strong correlations and disorder or topology.     

Simulation and detection of dirac fermions with cold atoms in an optical lattice

We propose an experimental scheme to simulate and observe relativistic Dirac fermions with cold atoms in a hexagonal optical lattice. By controlling the lattice anisotropy, one can realize both massive and massless Dirac fermions and observe the phase transition between them. Through explicit calculations, we show that both the Bragg spectroscopy and the atomic density profile in a trap can be used to demonstrate the Dirac fermions and the associated phase transition.     

Quantum simulation of quantum many-body systems with ultracold two-electron atoms in an optical lattice

Ultracold atoms in an optical lattice provide a unique approach to study quantum many-body systems, previously only possible by using condensed-matter experimental systems. This new approach, often called quantum simulation, becomes possible because of the high controllability of the system parameters and the inherent cleanness without lattice defects and impurities. In this article, we review recent developments in this rapidly growing field of ultracold atoms in an optical lattice, with special focus on quantum simulations using our newly created quantum many-body system of two-electron atoms of ytterbium. In addition, we also mention other interesting possibilities offered by this novel experimental platform, such as applications to precision measurements for studying fundamental physics and a Rydberg atom quantum computation.     

Nonspreading wave packets in three dimensions formed by an ultracold bose gas in an optical lattice

We predict that an ultracold Bose gas in an optical lattice can give rise to a new form of condensation, namely, nonspreading 3D wave packets that reflect the symmetry of the Laplacian with a negative effective mass along the lattice direction and are allowed to exist in the absence of any trapping potential even in the limit of noninteracting atoms. This result also has strong implications for optical propagation in periodic structures.     

Counterflow superfluidity of two-species ultracold atoms in a commensurate optical lattice

In the Mott-insulator regime, two species of ultracold atoms in an optical lattice can exhibit the low-energy counterflow motion. We construct effective Hamiltonians for the three classes of the two-species (fermion-fermion, boson-boson, and boson-fermion-type) insulators and reveal the conditions when the resulting ground state supports super-counter-fluidity (SCF), with the alternative being phase segregation. We emphasize a crucial role of breaking the isotopic symmetry between the species for realizing the SCF phase.     

Controlling and detecting spin correlations of ultracold atoms in optical lattices

We report on the controlled creation of a valence bond state of delocalized effective-spin singlet and triplet dimers by means of a bichromatic optical superlattice. We demonstrate a coherent coupling between the singlet and triplet states and show how the superlattice can be employed to measure the singlet-fraction employing a spin-blockade effect. Our method provides a reliable way to detect and control nearest-neighbor spin correlations in many-body systems of ultracold atoms. Being able to measure these correlations is an important ingredient in studying quantum magnetism in optical lattices. We furthermore employ a SWAP operation between atoms which are part of different triplets, thus effectively increasing their bond-length. Such a SWAP operation provides an important step towards the massively parallel creation of a multiparticle entangled state in the lattice.